Poisson image fusion based on Markov random field fusion model

191CASE区域治理基于博弈论的单点交叉口信号配时优化方法兰州交通大学数理学院 张继，陈京荣，王霞，陈琼摘要：为解决单点交叉口不合理信号配时引起的车辆及行人拥堵状况，以博弈论为基础，构建双层博弈模型。

上层对两相位交叉口东西向和南北向车辆进行斗鸡博弈，通过Nash均衡解分配绿灯时间；下层对人行横道处行人和机动车进行演化博弈，通过复制者动态方程达到演化稳定策略（ESS）后优化配时。

最后，用Matlab对比定时控制，方案能及时减少延误。

关键词：交叉口信号配时；博弈论；演化稳定策略中图分类号：TN911.6文献标识码：A文章编号：2096-4595（2020）25-0191-0002随着城市化进程加快，城市道路交通负担加重，交叉口拥堵状况愈发严重，亟需优化的配时方案缓解交叉口的拥堵状况。

1958年，韦伯斯特提出经典的信号配时，奠定了定时控制的基础[1]。

但定时控制在交通状况变化时容易造成交叉口拥堵。

博弈论是运筹学的一个重要分支，是研究含有竞争性质现象的数学方法。

国内外学者热衷于以博弈论为手段研究路口信号控制：Clempner 等人构建Stackelberg 博弈模型，利用C 变量法求最优信号配时[2]；李建明等人以平均延误最小为目标，提出基于演化博弈的单点交叉口优化配时模型 [3]；梁春岩等人改变行人相位配时，提高行人过街效率[4]。

本文以博弈论为基础，建立斗鸡博弈模型和演化博弈模型，固定周期下优化配时方案。

一、交叉口信号配时的博弈模型（一）交叉口机动车间的斗鸡博弈定义博弈双方中的一方为南北向车辆，记为参与者A；另一方为东西向车辆，记为参与者B 。

设a b c d e f、为交通延误值，令延误的相反数作为收益值。

该博弈的支付矩阵如表1所示。

表1中：()11t aA S dt −∫，2t b A dt =∫，1t c A dt =∫，()22t dA S dt =−∫，()13t e A S dt −∫，()24t f A S dt =−∫其中：12A A 、为南北向、东西向车辆到达率，12S S 、为南北向、东西向车辆离去率，34S S 、表示无信号交叉口南北向、东西向车辆离去率。

193This paper provides a model of the interactionbetween risk-management practices and market liquidity. Our main finding is that a feedback effect can arise. Tighter risk management leads to market illiquidity, and this illiquidity further tightens risk management.Risk management plays a central role in insti-tutional investors’ allocation of capital to trad-ing. For instance, a risk manager may limit a trading desk’s one-day 99 percent value at risk (VaR) to $1 million. This means that the trad-ing desk must choose a position such that, over the following day, its value drops no more than $1 million with 99 percent probability. Risk management helps control an institution’s use of capital while limiting default risk, and helps mitigate agency problems. Phillipe Jorion (2000, xxiii) states that VaR “is now increasingly used to allocate capital across traders, business units, products, and even to the whole institution.”We do not focus on the benefits of risk man-agement within an institution adopting such con-trols, but, rather, on the aggregate effects of such practices on liquidity and asset prices. An institu-tion may benefit from tightening its risk manage-ment and restricting its security position, but as a consequence it cannot provide as much liquidity to others. We show that, if everyone uses a tight risk management, then market liquidity is low-ered in that it takes longer to find a buyer with unused risk-bearing capacity, and, since liquidity is priced, prices fall.Search-and-Matching Financial MarketS †Liquidity and Risk ManagementBy Nicolae Gˆa rleanu and Lasse Heje Pedersen*Not only does risk management affect liquid-ity; liquidity can also affect risk-management practices. For instance, the Bank for International Settlements (2001, 15) states, “For the internal risk management, a number of institutions are exploring the use of liquidity adjusted-VaR, in which the holding periods in the risk assessment are adjusted to account for market liquidity, in particular by the length of time required to unwind positions.” For instance, if liquidation is expected to take two days, a two-day VaR might be used instead of a one-day VaR. Since a secu-rity’s risk over two days is greater than over one day, this means a trader must choose a smaller position to satisfy his liquidity-adjusted value at risk (LVaR) constraint. One motivation for this constraint is that, if an institution needs to sell, its maximum loss before the completion of the sale is limited by the LVaR.The main result of the paper is that subjecting traders to an LVaR gives rise to a multiplier effect. Tighter risk management leads to more restricted positions, hence longer expected selling times, implying higher risk over the expected selling period, which further tightens the risk manage-ment, and so on. This feedback between liquidity and risk management can help explain why liquid-ity can suddenly drop. We show that this “snow-balling” illiquidity can arise if volatility rises, or if more agents face reduced risk-bearing capac-ity—for instance, because of investor redemp-tions, losses, or increased risk aversion.Our link between liquidity and risk manage-ment is a testable prediction. While no formal empirical evidence is available, to our knowl-edge, our prediction is consistent with anecdotal evidence on financial market crises. For exam-ple, in August 1998 several traders lost money due to a default of Russian bonds and, simulta-neously, market volatility increased. As a result, the (L)VaR of many investment banks and other institutions increased. To bring risk back in line, many investment banks reportedly asked traders to reduce positions, leading to falling prices and†Discussants: Dimitri Vayanos, London School of Economics; Neil Wallace, Pennsylvania State University; Manuel Amador, Stanford University.* Gˆa rleanu: Wharton School, University of Pennsylva-nia, 3620 Locust Walk, Philadelphia, PA 19104-6367, and National Bureau of Economic Research, and Centre for Economic Policy Research (e-mail: garleanu@); Pedersen: Stern School of Business, New York University, 44 West Fourth Street, Suite 9-190, New York, NY 10012-1126, NBER, and CEPR (e-mail: lpederse@). We are grateful for helpful conversations with Franklin Allen, Dimitri Vayanos, and Jeff Wurgler.MAY 2007 194AEA PAPERS AND PROCEEDINGSlower liquidity. These market moves exacerbated the risk-management problems, fueling the crisis in a similar manner to the one modeled here. We capture these effects by extending the search model for financial securities of Darrell Duffie, Gârleanu, and Pedersen (2005, forthcom-ing, henceforth DGP). This framework of time-consuming search is well suited for modeling liquidity-based risk management as it provides a natural framework for studying endogenous sell-ing times. While DGP relied on exogenous posi-tion limits, we endogenize positions based on a risk-management constraint, and consider both a simple and a liquidity-adjusted VaR. Hence, we solve the fixed-point problem of jointly calculat-ing endogenous positions given the risk-manage-ment constraint and computing the equilibrium (L)VaR given the endogenous positions that deter-mine selling times and price volatility. Pierre-Olivier Weill (forthcoming) considers another extension of DGP in which market maker liquid-ity provision is limited by capital constraints. Our multiplier effect is similar to that of Markus K. Brunnermeier and Pedersen (2006) who show that liquidity and traders’ margin requirements can be mutually reinforcing.I. ModelThe economy has two securities: a “liquid” security with risk-free return r (i.e., a “money-market account”), and a risky illiquid security. The risky security has a dividend-rate process X and a price P(X), which is determined in equi-librium. The dividend rate is Lévy with finite variance. It has a constant drift normalized to zero, E t (X(t1T) − X(t)) 5 0, and a volatility s X . 0, i.e.,(1) var t (X(t1T) − X(t)) 5s2X T.Examples include Brownian motions, (com-pound) Poisson processes, and sums of these. The economy is populated by a continuum of agents who are risk neutral and infinitely lived, have a time-preference rate equal to the risk-free interest rate r. 0, and must keep their wealth bounded from below. Each agent is characterized by an intrinsic type i [ {h, l}, which is a Markov chain, independent across agents, and switching from l(“low”) to h (“high”) with intensity l u, and back with intensity l d. An agent of type i holding u t shares of the asset incurs a holding cost of d. 0 per share and per unit of time if he violates his risk-management constraint(2) v ar t (u t[P(X t1t) 2P(X t)]) # (s i)2, where s i is the risk-bearing capacity, defined by s h5s¯ . 0 and s l5 0. The low risk-bearing capacity of the low-type agents can be inter-preted as a need for more stable earnings, hedg-ing reasons to reduce a position, high financing costs, or a need for cash (e.g., an asset manager whose investors redeem capital).1We use this constraint as a parsimonious way of capturing risk constraints, such as the very popular VaR constraint,2which are used by most financial institutions. Our results are robust in that they rely on two natural proper-ties of the measure of risk: the risk measure increases with the size of the security position, and the length of the time period t over which the risk is assessed. While the constraint is not endogenized in the model, we note that its wide use in the financial world is probably due to agency problems, default risk, and the need to allocate scarce capital.We consider two types of risk management: (a) “simple risk management,” in which the vari-ance of the position in (2) is computed over a fixed time horizon t; and (b) “liquidity-adjusted risk management,” in which the variance is computed over the time required for selling the asset to an unconstrained buyer, which will be a random equilibrium quantity.Because agents are risk neutral and we are interested in a steady-state equilibrium, we restrict attention to equilibria in which, at any given time and state of the world, an agent holds either 0 or u¯ units of the asset, where u¯ is the largest1 An interesting extension of our model would consider the direct benefit of tighter risk management, which could be captured by a lower l d.2 A VaR constraint stipulates that Pr(−u[P(Xt1t) 2 P(X t )] $VaR) #p for some risk limit VaR and some con-fidence level p. If X is a Brownian motion, this is the same as (2). We note that rather than considering only price risk, we could alternatively consider the risk of the gains process(i.e., including dividend risk) G t,t5P(X(t1t)) − P(X(t))1 e t X(s) ds. This yields qualitatively similar results (and quantitatively similar for many reasonable parameters since dividend risk is orders of magnitude smaller than price risk over a small time period).TVOL. 97 NO. 2195LIquIDITY AND RISk MANAGEMENTposition that satisfies (2) with s i5s¯, taking the prices and search times as given.3 Hence, the set of agent types is T5 {ho, hn, lo, ln}, with the letters “h” and “l” designating the agent’s current intrinsic risk-bearing state as high or low, respec-tively, and with “o” or “n” indicating whether the agent currently owns u¯ shares or none, respec-tively. We let m z(t) denote the fraction at time t of agents of type z[T . These fractions add up to 1 and markets must clear:(3) 1 5m ho1m hn1m lo1m ln ,(4) Q 5 u¯(m ho1m lo),where Q . 0 is the total supply of shares per investor.Central to our analysis is the notion that the risky security is not perfectly liquid, in the sense that an agent can trade it only when she finds a counterparty. Every agent finds a potential counterparty, selected randomly from the set of all agents, with intensity l, where l . 0 is an exogenous parameter characterizing the mar-ket liquidity for the asset. Hence, the intensity of finding a type-z investor is lm z, that is, the search intensity multiplied by the fraction of investors of that type. When two agents meet, they bargain over the price, with the seller hav-ing bargaining power q[ [0, 1].This model of illiquidity directly captures the search that characterizes over-the-counter (OTC) markets. In these markets, traders must find an appropriate counterparty, which can be time consuming. Trading delays also arise due to time spent gathering information, reach-ing trading decisions, mobilizing capital, etc. Hence, trading delays are commonplace, and, therefore, the model can also capture features of other markets such as specialist and electronic limit-order-book markets, although these mar-kets are, of course, distinct from OTC markets.II. Equilibrium Risk Management, Liquidity, and PricesWe now proceed to derive the steady-state equilibrium agent fractions m, the maximum-3 Note that the existence of such an equilibrium requires that the risk limit s¯ not be too small relative to the total sup-ply Q, a condition that we assume throughout.holding u¯, and the price P. Naturally, low-type owners lo want to sell and high-type non-owners hn want to buy, which leads to(5) 05 22lm hn(t)m lo(t) 2l u m lo(t) 1l d m ho(t) and three more such steady-state equations. Equation (5) states that the change in the fraction of lo agents has three components, correspond-ing to the three terms on the right-hand-side of the equation. First, whenever a lo agent meets a hn investor, he sells his asset and is no longer a lo agent. Second, whenever the intrinsic type of a lo agent switches to high, he becomes a ho agent. Third, ho agents can switch type and become lo. Duffie, Gârleanu, and Pedersen (2005) show that, taking u¯ as fixed, there is a unique stable steady-state mass distribution as long as u¯$ Q. Here, agents’ positions u¯ are endogenous and depend on m, so that we must calculate a fixed point. Agents take the steady-state distribution m as fixed when they derive their optimal strategies and utilities for remaining lifetime consumption, as well as the bargained price P. The utility of an agent depends on his current type z(t) [T (i.e., whether he is a high or a low type and whether he owns zero or u¯ shares), the current dividend X(t), and the wealth W(t) in his bank account: (6) V z1X(t), W t25W t1 11z[{ho, lo}2u¯ X(t)/r1u¯ v z, where the type-dependent utility coefficients v z are to be determined. With q the bargaining power of the seller, bilateral Nash bargaining yields the price(7) P u¯ 5 (V lo2V ln) (1 2q) 1 (V ho2V hn) q. We conjecture, and later confirm, that the equi-librium asset price per share is of the form (8) P(X(t)) 5 X(t)/r 1p,for a constant p to be determined. The value-function coefficients v z and p are given by a set of Hamilton-Jacobi-Bellman equations, stated and solved in the Appendix available at www.e-aer. org/data/may07/p07048_app.pdf. The Appendix contains all the proofs.PROPOSITION 1: If the risk-limit s¯ is suffi-ciently large, there exists an equilibrium withMAY 2007196AEA PAPERS AND PROCEEDINGS holdings 0 and u¯ that satisfy the risk manage-ment constraint (2) with equality for low- and high-type agents, respectively. With simple risk management, the equilibrium is unique and (9)u¯With liquidity-adjusted risk management, u¯ depends on the equilibrium fraction of potential buyers m hn and satisfies(10) u¯In both cases, the equilibrium price is given by (11) P (X t )where the fractions of agents m depend on the type of risk management .These results are intuitive. The “position limit” u ¯ increases in the risk limit s ¯ and decreases in the asset volatility and in the square root of the VaR period length, which is t under simple risk management and (2lm hn )21 under liquid-ity-adjusted risk management. In the latter case, position limits increase in the search intensity and in the fraction of eligible buyers m hn .The price equals the present value of divi-dends, X t /r , minus a discount for illiquidity.Naturally, the liquidity discount is larger if there are more low-type owners in equilibrium (m lo is larger) and fewer high-type nonowners ready to buy (m hn is smaller).Of the equilibria with liquidity-adjusted risk management, we concentrate on the ones that arestable, in the sense that increasing u¯ marginally would result in equilibrium quantities violating the VaR constraint (2). Conversely, an equilib-rium is unstable if a marginal change in hold-ings that violates the constraint would result inthe equilibrium adjusting so that the constraint is not violated. If an equilibrium exists, then a stable equilibrium exists. Indeed, the equilib-rium with the largest u¯ is stable and has the high-est welfare among all equilibria.The main result of the paper characterizes the equilibrium connection between liquidity and risk management.PROPOSITION 2: Suppose that s ¯ is large enough for the existence of an equilibrium. Consider a stable equilibrium with liquidity-adjusted risk management and let t 5 1/(2lm hn ), which means that the equilibrium allocations and price are the same with simple risk man-agement. Consider any combination of the conditions (a) higher dividend volatility s X , (b) lower risk limit s ¯, (c) lower meeting intensity l , (d) lower switching intensity l u to the high risk-bearing state, and (e) higher switching intensity l d to the low risk-bearing state. Then, (i) theequilibrium position u¯ decreases, (ii) expected search times for selling increase, and (iii) prices decrease. All three effects are larger with liquid-ity-adjusted risk management .To see the intuition for these results, consider the impact of a higher dividend volatility. This makes the risk-management constraint tighter, inducing agents to reduce their positions and spreading securities among more agents, thus leaving a smaller fraction of agents with unused risk-bearing capacity. Hence, sellers’ search time increases and their bargaining position worsens, leading to lower prices. This price drop is due to illiquidity, as agents are risk neutral.4With liquidity-adjusted risk management, the increased search time for sellers means that the risk over the expected liquidation period rises, thus further tightening the risk-management constraint, reducing positions, increasing search times, and so on.This multiplier also increases the sensitiv-ity of the economy with liquidity-adjusted risk management to the other shocks (b)–(e). Indeed, a lower risk limit (b) is equivalent to a higher4In a Walrasian market with immediate trade, the priceis the present value of dividends X/r when (Q/ u¯ ) , l u / (l u 1 l d ), a condition that is satisfied in our examplesbelow. (When Q / u ¯ . l u /(l u 1 l d ), the Walrasian price is(X 2d ) /r .)VOL. 97 NO. 2197LIquIDITY AND RISk MANAGEMENTdividend risk. The “liquidity shocks” (c)–(e) donot affect the equilibrium position u¯ with simple risk management, but they do increase the sell-ers’ search times and reduce prices. With liquid-ity-adjusted risk management, these liquidity shocks reduce security positions, too, because of increased search times and, as explained above, a multiplier effect arises.The multiplier arising from the feedback between trading liquidity and risk manage-ment clearly magnifies the effects of changes in the economic environment on liquidity and prices. Our steady-state model illustrates this point using comparative static analyses that essentially compare across economies. Similar results would arise in the time series of a single economy if there were random variation in the model characteristic, e.g., parameters switched in a Markov chain as in Duffie, Gârleanu, and Pedersen (forthcoming). In the context of such time-series variation, our multiplier effect can generate the abrupt changes in prices and selling times that characterize crises.We illustrate our model with a numerical example in which l 5 100, r 5 0.1, X 0 5 1, l d 5 0.2, l u 5 2, d 5 3, q 5 0.5, Q 5 1, and s ¯ 5 1. Figure 1 shows how prices (right panel) and sellers’ expected search times (left panel) depend on asset volatility. The solid line shows this for liquidity-adjusted risk management and the dashed line for simple risk managementwith t 5 0.0086, which is chosen so that the risk management schemes are identical for s X 5 0.3. Search times increase and prices decrease with volatility. These sensitivities are stron-ger (i.e., the curves are steeper) with liquidity-adjusted risk management due to the interaction between market liquidity (i.e., search times) and risk management.REFERENCESBrunnermeier, Markus K., and Lasse Heje Pedersen. 2006. “Market Liquidity and Fund-ing Liquidity.” Unpublished.Duffie, Darrell, Nicolae Gârleanu, and Lasse Heje Pedersen. 2005. “Over-the-Counter Markets.”Econometrica , 73(6): 1815–47.Duffie, Darrell, Nicolae Gârleanu, and Lasse Heje Pedersen. Forthcoming. “Valuation in Over-the-Counter Markets.” Review of Financial Studies .Bank for International Settlements. 2001. “Final Report of the Multidisciplinary Working Group on Enhanced Disclosure.” /publ/joint01.htm.Jorion, Phillipe. 2000. Value at Risk . New York: McGraw-Hill.Weill, Pierre-Olivier. Forthcoming. “Leaning against the Wind.” Review of Economic Studies .Figure 1Note: The effects of dividend volatility on equilibrium seller search times (left panel) and prices (right panel) with simple (dashed line) and liquidity-adjusted (solid line) risk management, respectively.%JWJEFOE WPMBUJMJUZ S 9-JRVJEJUZ 7B34JNQMF 7B3&Y Q F D U F E T B M F U J N F T Z F B S T1S J D F-JRVJEJUZ 7B34JNQMF 7B3%JWJEFOE WPMBUJMJUZ S 9。

第37卷第13期2007年7月数学的实践与认识M AT HEMA TICS IN PRACTICE AND T HEORYV o l.37　No.13　July ,2007　具有可变抽样区间的Poisson EWMA 控制图丛方媛,　赵选民,　师义民,　王彩玲(西北工业大学应用数学系,陕西西安　710072)摘要:　传统的EW M A 控制图通常都是针对计量型质量特性值的,而对于计数型质量特征值少有研究.设计了单位缺陷数服从Pois son 分布的EW M A 控制图,并对Pois son EW M A 控制图进行了可变抽样区间设计,利用M arkov chain 方法计算了其平均报警时间,计算结果表明,所设计的动态Pois son EW M A 控制图较Sh ew hart c-图和固定抽样区间的Poiss in EWM A 控制图能更好的监控过程的变化.关键词:　Pois son EWM A 控制图;可变抽样区间;M arkov chain ;平均报警时间1　引 言收稿日期:2007-01-22基金项目:国家自然科学基金(79970022);航空科学基金(02J 53079);陕西省自然基金(NSG5002) 由于质量特性值通常有两大类,一类是计量型的,如温度,长度,电阻等;一类是计数型的,如不合格品数,缺陷数等,因此,常规的质量控制图也分计量型控制图和计数型控制图两种[1].自从1924年Shew har t 提出了控制图的概念以来,Shew hart 的x --图,R -图等,以及EWM A(指数加权移动平均)控制图和CU SU M (累积和)控制图已经对计量型控制图有了很好的研究,而对于计数型质量特征值控制图的研究还只停留在Shew har t c-图和u-图上.且由于传统的休哈特控制图的统计变量是由当前观测值得出的,而其他观测值经过了它所在的当前时刻就被弃置不用,因此浪费了大量的历史信息和相关信息,造成了传统的休哈特控制图无法具有较高的精度且对小波动的持续上升、下降不敏感.EWM A 控制图的统计变量是观测值的一个加权线性组合,其对过程均值的微小变化比较敏感,正好弥补了Shew hart 控制图的缺陷[2—5].因此,针对计数型质量特征值,为了能更有效的发现过程均值的微小变化,本文在单位缺陷数服从Poisson 分布的假设下,提出了Poisson EW MA 控制图模型.静态控制图都是假定抽样区间,样本容量以及其控制限是固定不变的,其不利于及时有效的发现过程的变化,尤其是过程的微小变化,于是Rey no lds et al 提出了具有可变抽样区间的Shew hart 均值控制图,从此开启了动态控制图这一新的研究领域[6—7].因此,本文在前人研究的基础上对Poisson EWM A 控制图进行可变抽样区间设计,并且利用Markov chain 方法计算出其平均报警时间,计算结果表明,与Shew hatr 控制图和静态Poisson EWMA 控制图相比,可变抽样区间Poisson EWM A 控制图在过程失控时具有较短的平均报警时间,从而能够更有效的提高生产效率.2　Poisson EWMA 控制图的描述设X 表示生产过程中的单位缺陷数,通常情况下假设X 服从Poisson 分布.从该过程中获得的一列质量特征观测值X1,X2,…独立同分布于期望为L的Poisson分布,当过程处于受控状态时,L=L0.要对这个过程进行控制,定义Poisson EWM A统计量为:Z0=L0Z t=K X t+(1-K)Z t-1(1)根据Z t的定义可以直接得出E(Z t)=L0Var(Z t)=K2-K[1-(1-K)2t]L0(2)当t充分大时,可以得到Z t方差的渐近形式:Var(Z t)≈K2-KL0=Var(Z∞)(3)其中K为平滑参数,且0<K F1.这时Po isso n EWMA控制图的控制限可以基于(2)式得出,也可以基于方差的渐进形式(3)式得出,这样就产生了两种控制效果不同的控制图.为方便计算,在本文中我们将仅考虑基于渐近形式(3)式所生成控制限的控制图.因此,当Z t> h U或者Z t<h L时,过程失控.其中h L=L0-A L Var(Z∞)=L0-A LK L0 2-K,h U=L0+A U Var(Z∞)=L0+A UK L0 2-K,A U和A L可根据特定的受控时的ARL(平均运行长度,Average Run Leng th)的大小来确定,有时取A=A L=A U.但需要注意的是,由于X1,X2,…独立同分布于期望为L的Po isso n分布,则由(1)式定义的Poisson EW MA统计量Z t是一个非负数,那么当控制下限小于或等于零时,对过程均值的向下偏移就不会发出报警信号,即不能检测出过程的向下偏移,所以这时取A L≠A U是很有必要的.3　Poisson EWMA控制图的动态设计3.1　动态控制图的描述动态控制图是指下一个样本的抽样区间或样本容量依赖于现时样本点统计量的控制图.控制图的动态设计一般有可变抽样区间(Variable Sampling Interval,VSI),可变样本容量(Variable Sample Size,VSS)及可变样本容量和抽样区间(V SSI)这三种情况.其主要思想为:在控制图的中心限和控制限之间加上警戒限,将中心限与警戒限之间的区域称为中心域,警戒限与控制限之间的区域称为警戒域.如果现时样本点统计量位于中心域,则表明其后的点子超出控制限的可能性相对较小,这时可等待较长的时间再去抽取下一个样本,且下一个样本的样本容量可以较小;反之,若现时样本点统计量位于警戒域内,这表明其后的点子很有可能超出控制限,为了能尽快地发现过程的偏移,应等待较短的时间就去抽取下一个样本,且其样本容量应该较大,也就是说下一个样本的抽样区间和样本容量的大小取决于现时样本点统计量的大小.一般只取两个抽样区间长度d1和d2,d1>d2和两个样本容量n1和n2,n1<n2.当现时样本点统计量位于中心域时,选取样本容量n1和抽样区间d1;当其位于警戒域时,选用样本容量n2和抽样区间d2;若其超出警戒限,则发出报警信号,过程失控. 80数　学　的　实　践　与　认　识37卷一般情况下,用检测过程偏移的速度来评价一个控制图的有效性.当抽样区间和样本容量固定时,一般采用ARL 的大小来进行比较.即在过程处于受控状态的ARL 一定时,其失控状态的ARL 越小,表明该控制图对过程偏移检测的效果越好,越能及时地发现偏移.但是可变抽样区间控制图的抽样区间长度是变化的,故其无法采用ARL 来进行比较.这时我们将采用另外一种比较法则:平均报警时间(Aver age Time to Signal ,AT S )来比较.平均报警时间(AT S)是指从过程发生偏移到控制图发出报警信号所需要的平均时间.若过程偏移在零时刻发生,那么ATS 就是从过程开始检测到发出报警信号所需要的平均时间.本文将只考虑可变抽样区间Poisson EWM A 控制图.令<i 表示报警前采用抽样区间d i 的样本数(i =1,2),d 0表示从过程开始到第一个样本之间的抽样区间,可取d 0=d 1或d 2.则根据AT S 的定义可知:A T S =d 0+<1d 1+<2d 2计算ATS 的方法很多,本文我们采用M arko r chain 的方法计算Poisson EWM A 控制图的AT S.3.2　Poisson EWMA 控制图ATS 计算本文只考虑偏移L ′>L 0的情况.假设过程失控从零时刻开始,过程均值从L 0偏移到L 0+D L 0,为了能用M arkov chain 方法来计算失控过程的平均报警时间,如图1所示,将控制图的受控区域分成N 个长度相同的小区间,每个区间的长度为h U -h LN,第j 个子区间是(L j ,U j ),其中L j =h L +(j -1)(h U -h L )N ,U j =h L +j (h U -h L )N,第j 个子区间的中点m j =h L +(2j -1)(h U -h L )2N .这样对应于N 个M ar ko v chain 状态,从下到上分别记为E 1,E 2,…,E N ,第N +1个状态是吸收状态,表示超出h U 或小于h L 的失控区域.定义b =(b 1,b 2,…,b N )T ,若状态E i (i =1,2,…,N )的中心点位于中心域,则b i =d 1;若状态E i 的中心点位于警戒域内,则取b i =d 2.那么从状态E i (i =1,2,…,N )到状态E j (j =1,2,…,N )的转移概率记为p i ,j ,p i ,j =P (L j <Z t <U j ûZ t -1=m i )=P (L j <K X t +(1-K )Z t -1<U j ûZ t -1=m i )=P (L j <K X t +(1-K )m i <U j )=h L +(j -1)(h U -h L )N<K X t +(1-K )h L +(2i -1)(h U -h L )2N<h L +j (h U -h L )N =P h L +h U -h L2N K [(2(j -1)-(1-K)(2i -1)]<X t<h L +h U -h L2N K[(2j -(1-K )(2i -1)]令该M ar ko v chain 对于这N 个状态的转移矩阵为P =[p i ,j ]N ×N .令Q =(I -P )-1=(m ij )k ×k .其中I 为N ×N 的单位矩阵.则根据参考文献[2]推广可得到可变抽样区间的8113期丛方媛,等:具有可变抽样区间的P oisson EW M A 控制图图1　把受控区域划分成N 个相等的子区间Po isso n EWMA 控制图的平均报警时间AT S 为:A TS =∑Ni =1mk 0,i b i,(4)其中k 0表示中心限L 0处于状态E k 0.(若控制图的上控制限和下控制限关于中心限对称时,应取N 为奇数,这样可以使得中心限L 0正好处于状态E (N +1)/2的中点处,即k 0=(N +1)/2.因此根据AT S 的计算公式(4)即可求出过程质量特性对于不同偏移量D 的平均报警时间,当过程的质量特性X 的偏移量D =0时,由公式(4)求出的平均报警时间即为过程受控时平均报警时间.4　VSI Poisson EWMA 控制图与Poisson EWMA 控制图及c -图的比较要对不同控制图的控制效果进行比较,应使这些控制图处于同样的条件下进行比较,即使控制图在受控状态时具有相同的平均报警时间AT S .首先我们假设过程的单位缺陷数X 服从均值为4的Poisson 分布,即L 0= 4.则标准c -图的上控制限和下控制限可分别计算得:L CL =L 0-3L 0=4-34=-2UCL =L 0+3L 0=4+34=10此时的LCL 小于0,这时应重新设置LCL 为0.对于c -图,该过程受控时的平均报警时间AT S 为:82数　学　的　实　践　与　认　识37卷A T S =1P (x >10ûL 0=4)≈352即在受控时的AT S 约为352时,来比较这三种控制图的控制效果.具体数据见表1所示:表1　对于L 0=4时的c -图,P oisso n EW M A 和V SI P oisso n EW M A 控制图AT S 的比较,其中V SI 图上下警戒限分别为4.8和3.2,N =11D c -图Pois son EWM A 控制图(K =0.2)VS I Poiss on EW M A 控制图(K =0.2)(d 1,d 2)=(1.05,0.6)(d 1,d 2)=(1.10,0.80)0352348.70339.70358.330.5149.2588.0978.0085.851.071.9929.8126.0529.401.539.5315.2212.7214.632.023.479.657.909.172.514.96 6.95 5.66 6.593.010.155.424.425.14同样我们还可以得出这三种控制图对各种不同均值的控制效果的比较,表2为这三种控制图对L 0=10时的控制效果的比较:表2　对于L 0=10时的c -图,P oisso n EW M A 和V SI P oisso n EW M A 控制图A T S 的比较,其中V SI 图上下警戒限分别为11和9,N =11D c -图Pois son EWM A 控制图(K =0.2)VS I Poiss on EW M A 控制图(K =0.2)(d 1,d 2)=(1.3,0.65)(d 1,d 2)=(1.1,0.8)0284.74276.48275.20283.540.5171.87147.25144.87148.651.0107.4665.6661.9863.471.569.7934.2430.8731.532.046.9820.8218.1518.512.532.6814.2012.1712.393.023.4410.528.979.14从表1和表2中的数据可以看出,静态的Poisson EWM A 控制图的平均报警时间较标准的Shewhart 的c -图要小,而VSI Poisson EWMA 控制图的平均报警时间又较静态的Po isso n EWMA 控制图要小,即在这三种控制图中,VSI Poisson EW MA 控制图对过程均值的偏移最为敏感,能够最快最准确的检测出过程均值的偏移.因此,在实际的应用中,对于单位缺陷数,可以采取VSI Po isso n EWM A 控制图来提高生产的效率,降低生产成本.参考文献:[1]　周纪芗,茆诗松.质量管理统计方法[M ].北京:中国统计出版社,1999.[2]　Douglas C M ontgomery.Introduction to Statis tical Quality Control[M ].Fourth Edition J oh n Wiley &Sons Inc,2001.8313期丛方媛,等:具有可变抽样区间的P oisson EW M A 控制图84数　学　的　实　践　与　认　识37卷[3]　Gan F F.Joint monitoring of proces s mean an d variance u sing ex ponentially w eig hted moving average controlchart[J].T echnometrics,1995,37:446—453.[4]　Connie M B,Charles W C,S teven E R.Poisson EW M A control charts[J].Journ al of Quality Techn ology,1998,30(4):352—361.[5]　Gan F F.Designs of one-and tw o-sided expon ential EW M A chart[J].Journ al of Quality Tech nology,1998,30(1):55—69.[6]　Antonio F B Costa.X-bar chart w ith varialb e sample s ize and samplin g intervals[J].Journ al of QualityTech nology,1997,29(2):197—204.[7]　Baxley R V,Jr.An ap plication of variable sampling inter val control char ts[J].Jour nal of Q uality Technology,1995,27:275—282.[8]　王兆军.关于动态质量控制图的设计理论[J].应用概率统计,2002,18(3):316—333.[9]　赵选民,徐伟等.数理统计[M].北京:科学出版社.Poisson EWMA Control Chart withVariable Sampling Intervals　ZHAO Xuan-min,　SHI Yi-min,　WAN G Cai-lingCONG Fang-yuan, Array (Dept.o f A pplied M athematics,N o rt hw ester n P olyt echnical U niver sity,X i′an710072,China)Abstract:　T he measur ing quality character istic has been w idely studied by the t raditionalEWM A contr ol chart,but the counting quality char acter istic ha s been unusual resear ched.APo isson EWM A co nt ro l char t is pr oposed.A nd the Po isson EW M A contr ol char t w ith var iablesampling interv als is constructed also.T he M ar ko v chain method is used t o calculate theaver ag e time to signal.T he computing r esults show that the VSI P oisso n EW M A co nt ro l chartis the most efficient in detecting shift s amo ng the Shew har t c-chart,the fix ed sampling interv alPo isson EWM A co nt ro l char t and the V SI P oisson EW M A co ntr ol char t.Keywords:　po isson EW M A co ntr o l chart;var iable sampling inter vals;marko v chain;aver ag etime t o sig nal。

2021⁃04⁃10计算机应用,Journal of Computer Applications2021,41(4):1142-1147ISSN 1001⁃9081CODEN JYIIDU http ：//基于多通道图像深度学习的恶意代码检测蒋考林，白玮，张磊，陈军，潘志松*，郭世泽（陆军工程大学指挥控制工程学院，南京210007）（∗通信作者电子邮箱hotpzs@ ）摘要：现有基于深度学习的恶意代码检测方法存在深层次特征提取能力偏弱、模型相对复杂、模型泛化能力不足等问题。

同时，代码复用现象在同一类恶意样本中大量存在，而代码复用会导致代码的视觉特征相似，这种相似性可以被用来进行恶意代码检测。

因此，提出一种基于多通道图像视觉特征和AlexNet 神经网络的恶意代码检测方法。

该方法首先将待检测的代码转化为多通道图像，然后利用AlexNet 神经网络提取其彩色纹理特征并对这些特征进行分类从而检测出可能的恶意代码；同时通过综合运用多通道图像特征提取、局部响应归一化（LRN ）等技术，在有效降低模型复杂度的基础上提升了模型的泛化能力。

利用均衡处理后的Malimg 数据集进行测试，结果显示该方法的平均分类准确率达到97.8%；相较于VGGNet 方法在准确率上提升了1.8%，在检测效率上提升了60.2%。

实验结果表明，多通道图像彩色纹理特征能较好地反映恶意代码的类别信息，AlexNet 神经网络相对简单的结构能有效地提升检测效率，而局部响应归一化能提升模型的泛化能力与检测效果。

关键词：多通道图像；彩色纹理特征；恶意代码；深度学习；局部响应归一化中图分类号：TP309文献标志码：AMalicious code detection based on multi -channel image deep learningJIANG Kaolin ，BAI Wei ，ZHANG Lei ，CHEN Jun ，PAN Zhisong *，GUO Shize（Command and Control Engineering College ，Army Engineering University Nanjing Jiangsu 210007，China ）Abstract:Existing deep learning -based malicious code detection methods have problems such as weak deep -level feature extraction capability ，relatively complex model and insufficient model generalization capability.At the same time ，code reuse phenomenon occurred in large number of malicious samples of the same type ，resulting in similar visual features of the code.This similarity can be used for malicious code detection.Therefore ，a malicious code detection method based on multi -channel image visual features and AlexNet was proposed.In the method ，the codes to be detected were converted into multi -channel images at first.After that ，AlexNet was used to extract and classify the color texture features of the images ，so as to detect the possible malicious codes.Meanwhile ，the multi -channel image feature extraction ，the Local Response Normalization （LRN ）and other technologies were used comprehensively ，which effectively improved the generalization ability of the model with effective reduction of the complexity of the model.The Malimg dataset after equalization was used for testing ，the results showed that the average classification accuracy of the proposed method was 97.8%，and the method had the accuracy increased by 1.8%and the detection efficiency increased by 60.2%compared with the VGGNet method.Experimental results show that the color texture features of multi -channel images can better reflect the type information of malicious codes ，the simple network structure of AlexNet can effectively improve the detection efficiency ，and the local response normalization can improve the generalization ability and detection effect of the model.Key words:multi -channel image;color texture feature;malicious code;deep learning;Local Response Normalization (LRN)引言恶意代码已经成为网络空间的主要威胁来源之一。

1610IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 6, JUNE 2010A Label Field Fusion Bayesian Model and Its Penalized Maximum Rand Estimator for Image SegmentationMax MignotteAbstract—This paper presents a novel segmentation approach based on a Markov random field (MRF) fusion model which aims at combining several segmentation results associated with simpler clustering models in order to achieve a more reliable and accurate segmentation result. The proposed fusion model is derived from the recently introduced probabilistic Rand measure for comparing one segmentation result to one or more manual segmentations of the same image. This non-parametric measure allows us to easily derive an appealing fusion model of label fields, easily expressed as a Gibbs distribution, or as a nonstationary MRF model defined on a complete graph. Concretely, this Gibbs energy model encodes the set of binary constraints, in terms of pairs of pixel labels, provided by each segmentation results to be fused. Combined with a prior distribution, this energy-based Gibbs model also allows for definition of an interesting penalized maximum probabilistic rand estimator with which the fusion of simple, quickly estimated, segmentation results appears as an interesting alternative to complex segmentation models existing in the literature. This fusion framework has been successfully applied on the Berkeley image database. The experiments reported in this paper demonstrate that the proposed method is efficient in terms of visual evaluation and quantitative performance measures and performs well compared to the best existing state-of-the-art segmentation methods recently proposed in the literature. Index Terms—Bayesian model, Berkeley image database, color textured image segmentation, energy-based model, label field fusion, Markovian (MRF) model, probabilistic Rand index.I. INTRODUCTIONIMAGE segmentation is a frequent preprocessing step which consists of achieving a compact region-based description of the image scene by decomposing it into spatially coherent regions with similar attributes. This low-level vision task is often the preliminary and also crucial step for many image understanding algorithms and computer vision applications. A number of methods have been proposed and studied in the last decades to solve the difficult problem of textured image segmentation. Among them, we can cite clustering algorithmsManuscript received February 20, 2009; revised February 06, 2010. First published March 11, 2010; current version published May 14, 2010. This work was supported by a NSERC individual research grant. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Peter C. Doerschuk. The author is with the Département d’Informatique et de Recherche Opérationnelle (DIRO), Université de Montréal, Faculté des Arts et des Sciences, Montréal H3C 3J7 QC, Canada (e-mail: mignotte@iro.umontreal.ca). Color versions of one or more of the figures in this paper are available online at . Digital Object Identifier 10.1109/TIP.2010.2044965[1], spatial-based segmentation methods which exploit the connectivity information between neighboring pixels and have led to Markov Random Field (MRF)-based statistical models [2], mean-shift-based techniques [3], [4], graph-based [5], [6], variational methods [7], [8], or by region-based split and merge procedures, sometimes directly expressed by a global energy function to be optimized [9]. Years of research in segmentation have demonstrated that significant improvements on the final segmentation results may be achieved either by using notably more sophisticated feature selection procedures, or more elaborate clustering techniques (sometimes involving a mixture of different or non-Gaussian distributions for the multidimensional texture features [10], [11]) or by taking into account prior distribution on the labels, region process, or the number of classes [9], [12], [13]. In all cases, these improvements lead to computationally expensive segmentation algorithms and, in the case of energy-based segmentation models, to costly optimization techniques. The segmentation approach, proposed in this paper, is conceptually different and explores another strategy initially introduced in [14]. Instead of considering an elaborate and better designed segmentation model of textured natural image, our technique explores the possible alternative of fusing (i.e., efficiently combining) several quickly estimated segmentation maps associated with simpler segmentation models for a final reliable and accurate segmentation result. These initial segmentations to be fused can be given either by different algorithms or by the same algorithm with different values of the internal parameters such as several -means clustering results with different values of , or by several -means results using different distance metrics, and applied on an input image possibly expressed in different color spaces or by other means. The fusion model, presented in this paper, is derived from the recently introduced probabilistic rand index (PRI) [15], [16] which measures the agreement of one segmentation result to multiple (manually generated) ground-truth segmentations. This measure efficiently takes into account the inherent variation existing across hand-labeled possible segmentations. We will show that this non-parametric measure allows us to derive an appealing fusion model of label fields, easily expressed as a Gibbs distribution, or as a nonstationary MRF model defined on a complete graph. Finally, this fusion model emerges as a classical optimization problem in which the Gibbs energy function related to this model has to be minimized. In other words, or analytically expressed in the regularization framework, each quickly estimated segmentation (to be fused) provides a set of constraints in terms of pairs of pixel labels (i.e., binary cliques) that should be equal or not. Finally, our fusion result is found1057-7149/$26.00 © 2010 IEEEMIGNOTTE: LABEL FIELD FUSION BAYESIAN MODEL AND ITS PENALIZED MAXIMUM RAND ESTIMATOR FOR IMAGE SEGMENTATION1611by searching for a segmentation map that minimizes an energy function encoding this precomputed set of binary constraints (thus optimizing the so-called PRI criterion). In our application, this final optimization task is performed by a robust multiresolution coarse-to-fine minimization strategy. This fusion of simple, quickly estimated segmentation results appears as an interesting alternative to complex, computationally demanding segmentation models existing in the literature. This new strategy of segmentation is validated in the Berkeley natural image database (also containing, for quantitative evaluations, ground truth segmentations obtained from human subjects). Conceptually, our fusion strategy is in the framework of the so-called decision fusion approaches recently proposed in clustering or imagery [17]–[21]. With these methods, a series of energy functions are first minimized before their outputs (i.e., their decisions) are merged. Following this strategy, Fred et al. [17] have explored the idea of evidence accumulation for combining the results of multiple clusterings. Reed et al. have proposed a Gibbs energy-based fusion model that differs from ours in the likelihood and prior energy design, as final merging procedure (for the fusion of large scale classified sonar image [21]). More precisely, Reed et al. employed a voting scheme-based likelihood regularized by an isotropic Markov random field priorly used to inpaint regions where the likelihood decision is not available. More generally, the concept of combining classifiers for the improvement of the performance of individual classifiers is known, in machine learning field, as a committee machine or mixture of experts [22], [23]. In this context, Dietterich [23] have provided an accessible and informal reasoning, from statistical, computational and representational viewpoints, of why ensembles can improve results. In this recent field of research, two major categories of committee machines are generally found in the literature. Our fusion decision approach is in the category of the committee machine model that utilizes an ensemble of classifiers with a static structure type. In this class of committee machines, the responses of several classifiers are combined by means of a mechanism that does not involve the input data (contrary to the dynamic structure type-based mixture of experts). In order to create an efficient ensemble of classifiers, three major categories of methods have been suggested whose goal is to promote diversity in order to increase efficiency of the final classification result. This can be done either by using different subsets of the input data, either by using a great diversity of the behavior between classifiers on the input data or finally by using the diversity of the behavior of the input data. Conceptually, our ensemble of classifiers is in this third category, since we intend to express the input data in different color spaces, thus encouraging diversity and different properties such as data decorrelation, decoupling effects, perceptually uniform metrics, compaction and invariance to various features, etc. In this framework, the combination itself can be performed according to several strategies or criteria (e.g., weighted majority vote, probability rules: sum, product, mean, median, classifier as combiner, etc.) but, none (to our knowledge) uses the PRI fusion (PRIF) criterion. Our segmentation strategy, based on the fusion of quickly estimated segmentation maps, is similar to the one proposed in [14] but the criterion which is now used in this new fusion model is different. In [14], the fusion strategy can be viewed as a two-stephierarchical segmentation procedure in which the first step remains identical and a set of initial input texton segmentation maps (in each color space) is estimated. Second, a final clustering, taking into account this mixture of textons (expressed in the set of different color space) is then used as a discriminant feature descriptor for a final -mean clustering whose output is the final fused segmentation map. Contrary to the fusion model presented in this paper, this second step (fusion of texton segmentation maps) is thus achieved in the intra-class inertia sense which is also the so-called squared-error criterion of the -mean algorithm. Let us add that a conceptually different label field fusion model has been also recently introduced in [24] with the goal of blending a spatial segmentation (region map) and a quickly estimated and to-be-refined application field (e.g., motion estimation/segmentation field, occlusion map, etc.). The goal of the fusion procedure explained in [24] is to locally fuse label fields involving labels of two different natures at different level of abstraction (i.e., pixel-wise and region-wise). More precisely, its goal is to iteratively modify the application field to make its regions fit the color regions of the spatial segmentation with the assumption that the color segmentation is more detailed than the regions of the application field. In this way, misclassified pixels in the application field (false positives and false negatives) are filtered out and blobby shapes are sharpened, resulting in a more accurate final application label field. The remainder of this paper is organized as follows. Section II describes the proposed Bayesian fusion model. Section III describes the optimization strategy used to minimize the Gibbs energy field related to this model and Section IV describes the segmentation model whose outputs will be fused by our model. Finally, Section V presents a set of experimental results and comparisons with existing segmentation techniques.II. PROPOSED FUSION MODEL A. Rand Index The Rand index [25] is a clustering quality metric that measures the agreement of the clustering result with a given ground truth. This non-parametric statistical measure was recently used in image segmentation [16] as a quantitative and perceptually interesting measure to compare automatic segmentation of an image to a ground truth segmentation (e.g., a manually hand-segmented image given by an expert) and/or to objectively evaluate the efficiency of several unsupervised segmentation methods. be the number of pixels assigned to the same region Let (i.e., matched pairs) in both the segmentation to be evaluated and the ground truth segmentation , and be the number of pairs of pixels assigned to different regions (i.e., misand . The Rand index is defined as matched pairs) in to the total number of pixel pairs, i.e., the ratio of for an image of size pixels. More formally [16], and designate the set of region labels respecif tively associated to the segmentation maps and at pixel location and where is an indicator function, the Rand index1612IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 6, JUNE 2010is given by the following relation:given by the empirical proportion (3) where is the delta Kronecker function. In this way, the PRI measure is simply the mean of the Rand index computed between each [16]. As a consequence, the PRI pair measure will favor (i.e., give a high score to) a resulting acceptable segmentation map which is consistent with most of the segmentation results given by human experts. More precisely, the resulting segmentation could result in a compromise or a consensus, in terms of level of details and contour accuracy exhibited by each ground-truth segmentations. Fig. 8 gives a fusion map example, using a set of manually generated segmentations exhibiting a high variation, in terms of level of details. Let us add that this probabilistic metric is not degenerate; all the bad segmentations will give a low score without exception [16]. C. Generative Gibbs Distribution Model of Correct Segmentations (i.e., the pairwise empirical As indicated in [15], the set ) defines probabilities for each pixel pair computed over an appealing generative model of correct segmentation for the image, easily expressed as a Gibbs distribution. In this way, the Gibbs distribution, generative model of correct segmentation, which can also be considered as a likelihood of , in the PRI sense, may be expressed as(1) which simply computes the proportion (value ranging from 0 to 1) of pairs of pixels with compatible region label relationships between the two segmentations to be compared. A value of 1 indicates that the two segmentations are identical and a value of 0 indicates that the two segmentations do not agree on any pair of points (e.g., when all the pixels are gathered in a single region in one segmentation whereas the other segmentation assigns each pixel to an individual region). When the number of and are much smaller than the number of data labels in points , a computationally inexpensive estimator of the Rand index can be found in [16]. B. Probabilistic Rand Index (PRI) The PRI was recently introduced by Unnikrishnan [16] to take into accounttheinherentvariabilityofpossible interpretationsbetween human observers of an image, i.e., the multiple acceptable ground truth segmentations associated with each natural image. This variability between observers, recently highlighted by the Berkeley segmentation dataset [26] is due to the fact that each human chooses to segment an image at different levels of detail. This variability is also due image segmentation being an ill-posed problem, which exhibits multiple solutions for the different possible values of the number of classes not known a priori. Hence, in the absence of a unique ground-truth segmentation, the clustering quality measure has to quantify the agreement of an automatic segmentation (i.e., given by an algorithm) with the variation in a set of available manual segmentations representing, in fact, a very small sample of the set of all possible perceptually consistent interpretations of an image [15]. The authors [16] address this concern by soft nonuniform weighting of pixel pairs as a means of accounting for this variability in the ground truth set. More formally, let us consider a set of manually segmented (ground truth) images corresponding to an be the segmentation to be compared image of size . Let with the manually labeled set and designates the set of reat pixel gion labels associated with the segmentation maps location , the probabilistic RI is defined bywhere is the set of second order cliques or binary cliques of a Markov random field (MRF) model defined on a complete graph (each node or pixel is connected to all other pixels of is the temperature factor of the image) and this Boltzmann–Gibbs distribution which is twice less than the normalization factor of the Rand Index in (1) or (2) since there than pairs of pixels for which are twice more binary cliques . is the constant partition function. After simplification, this yields(2) where a good choice for the estimator of (the probability of the pixel and having the same label across ) is simply (4)MIGNOTTE: LABEL FIELD FUSION BAYESIAN MODEL AND ITS PENALIZED MAXIMUM RAND ESTIMATOR FOR IMAGE SEGMENTATION1613where is a constant partition function (with a factor which depends only on the data), namelywhere is the set of all possible (configurations for the) segof size pixels. Let us add mentations into regions that, since the number of classes (and thus the number of regions) of this final segmentation is not a priori known, there are possibly, between one and as much as regions that the number of pixels in this image (assigning each pixel to an individual can region is a possible configuration). In this setting, be viewed as the potential of spatially variant binary cliques (or pairwise interaction potentials) of an equivalent nonstationary MRF generative model of correct segmentations in the case is assumed to be a set of representative ground where truth segmentations. Besides, , the segmentation result (to be ), can be considered as a realization of this compared to generative model with PRand, a statistical measure proportional to its negative likelihood energy. In other words, an estimate of , in the maximum likelihood sense of this generative model, will give a resulting segmented map (i.e., a fusion result) with a to be fused. high fidelity to the set of segmentations D. Label Field Fusion Model for Image Segmentation Let us consider that we have at our disposal, a set of segmentations associated to an image of size to be fused (i.e., to efficiently combine) in order to obtain a final reliable and accurate segmentation result. The generative Gibbs distribution model of correct segmentations expressed in (4) gives us an interesting fusion model of segmentation maps, in the maximum PRI sense, or equivalently in the maximum likelihood (ML) sense for the underlying Gibbs model expressed in (4). In this framework, the set of is computed with the empirical proportion estimator [see (3)] on the data . Once has been estimated, the resulting ML fusion segmentation map is thus defined by maximizing the likelihood distributiontions for different possible values of the number of classes which is not a priori known. To render this problem well-posed with a unique solution, some constraints on the segmentation process are necessary, favoring over segmentation or, on the contrary, merging regions. From the probabilistic viewpoint, these regularization constraints can be expressed by a prior distribution of treated as a realization of the unknown segmentation a random field, for example, within a MRF framework [2], [27] or analytically, encoded via a local or global [13], [28] prior energy term added to the likelihood term. In this framework, we consider an energy function that sets a particular global constraint on the fusion process. This term restricts the number of regions (and indirectly, also penalizes small regions) in the resulting segmentation map. So we consider the energy function (6) where designates the number of regions (set of connected pixels belonging to the same class) in the segmented is the Heaviside (or unit step) function, and an image , internal parameter of our fusion model which physically represents the number of classes above which this prior constraint, limiting the number of regions, is taken into account. From the probabilistic viewpoint, this regularization constraint corresponds to a simple shifted (from ) exponential distribution decreasing with the number of regions displayed by the final segmentation. In this framework, a regularized solution corresponds to the maximum a posteriori (MAP) solution of our fusion model, i.e., that maximizes the posterior distribution the solution , and thus(7) with is the regularization parameter controlling the contribuexpressing fidelity to the set of segtion of the two terms; encoding our prior knowledge or mentations to be fused and beliefs concerning the types of acceptable final segmentations as estimates (segmentation with a number of limited regions). In this way, the resulting criteria used in this resulting fusion model can be viewed as a penalized maximum rand estimator. III. COARSE-TO-FINE OPTIMIZATION STRATEGY A. Multiresolution Minimization Strategy Our fusion procedure of several label fields emerges as an optimization problem of a complex non-convex cost function with several local extrema over the label parameter space. In order to find a particular configuration of , that efficiently minimizes this complex energy function, we can use a global optimization procedure such as a simulated annealing algorithm [27] whose advantages are twofold. First, it has the capability of avoiding local minima, and second, it does not require a good solution. initial guess in order to estimate the(5) where is the likelihood energy term of our generative fusion . model which has to be minimized in order to find Concretely, encodes the set of constraints, in terms of pairs of pixel labels (identical or not), provided by each of the segmentations to be fused. The minimization of finds the resulting segmentation which also optimizes the PRI criterion. E. Bayesian Fusion Model for Image Segmentation As previously described in Section II-B, the image segmentation problem is an ill-posed problem exhibiting multiple solu-1614IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 6, JUNE 2010Fig. 1. Duplication and “coarse-to-fine” minimization strategy.An alternative approach to this stochastic and computationally expensive procedure is the iterative conditional modes (ICM) introduced by Besag [2]. This method is deterministic and simple, but has the disadvantage of requiring a proper initialization of the segmentation map close to the optimal solution. Otherwise it will converge towards a bad local minima . In order associated with our complex energy function to solve this problem, we could take, as initialization (first such as iteration), the segmentation map (8) i.e., in choosing for the first iteration of the ICM procedure amongst the segmentation to be fused, the one closest to the optimal solution of the Gibbs energy function of our fusion model [see (5)]. A more robust optimization method consists of a multiresolution approach combined with the classical ICM optimization procedure. In this strategy, rather than considering the minimization problem on the full and original configuration space, the original inverse problem is decomposed in a sequence of approximated optimization problems of reduced complexity. This drastically reduces computational effort and provides an accelerated convergence toward improved estimate. Experimentally, estimation results are nearly comparable to those obtained by stochastic optimization procedures as noticed, for example, in [10] and [29]. To this end, a multiresolution pyramid of segmentation maps is preliminarily derived, in order to for each at different resolution levels, and a set estimate a set of of similar spatial models is considered for each resolution level of the pyramidal data structure. At the upper level of the pyramidal structure (lower resolution level), the ICM optimization procedure is initialized with the segmentation map given by the procedure defined in (8). It may also be initialized by a random solution and, starting from this initial segmentation, it iterates until convergence. After convergence, the result obtained at this resolution level is interpolated (see Fig. 1) and then used as initialization for the next finer level and so on, until the full resolution level. B. Optimization of the Full Energy Function Experiments have shown that the full energy function of our model, (with the region based-global regularization constraint) is complex for some images. Consequently it is preferable toFig. 2. From top to bottom and left to right; A natural image from the Berkeley database (no. 134052) and the formation of its region process (algorithm PRIF ) at the (l = 3) upper level of the pyramidal structure at iteration [0–6], 8 (the last iteration) of the ICM optimization algorithm. Duplication and result of the ICM relaxation scheme at the finest level of the pyramid at iteration 0, 1, 18 (last iteration) and segmentation result (region level) after the merging of regions and the taking into account of the prior. Bottom: evolution of the Gibbs energy for the different steps of the multiresolution scheme.perform the minimization in two steps. In a first step, the minimization is performed without considering the global constraint (considering only ), with the previously mentioned multiresolution minimization strategy and the ICM optimization procedure until its convergence at full resolution level. At this finest resolution level, the minimization is then refined in a second step by identifying each region of the resulting segmentation map. This creates a region adjacency graph (a RAG is an undirected graph where the nodes represent connected regions of the image domain) and performs a region merging procedure by simply applying the ICM relaxation scheme on each region (i.e., by merging the couple of adjacent regions leading to a reduction of the cost function of the full model [see (7)] until convergence). In the second step, minimization can also be performed . according to the full modelMIGNOTTE: LABEL FIELD FUSION BAYESIAN MODEL AND ITS PENALIZED MAXIMUM RAND ESTIMATOR FOR IMAGE SEGMENTATION1615with its four nearest neighbors and a fixed number of connections (85 in our application), regularly spaced between all other pixels located within a square search window of fixed size 30 pixels centered around . Fig. 3 shows comparison of segmentation results with a fully connected graph computed on a search window two times larger. We decided to initialize the lower (or third upper) level of the pyramid with a sequence of 20 different random segmentations with classes. The full resolution level is then initialized with the duplication (see Fig. 1) of the best segmentation result (i.e., the one associated to the lowest Gibbs energy ) obtained after convergence of the ICM at this lower resolution level (see Fig. 2). We provide details of our optimization strategy in Algorithm 1. Algo I. Multiresolution minimization procedure (see also Fig. 2). Two-Step Multiresolution Minimization Set of segmentations to be fusedPairwise probabilities for each pixel pair computed over at resolution level 1. Initialization Step • Build multiresolution Pyramids from • Compute the pairwise probabilities from at resolution level 3 • Compute the pairwise probabilities from at full resolution PIXEL LEVEL Initialization: Random initialization of the upper level of the pyramidal structure with classes • ICM optimization on • Duplication (cf. Fig 1) to the full resolution • ICM optimization on REGION LEVEL for each region at the finest level do • ICM optimization onFig. 4. Segmentation (image no. 385028 from Berkeley database). From top to bottom and left to right; segmentation map respectively obtained by 1] our multiresolution optimization procedure: = 3402965 (algo), 2] SA : = 3206127, 3] rithm PRIF : = 3312794, 4] SA : = 3395572, 5] SA : = 3402162. SAFig. 3. Comparison of two segmentation results of our multiresolution fusion procedure (algorithm PRIF ) using respectively: left] a subsampled and fixed number of connections (85) regularly spaced and located within a square search window of size = 30 pixels. right] a fully connected graph computed on a search window two times larger (and requiring a computational load increased by 100).NUU 0 U 00 U 0 U 0D. Comparison With a Monoresolution Stochastic Relaxation In order to test the efficiency of our two-step multiresolution relaxation (MR) strategy, we have compared it to a standard monoresolution stochastic relaxation algorithm, i.e., a so-called simulated annealing (SA) algorithm based on the Gibbs sampler [27]. In order to restrict the number of iterations to be finite, we have implemented a geometric temperature cooling schedule , where is the [30] of the form starting temperature, is the final temperature, and is the maximal number of iterations. In this stochastic procedure, is crucial. The temperathe choice of the initial temperature ture must be sufficiently high in the first stages of simulatedC. Algorithm In order to decrease the computational load of our multiresolution fusion procedure, we only use two levels of resolution in our pyramidal structure (see Fig. 2): the full resolution and an image eight times smaller (i.e., at the third upper level of classical data pyramidal structure). We do not consider a complete graph: we consider that each node (or pixel) is connected。

基础理论课考试大纲（2020）《高等电磁理论》考试大纲考试内容：Maxwell方程组，平面电磁波，复杂媒质中的电磁波，各项异性媒质，导波理论，金属波导理论，介质波导理论，谐振腔，谐振腔的微扰，电磁波的辐射与反射，口面天线理论。

参考书目：1.Fields & Waves in Communication Electronics S.Ramo & J.Whinnery John Wiley & Sons；2.导波场论 R.E.柯林著上海科学技术出版社。

3.正弦场电磁场哈林顿著上海科学技术出版社（2021）《信号检测与估计》考试大纲考试内容：1.随机信号分析平稳随机信号与非平稳随机信号，随机信号的数字特征，平稳随机过程，复随机过程，随机信号通过线性系统。

2.信号检测信号检测的基本概念，确知信号的检测（包括匹配滤波原理、高斯白噪声中已知信号检测、简单二元检测）3.信号估计信号参数（包括贝叶斯估计、最大似然估计、线性均方估计和最小二乘估计），信号波形估计（主要指卡尔曼滤波）。

参考书目：1.景占荣，羊彦，信号检测与估计，化学工业出版社 20042.赵树杰，信号检测与估计理论，西安电子科技大学出版社 2001（2022）《现代网络分析》考试大纲考试内容：1.网络元件和网络特性：二端元件的参数与性质、二端口元件、性质及六组参数、受控电源、网络特性。

2.网络图论：图的概念与定义、节点关联矩阵、回路关联矩阵、割集关联矩阵、独立变量组、非基本关联矩阵、图形的树数、求全部树、由矩阵求图。

3.网络方程：支路电流方程和支路电压方程、回路电流方程和网孔电流方程、割集电压方程和节点电位方程、混合方程、含受控源网络和理想运放器网络的节点方程。

4.网络的拓扑分析：割集方程和回路方程的拓扑解、驱动点函数的拓扑公式、传输函数的拓扑公式、含受控源网络的传输导纳、节点方程的拓扑解。

5.信号流图：信号流图基本概念、信号流图的构成方法、梅森公式、状态变换图解、线图到流图、Shannon-Happ公式、Coates公式。

基于参考图像梯度方向先验的压缩感知磁共振快速成像朱庆永;彭玺;王珊珊;梁栋【摘要】压缩感知理论为快速磁共振成像提供了一种系统的理论框架，即通过少量非相干的采样数据便可实现精确的图像重建。

然而，在高度欠采样的情况下，混叠伪影依然很严重。

目前，已有大量的研究工作探讨了利用来自参考图像的先验信息来提高重建质量的方法。

文章提出基于参考图像梯度方向先验的压缩感知磁共振成像方法。

该方法通过约束目标图像中结构边缘的切向量与参考图像中对应位置的法向量相垂直，以使目标图像中结构边缘的方向和参考图像保持一致。

最后，运用多对比度扫描的实验数据，通过与传统的压缩感知磁共振成像方法相比较，验证了该方法能够实现快速且高质量的磁共振成像。

%The theory of compressed sensing (CS) provides a systematic framework for magnetic resonance (MR) image reconstruction from incoherently under-sampledk-space data. However, severe aliasing artifacts may still occur in cases of high acceleration and noisy measurements. Thereupon, an extensive body of work investigates exploiting additional prior information extracted from a reference image which can be acquired with relative ease in many MR applications. In this work, a CS-based MR image reconstruction method using reference gradient orientation priors was proposed. Specifically, the tangent vector in the target image was regularized to be perpendicular to the corresponding normal vector in the reference image over allspatial&nbsp;locations to make the gradient orientations in the reference and the target image consistent. The proposed method is validated usingmulti-scan experiment data and is shown to provide high speed and high quality imaging.【期刊名称】《集成技术》【年(卷),期】2016(005)003【总页数】7页(P47-53)【关键词】压缩感知;参考图像;梯度方向先验;约束重建【作者】朱庆永;彭玺;王珊珊;梁栋【作者单位】中国科学院深圳先进技术研究院深圳 518055;中国科学院深圳先进技术研究院深圳 518055;中国科学院深圳先进技术研究院深圳 518055;中国科学院深圳先进技术研究院深圳 518055【正文语种】中文【中图分类】R445.2通过适当的离散化，磁共振成像（Magnetic Resonance Imaging，MRI）数据采集模式的数学形式可以表示为：其中，为目标图像；表示 k 空间数据；为傅里叶编码矩阵。

A very brief guide to using MXMMichail Tsagris,Vincenzo Lagani,Ioannis Tsamardinos1IntroductionMXM is an R package which contains functions for feature selection,cross-validation and Bayesian Networks.The main functionalities focus on feature selection for different types of data.We highlight the option for parallel computing and the fact that some of the functions have been either partially or fully implemented in C++.As for the other ones,we always try to make them faster.2Feature selection related functionsMXM offers many feature selection algorithms,namely MMPC,SES,MMMB,FBED,forward and backward regression.The target set of variables to be selected,ideally what we want to discover, is called Markov Blanket and it consists of the parents,children and parents of children(spouses) of the variable of interest assuming a Bayesian Network for all variables.MMPC stands for Max-Min Parents and Children.The idea is to use the Max-Min heuristic when choosing variables to put in the selected variables set and proceed in this way.Parents and Children comes from the fact that the algorithm will identify the parents and children of the variable of interest assuming a Bayesian Network.What it will not recover is the spouses of the children of the variable of interest.For more information the reader is addressed to[23].MMMB(Max-Min Markov Blanket)extends the MMPC to discovering the spouses of the variable of interest[19].SES(Statistically Equivalent Signatures)on the other hand extends MMPC to discovering statistically equivalent sets of the selected variables[18,9].Forward and Backward selection are the two classical procedures.The functionalities or the flexibility offered by all these algorithms is their ability to handle many types of dependent variables,such as continuous,survival,categorical(ordinal,nominal, binary),longitudinal.Let us now see all of them one by one.The relevant functions are1.MMPC and SES.SES uses MMPC to return multiple statistically equivalent sets of vari-ables.MMPC returns only one set of variables.In all cases,the log-likelihood ratio test is used to assess the significance of a variable.These algorithms accept categorical only, continuous only or mixed data in the predictor variables side.2.wald.mmpc and wald.ses.SES uses MMPC using the Wald test.These two algorithmsaccept continuous predictor variables only.3.perm.mmpc and perm.ses.SES uses MMPC where the p-value is obtained using per-mutations.Similarly to the Wald versions,these two algorithms accept continuous predictor variables only.4.ma.mmpc and ma.ses.MMPC and SES for multiple datasets measuring the same variables(dependent and predictors).5.MMPC.temporal and SES.temporal.Both of these algorithms are the usual SES andMMPC modified for correlated data,such as clustered or longitudinal.The predictor vari-ables can only be continuous.6.fbed.reg.The FBED feature selection method[2].The log-likelihood ratio test or the eBIC(BIC is a special case)can be used.7.fbed.glmm.reg.FBED with generalised linear mixed models for repeated measures orclustered data.8.fbed.ge.reg.FBED with GEE for repeated measures or clustered data.9.ebic.bsreg.Backward selection method using the eBIC.10.fs.reg.Forward regression method for all types of predictor variables and for most of theavailable tests below.11.glm.fsreg Forward regression method for logistic and Poisson regression in specific.Theuser can call this directly if he knows his data.12.lm.fsreg.Forward regression method for normal linear regression.The user can call thisdirectly if he knows his data.13.bic.fsreg.Forward regression using BIC only to add a new variable.No statistical test isperformed.14.bic.glm.fsreg.The same as before but for linear,logistic and Poisson regression(GLMs).15.bs.reg.Backward regression method for all types of predictor variables and for most of theavailable tests below.16.glm.bsreg.Backward regression method for linear,logistic and Poisson regression(GLMs).17.iamb.The IAMB algorithm[20]which stands for Incremental Association Markov Blanket.The algorithm performs a forward regression at first,followed by a backward regression offering two options.Either the usual backward regression is performed or a faster variation, but perhaps less correct variation.In the usual backward regression,at every step the least significant variable is removed.In the IAMB original version all non significant variables are removed at every step.18.mmmb.This algorithm works for continuous or categorical data only.After applying theMMPC algorithm one can go to the selected variables and perform MMPC on each of them.A list with the available options for this argument is given below.Make sure you include the test name within””when you supply it.Most of these tests come in their Wald and perm (permutation based)versions.In their Wald or perm versions,they may have slightly different acronyms,for example waldBinary or WaldOrdinal denote the logistic and ordinal regression respectively.1.testIndFisher.This is a standard test of independence when both the target and the setof predictor variables are continuous(continuous-continuous).2.testIndSpearman.This is a non-parametric alternative to testIndFisher test[6].3.testIndReg.In the case of target-predictors being continuous-mixed or continuous-categorical,the suggested test is via the standard linear regression.If the robust option is selected,M estimators[11]are used.If the target variable consists of proportions or percentages(within the(0,1)interval),the logit transformation is applied beforehand.4.testIndRQ.Another robust alternative to testIndReg for the case of continuous-mixed(or continuous-continuous)variables is the testIndRQ.If the target variable consists of proportions or percentages(within the(0,1)interval),the logit transformation is applied beforehand.5.testIndBeta.When the target is proportion(or percentage,i.e.,between0and1,notinclusive)the user can fit a regression model assuming a beta distribution[5].The predictor variables can be either continuous,categorical or mixed.6.testIndPois.When the target is discrete,and in specific count data,the default test isvia the Poisson regression.The predictor variables can be either continuous,categorical or mixed.7.testIndNB.As an alternative to the Poisson regression,we have included the Negativebinomial regression to capture cases of overdispersion[8].The predictor variables can be either continuous,categorical or mixed.8.testIndZIP.When the number of zeros is more than expected under a Poisson model,thezero inflated poisson regression is to be employed[10].The predictor variables can be either continuous,categorical or mixed.9.testIndLogistic.When the target is categorical with only two outcomes,success or failurefor example,then a binary logistic regression is to be used.Whether regression or classifi-cation is the task of interest,this method is applicable.The advantage of this over a linear or quadratic discriminant analysis is that it allows for categorical predictor variables as well and for mixed types of predictors.10.testIndMultinom.If the target has more than two outcomes,but it is of nominal type(political party,nationality,preferred basketball team),there is no ordering of the outcomes,multinomial logistic regression will be employed.Again,this regression is suitable for clas-sification purposes as well and it to allows for categorical predictor variables.The predictor variables can be either continuous,categorical or mixed.11.testIndOrdinal.This is a special case of multinomial regression,in which case the outcomeshave an ordering,such as not satisfied,neutral,satisfied.The appropriate method is ordinal logistic regression.The predictor variables can be either continuous,categorical or mixed.12.testIndTobit(Tobit regression for left censored data).Suppose you have measurements forwhich values below some value were not recorded.These are left censored values and by using a normal distribution we can by pass this difficulty.The predictor variables can be either continuous,categorical or mixed.13.testIndBinom.When the target variable is a matrix of two columns,where the first one isthe number of successes and the second one is the number of trials,binomial regression is to be used.The predictor variables can be either continuous,categorical or mixed.14.gSquare.If all variables,both the target and predictors are categorical the default test isthe G2test of independence.An alternative to the gSquare test is the testIndLogistic.With the latter,depending on the nature of the target,binary,un-ordered multinomial or ordered multinomial the appropriate regression model is fitted.The predictor variables can be either continuous,categorical or mixed.15.censIndCR.For the case of time-to-event data,a Cox regression model[4]is employed.Thepredictor variables can be either continuous,categorical or mixed.16.censIndWR.A second model for the case of time-to-event data,a Weibull regression modelis employed[14,13].Unlike the semi-parametric Cox model,the Weibull model is fully parametric.The predictor variables can be either continuous,categorical or mixed.17.censIndER.A third model for the case of time-to-event data,an exponential regressionmodel is employed.The predictor variables can be either continuous,categorical or mixed.This is a special case of the Weibull model.18.testIndIGreg.When you have non negative data,i.e.the target variable takes positivevalues(including0),a suggested regression is based on the the inverse Gaussian distribution.The link function is not the inverse of the square root as expected,but the logarithm.This is to ensure that the fitted values will be always be non negative.An alternative model is the Weibull regression(censIndWR).The predictor variables can be either continuous, categorical or mixed.19.testIndGamma(Gamma regression).Gamma distribution is designed for strictly positivedata(greater than zero).It is used in reliability analysis,as an alternative to the Weibull regression.This test however does not accept censored data,just the usual numeric data.The predictor variables can be either continuous,categorical or mixed.20.testIndNormLog(Gaussian regression with a log link).Gaussian regression using the loglink(instead of the identity)allows non negative data to be handled naturally.Unlike the gamma or the inverse gaussian regression zeros are allowed.The predictor variables can be either continuous,categorical or mixed.21.testIndClogit.When the data come from a case-control study,the suitable test is via con-ditional logistic regression[7].The predictor variables can be either continuous,categorical or mixed.22.testIndMVReg.In the case of multivariate continuous target,the suggested test is viaa multivariate linear regression.The target variable can be compositional data as well[1].These are positive data,whose vectors sum to1.They can sum to any constant,as long as it the same,but for convenience reasons we assume that they are normalised to sum to1.In this case the additive log-ratio transformation(multivariate logit transformation)is applied beforehand.The predictor variables can be either continuous,categorical or mixed.23.testIndGLMMReg.In the case of a longitudinal or clustered target(continuous,propor-tions within0and1(not inclusive)),the suggested test is via a(generalised)linear mixed model[12].The predictor variables can only be continuous.This test is only applicable in SES.temporal and MMPC.temporal.24.testIndGLMMPois.In the case of a longitudinal or clustered target(counts),the suggestedtest is via a(generalised)linear mixed model[12].The predictor variables can only be continuous.This test is only applicable in SES.temporal and MMPC.temporal.25.testIndGLMMLogistic.In the case of a longitudinal or clustered target(binary),thesuggested test is via a(generalised)linear mixed model[12].The predictor variables can only be continuous.This test is only applicable in SES.temporal and MMPC.temporal.To avoid any mistakes or wrongly selected test by the algorithms you are advised to select the test you want to use.All of these tests can be used with SES and MMPC,forward and backward regression methods.MMMB accepts only testIndFisher,testIndSpearman and gSquare.The reason for this is that MMMB was designed for variables(dependent and predictors)of the same type.For more info the user should see the help page of each function.2.1A more detailed look at some arguments of the feature selection algorithmsSES,MMPC,MMMB,forward and backward regression offer the option for robust tests(the argument robust).This is currently supported for the case of Pearson correlation coefficient and linear regression at the moment.We plan to extend this option to binary logistic and Poisson regression as well.These algorithms have an argument user test.In the case that the user wants to use his own test,for example,mytest,he can supply it in this argument as is,without””. For all previously mentioned regression based conditional independence tests,the argument works as test=”testIndFisher”.In the case of the user test it works as user test=mytest.The max kargument must always be at least1for SES,MMPC and MMMB,otherwise it is a simple filtering of the variables.The argument ncores offers the option for parallel implementation of the first step of the algorithms.The filtering step,where the significance of each predictor is assessed.If you have a few thousands of variables,maybe this option will do no significant improvement.But, if you have more and a”difficult”regression test,such as quantile regression(testIndRQ),then with4cores this could reduce the computational time of the first step up to nearly50%.For the Poisson,logistic and normal linear regression we have included C++codes to speed up this process,without the use of parallel.The FBED(Forward Backward Early Dropping)is a variant of the Forward selection is per-formed in the first phase followed by the usual backward regression.In some,the variation is that every non significant variable is dropped until no mre significant variables are found or there is no variable left.The forward and backward regression methods have a few different arguments.For example stopping which can be either”BIC”or”adjrsq”,with the latter being used only in the linear regression case.Every time a variable is significant it is added in the selected variables set.But, it may be the case,that it is actually not necessary and for this reason we also calculate the BIC of the relevant model at each step.If the difference BIC is less than the tol(argument)threshold value the variable does not enter the set and the algorithm stops.The forward and backward regression methods can proceed via the BIC as well.At every step of the algorithm,the BIC of the relevant model is calculated and if the BIC of the model including a candidate variable is reduced by more that the tol(argument)threshold value that variable is added.Otherwise the variable is not included and the algorithm stops.2.2Other relevant functionsOnce SES or MMPC are finished,the user might want to see the model produced.For this reason the functions ses.model and mmpc.model can be used.If the user wants to get some summarised results with MMPC for many combinations of max k and treshold values he can use the mmpc.path function.Ridge regression(ridge.reg and ridge.cv)have been implemented. Note that ridge regression is currently offered only for linear regression with continuous predictor variables.As for some miscellaneous,we have implemented the zero inflated Poisson and beta regression models,should the user want to use them.2.3Cross-validationcv.ses and cv.mmpc perform a K-fold cross validation for most of the aforementioned regression models.There are many metric functions to be used,appropriate for each case.The folds can be generated in a stratified fashion when the dependent variable is categorical.3NetworksCurrently three algorithms for constructing Bayesian Networks(or their skeleton)are offered,plus modifications.MMHC(Max-Min Hill-Climbing)[23],(mmhc.skel)which constructs the skeleton of the Bayesian Network(BN).This has the option of running SES[18]instead.MMHC(Max-Min Hill-Climbing)[23],(local.mmhc.skel)which constructs the skeleton around a selected node.It identifies the Parents and Children of that node and then finds their Parents and Children.MMPC followed by the PC rules.This is the command mmpc.or.PC algorithm[15](pc.skel for which the orientation rules(pc.or)have been implemented as well.Both of these algorithms accept continuous only,categorical data only or a mix of continuous,multinomial and ordinal.The skeleton of the PC algorithm has the option for permutation based conditional independence tests[21].The functions ci.mm and ci.fast perform a symmetric test with mixed data(continuous, ordinal and binary data)[17].This is employed by the PC algorithm as well.Bootstrap of the PC algorithm to estimate the confidence of the edges(pc.skel.boot).PC skeleton with repeated measures(glmm.pc.skel).This uses the symetric test proposed by[17]with generalised linear models.Skeleton of a network with continuous data using forward selection.The command work does a similar to MMHC task.It goes to every variable and instead applying the MMPC algorithm it applies the forward selection regression.All data must be continuous,since the Pearson correlation is used.The algorithm is fast,since the forward regression with the Pearson correlation is very fast.We also have utility functions,such as1.rdag and rdag2.Data simulation assuming a BN[3].2.findDescendants and findAncestors.Descendants and ancestors of a node(variable)ina given Bayesian Network.3.dag2eg.Transforming a DAG into an essential(mixed)graph,its class of equivalent DAGs.4.equivdags.Checking whether two DAGs are equivalent.5.is.dag.In fact this checks whether cycles are present by trying to topologically sort theedges.BNs do not allow for cycles.6.mb.The Markov Blanket of a node(variable)given a Bayesian Network.7.nei.The neighbours of a node(variable)given an undirected graph.8.undir.path.All paths between two nodes in an undirected graph.9.transitiveClosure.The transitive closure of an adjacency matrix,with and without arrow-heads.10.bn.skel.utils.Estimation of false discovery rate[22],plus AUC and ROC curves based onthe p-values.11.bn.skel.utils2.Estimation of the confidence of the edges[16],plus AUC and ROC curvesbased on the confidences.12.plotnetwork.Interactive plot of a graph.4AcknowledgmentsThe research leading to these results has received funding from the European Research Coun-cil under the European Union’s Seventh Framework Programme(FP/2007-2013)/ERC Grant Agreement n.617393.References[1]John Aitchison.The statistical analysis of compositional data.Chapman and Hall London,1986.[2]Giorgos Borboudakis and Ioannis Tsamardinos.Forward-Backward Selection with Early Drop-ping,2017.[3]Diego Colombo and Marloes H Maathuis.Order-independent constraint-based causal structurelearning.Journal of Machine Learning Research,15(1):3741–3782,2014.[4]David Henry Cox.Regression Models and Life-Tables.Journal of the Royal Statistical Society,34(2):187–220,1972.[5]Silvia Ferrari and Francisco Cribari-Neto.Beta regression for modelling rates and proportions.Journal of Applied 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