Migratory Logistic Regression for Learning Concept Drift Between Two Data Sets with Applica

格式：pdf
大小：548.30 KB
文档页数：11

下载文档原格式

Logistic回归(逻辑回归)总结

3.3 梯度下降法求 J ( ) 的最小值
求 J ( ) 的最小值可以使用梯度下降法，根据梯度下降法可得的更新过程：
j : j -
式中为学习步长，下面来求偏导：
J ( ), ( j 0 n) j
（11）
1 m 1 1 J ( ) y ( i ) h (x (i) ) (1 y ( i ) ) h (x (i) ) (i) (i) j m i 1 h (x ) j 1 h (x ) j 1 m (i ) 1 1 (1 y ( i ) ) g ( T x (i) ) y T (i) T (i) m i 1 g ( x ) 1 g ( x ) j 1 m (i ) 1 1 T (i) (1 y ( i ) ) g ( T x (i) ) 1 g ( T x (i) ) x y T (i) T (i) m i 1 g ( x ) 1 g ( x ) j
i 1
for 语句循环 m 次，所以根本没有完全的实现 vectorization，不像《机器学习实战》的代码中一条语句就可以完成的更新。下面说明一下我理解《机器学习实战》中代码实现的 vectorization 过程。约定训练数据的矩阵形式如下， x 的每一行为一条训练样本，而每一列为不同的特称取值：
（5）
（6）实际上这里的 Cost 函数和 J 函数是基于最大似然估计推导得到的。下面详细说明推导的过程。（4）式综合起来可以写成：
P ( y | x; ) (h ( x)) y (1- h ( x))1- y
取似然函数为：
（7）
L( ) P ( y (i) | x (i) ; )

logistic regression法

logistic regression法
（原创实用版）
目录
1.线性回归概述
2.Logistic 回归法的原理
3.Logistic 回归法的应用
4.Logistic 回归法的优缺点
正文
线性回归是一种常见的统计分析方法，主要用于研究因变量和自变量之间的关系。

在线性回归中，因变量通常是连续的，而自变量可以是连续的或离散的。

然而，当因变量为二分类或多分类时，线性回归就不再适用。

这时，Logistic 回归法就被引入了。

Logistic 回归法是一种用于解决分类问题的统计方法，其原理是基于逻辑斯蒂函数。

逻辑斯蒂函数是一种 S 型函数，其取值范围在 0 到 1 之间，可以用来表示一个事件发生的概率。

在 Logistic 回归法中，我们通过将自变量输入逻辑斯蒂函数，得到一个概率值，然后根据这个概率值来判断因变量所属的类别。

Logistic 回归法广泛应用于二分类和多分类问题中，例如信用风险评估、疾病预测、市场营销等。

在我国，Logistic 回归法也被广泛应用于各种领域，如金融、医疗、教育等。

Logistic 回归法虽然具有很多优点，但也存在一些缺点。

首先，Logistic 回归法对于自变量过多或者数据量过小的情况不太适用，因为这样容易导致过拟合。

其次，Logistic 回归法的计算过程比较复杂，需要用到特种数学知识，对计算资源的要求也比较高。

总的来说，Logistic 回归法是一种重要的分类方法，具有广泛的应
用前景。

逻辑回归

Comparing the Linear Probability and Logit Models 比较线性回归和逻辑回归模型
The logistic regression model is the non-lineion 逻辑回归模型只是对线性回归的非线性转换
Y=0 X
A06-4
Why Use Logistic Regression? 为什么使用逻辑回归？
In using ordinary linear regression, if you move far enough along the X-axis, the predicted values will become greater than 1 and less than 0. 当使用一般线性回归，如果沿着X轴移动太远的话，预测的数值就会大于1或者小于0
Logistic Regression 逻辑回归
Learning Objectives 学习目标
Understand the application of Logistic Regression 了解逻辑回归的应用场合
Understand the three types of Logistic Regression 了解逻辑回归的三种类型 1. Binary Response Variables 二进制响应变量 2. Ordinal Response Variables 有序响应变量 3. Nominal Response Variables 名义响应变量
Linear regression techniques are used with continuous Output variables. 线性回归技术用于连续型输出变量

logistic regression算法

logistic regression算法
Logistic regression (逻辑回归) 是一种用于二分类问题的统计学
习方法。

它基于一个由逻辑函数或Sigmoid函数表示的非线性
回归模型。

逻辑回归的目标是根据输入的特征，将样本分为两个离散的类别。

与线性回归不同，逻辑回归在结果上给出了0
和1之间的概率估计。

逻辑回归的实现步骤如下：
1. 收集训练数据集，该数据集应包含输入特征和对应的类别标签。

2. 准备数据，例如通过对特征进行归一化或者处理缺失数据。

3. 定义逻辑函数，该函数将输入特征映射到一个概率值，通常使用Sigmoid函数。

4. 定义损失函数，通常使用最大似然估计来定义损失函数，并使用梯度下降等优化算法来最小化该损失函数。

5. 训练模型，通过迭代优化算法，找到最优的参数值，使得损失函数最小化。

6. 对新样本进行预测，使用学习到的参数和逻辑函数，将输入特征映射到一个概率值，并根据阈值将其分类为正类或负类。

逻辑回归可以用于线性可分的和线性不可分的数据集。

它在进行预测时计算复杂度较低，模型也相对简单，易于解释和理解。

然而，逻辑回归对于非线性关系的学习能力较弱，因此在处理非线性问题时可能不够准确。

第17章Logistic回归分析..

2018Biblioteka 10/5 52018/10/5
北京大学光华管理学院涂平教授
6
讨论：非诚勿扰中的男嘉宾
每次出场的男嘉宾有几种可能的下场？影响结局的主要因素可能有哪些？如何衡量这些因素对结局的影响？结局是否可以预测？
2018/10/5
7
与普通线性回归的比较
当因变量是二分变量时，普通线性回归的主要假设并不能得到满足。
2018/10/5
13
估计回归系数
Logistic 回归系数一般由极大似然法 (maximum likelihood method）估算，这通常通过迭代方法实现。
自变量的取舍通常根据极大似然比（ MLR）或协方差近似估计(ACE)，以逐步回归的方式进行。
2018/10/5
14
回归系数的含义
截距 ß 0 决定假设所有其它变量取值为 0时事件发生的概率。回归系数j 表示事件发生概率与变量j 的关系。
q = 1/[1 + exp(ß 0 + jxj)]
(6)
2018/10/5
11
二、分析步骤
定义问题估算回归系数
确定回归系数的显著性解释结果模型评估
2018/10/5 12
定义问题
对问题的定义包括：
确定因变量
• 购买、入网、离网、投诉、开户、赖账……
确定预测变量
• 即对因变量有影响的变量，主要根据文献和经验
j > 0 正相关 j < 0 负相关 j = 0 无关
2018/10/5 15
因变量不呈正态分布；根据多元方程得到的预测值不能保证在0-1之间。
这时可以采用 binary logistic 回归, 简称logistic 回归。

逻辑回归 logistic regression

Logistic Regression
Marc Deisenroth
@Imperial College London, February 8, 2019
2
Binary Classiﬁcation
x2
3
2
1
0
−1
−2
−4
−2
0
2
x1
§ Supervised learning setting with inputs xn P RD and binary targets yn P t0, 1u belonging to classes C1, C2.
@Imperial College London, February 8, 2019
7
Implicit Modeling Assumptions
§ Assume Gaussian class conditionals
ppx|Ckq “ N `x | µk, Σ˘ where the covariance matrix Σ is shared across all K classes. § For K “ 2 we get (Bishop, 2006)
7
Implicit Modeling Assumptions
§ Assume Gaussian class conditionals
ppx|Ckq “ N `x | µk, Σ˘ where the covariance matrix Σ is shared across all K classes. § For K “ 2 we get (Bishop, 2006)
§ Then
a
:“
log
ppC1|xq ppC2|xq

Maximun likelihood linear regression for speaker adaptation of

• Consider the case of a continuous density HMM system with Gaussian output distributions.
• A particular distribution s ,is characterized by a mean vector s ,
data, a transformation may still be applied (global transformation)
6
Estimation of MLLR regression matrices
• 1.Definition of auxiliary function
S
– Assume the adaptation data, O, is a series of T observations.
and a covariance matrix C s
• Given a parameterized speech frame vector o , the probability
density of that vector being generated by distribution s is bs o
j 1
T j t log2 n / 2
t 1
log C j
1/ 2
1 2
ot
j
' C j 1
ot
j
S
constant FO |
j 1
T t 1
j
t
1 2
n
log2
1 2
log
C
j
1 2
ot
j
' C j 1

logistic回归分析PPT优秀课件

（2）线性回归分析：由于因变量是分类变量，不能满足其正态性要求；有些自变量对因变量的影响并非线性。
2
logistic回归:不仅适用于病因学分析，也可用于其他方面的研究，研究某个二分类（或无序及有序多分类）目标变量与有关因素的关系。
logistic回归的分类：（1）二分类资料logistic回归：因变量为两分类变量的资料，可用
非条件logistic回归和条件logistic回归进行分析。非条件logistic回归多用于非配比病例-对照研究或队列研究资料，条件logistic回归多用于配对或配比资料。（2）多分类资料logistic回归：因变量为多项分类的资料，可用多项分类logistic回归模型或有序分类logistic回归模型进行分析。
比较
调查方向：收集回顾性资料
人数暴露
疾病
a/(a+b) c/(c+d)
a
+
b
-
病例
c
病例对照原理示意图
6
是否暴露暴露组未暴露组合计
病例 a c a+c
对照 b d b+d
合计 a+b(n1) c+d(n2) n
比数比（odds ratio、OR）：病例对照研究中表示疾病与暴露间
联系强度的指标，也称比值比。
相对危险度RR的本质是暴露组与非暴露组发病率之比或发病概率之比。但病例对照研究不能计算发病率，只能计算比值比OR值。 OR与RR的含义是相同的，也是指暴露组的疾病危险性为非暴露组的多少倍。当疾病发病率小于5%时，OR是RR的极好近似值。
OR>1,说明该因素使疾病的危险性增加，为危险因素；
OR<1,说明该因素使疾病的危险性减小，为保护因素；

logistic regression原理(一)

logistic regression原理(一)Logistic Regression原理1. 介绍•Logistic Regression（逻辑回归）是一种用于处理分类问题的机器学习算法。

•它可以用于二分类问题，也可以通过扩展用于多分类问题。

2. 基本概念•Logistic Regression的基本原理是通过拟合一个逻辑函数来预测分类概率。

•逻辑函数是一个S形曲线，将输入映射到0到1之间的值。

3. Sigmoid函数•逻辑函数通常使用Sigmoid函数来表示，公式如下：[Sigmoid Function](其中，z是线性方程的输出。

4. 线性方程•Logistic Regression使用一个线性方程加权求和输入特征来预测分类概率。

•线性方程的表示为：[Linear Equation](其中，x是输入特征，β是线性方程的权重。

5. 模型训练•训练Logistic Regression模型的目标是找到最佳的权重值，使得模型的预测结果与实际情况最为接近。

•常用的方法是最大似然估计，根据已有的训练数据，最大化模型预测正确性的概率。

6. 损失函数•损失函数用于衡量模型预测结果与实际情况之间的差异。

•在Logistic Regression中，常用的损失函数是对数损失函数（Log Loss）。

7. 模型预测•模型训练完成后，可以使用它来进行分类预测。

•根据输入特征，通过线性方程和Sigmoid函数，得到分类的概率值。

•一般而言，当概率大于时，预测为正类；当概率小于等于时，预测为负类。

8. 优点和局限性•优点：–算法简单，易于理解和实现；–训练速度快；–可以处理大规模数据；–可以输出分类概率值。

•局限性：–对特征之间的相关性敏感；–很难处理非线性关系。

9. 应用领域•Logistic Regression在许多领域都有广泛应用，例如：–金融行业中的风险评估和信用评分；–医疗领域中的疾病诊断；–电子商务中的用户购买行为预测。

用Logistic回归模型预测糖尿病人病情程度毕业论文

用Logistic回归模型预测糖尿病人病情程度目录摘要 (Ⅰ)关键词 (Ⅰ)Abstract (Ⅱ)Keywords (Ⅱ)前言 (1)1.绪论 (1)1.1 研究意义 (1)1.2 研究背景 (2)2.Logistic回归模型简介 (2)2.1二分类Logistic回归模型 (3)2.2多分类Logistic回归模型 (4)2.3 Logisti c回归模型的参数估计方法 (5)3.用Logistic回归模型预测糖尿病人病情程度 (7)3.1问题分析 (7)3.2相关性分析 (8)3.3模型建立及检验 (10)3.4结论 (12)参考文献 (13)附表1 (14)附表2 (15)附表3 (17)附表4 (20)致谢 (22)用Logistic回归模型预测糖尿病人病情程度摘要：本文首先总结近年来有关Logistic回归模型的研究概况。

然后在Logistic回归模型的基础上，重点介绍了二分类和多分类变量Logistic回归模型。

并使用最大似然估计法对模型中的参数进行估计，然后根据拟合优度检验法对模型进行检验。

最后利用SPSS统计软件对糖尿病人的病情程度建立模型，进行系统的分析并将预测结果与实际结果进行比对。

关键词：Logistic回归模型；拟合优度；最大似然估计；回归系数Logistic regression model was used to predict the severity of diabeticpatientsAbstract：This topic summarizes some surveys researched in recent years about Logistic Regression Model. Then on the basis of Logistic Regression Model, introduce two categories and multiple categories variable of Logistic Regression Model, .Firstly, use maximum likelihood to estimste parameters of the model, and secondly, use the goodness of fit test for the model, thirdly, use SPSS statistical software to build model for the severity of patients with diabetes mellitus, carry out the system analysis and contrast the forecast and real result.Keywords：Logistic regression model; goodness of fit；maximum likelihood estimate; regression coefficients.前言Logistic回归模型作为重要的统计模型,对种群生态学的研究具有核心理论价值。

R语言英文回归教案Logistic Regression Multinomial Data

About Logistic Regression

It uses a maximum likelihood estimation rather than the least squares estimation used in traditional multiple regression. The general form of the distribution is assumed. Starting values of the estimated parameters are used and the likelihood that the sample came from a population with those parameters is computed. The values of the estimated parameters are adjusted iteratively until the maximum likelihood value for the estimated parameter means of the dependent variables at each level of the independent variable are not on a straight line, i.e., no linearity. The variance of the errors are not constant, i.e., no homogeneity of variance. The errors are not normally distributed, i.e., no normality.
linear regression, the impact of an independent variable X depends on its value And the values of all other independent variables

机器学习笔记04（LogisticRegression）

机器学习笔记04（LogisticRegression）Logistic Regression思路：1、逻辑回归 vs 线性回归（Logistics Regression VS Linear Regression ）2、⽣成模型 vs 判别模型（Generative Model VS Discriminative Model）3、逻辑回归 vs 深度学习（Logistics Regression VS Deep Learning）前⾯已经学过 Regression ，其建⽴的 model 是 Linear model，现在与Logistics Regression对⽐学习。

此节与上节内容联系⽐较紧密，可回头复习⼀下。

1、逻辑回归 vs 线性回归（Logistics Regression VS Linear Regression ）什么是逻辑回归：逻辑回归是解决分类问题的⼀种算法它与linear regression 形式上有点像（本质上是在线性模型外⾯“裹”⼀个sigmoid激活函数，来表⽰概率的函数）它是⼀种判别模型，与前⾯说的⽣成模型不同它是深度学习的基础1）model 不同model 对⽐：2）Loss Function 不同回顾我们线性回归的Loss函数中是跟训练数据（x1,y^1）中的y^1的差值平⽅和，那么逻辑回归是否也要建⽴与y^的联系呢。

下⾯就要开始拼凑了！Loss function对⽐：为什么不是⽤平⽅差？3）step 3 是类似的先算左边（红⾊框）的偏导，再算右边红⾊框的偏导，再整理式⼦：对⽐：2、⽣成模型 vs 判别模型（Generative Model VS Discriminative Model）两种不同的model，得到的 w，b 的参数不同。

但⼀般来说，判别模型表现得会⽐⽣成模型好，为什么？举例⽣成模型是基于假想的概率模型的，如果样本不平衡的话，计算出来的概率是会有误差的但是⽣成模型也有优点： 1、样本量少的时候表现⽐判别模型好，因为它能⾃⼰脑补出⼀个假想模型 2、噪声对它影响较⼩，因为它没有过分依赖数据，它是按照⾃⼰假想模型⾛的3、逻辑回归 vs 深度学习（Logistics Regression VS Deep Learning）逻辑回归是解决分类问题的，实际中的问题⼤多是多分类的问题，多分类问题会⽤到softmax 以下⾯三分类问题为例：逻辑回归是有它的局限性的，这时候就需要深度学习了！举例：我们要⽤逻辑回归⽅法分类出下⾯的红点与蓝点，是需要⽤特征⼯程的⽅法的，⽽特征⼯程是需要我们⼈为地去建⽴⼀个特征函数去把这些点转化，实际上是⽐较难的，或者说⽐较费⼯夫的。

logisticregression简介

logisticregression简介Logistic Regression简介Logistic Regression（逻辑回归）是一种统计学习方法，用于解决分类问题。

它是由人们对线性回归模型的改进而来，通过引入逻辑函数将线性模型的输出限制在[0,1]之间，从而实现对二分类问题的建模。

Logistic Regression的基本原理是通过构建一个逻辑函数，将输入的特征与输出的概率联系起来。

逻辑函数一般采用Sigmoid函数，形式为：$$f(x) = \frac{1}{1+e^{-x}}$$其中，x为输入特征的线性组合。

Sigmoid函数具有将输入映射到[0,1]之间的特性，因此可以将输出解释为概率。

在Logistic Regression中，模型的参数是通过最大似然估计来求解的。

给定一个训练集，我们希望找到一组参数，使得模型对训练集的预测概率尽可能接近真实标签的概率。

具体来说，我们希望最大化似然函数：$$L(\theta) = \prod_{i=1}^{n}P(y^{(i)}|x^{(i)};\theta)$$其中，$y^{(i)}$为第i个样本的真实标签，$x^{(i)}$为其对应的特征向量，$\theta$为模型的参数。

对上式取对数，可以得到对数似然函数：$$l(\theta) = \sum_{i=1}^{n}\log P(y^{(i)}|x^{(i)};\theta)$$为了最大化对数似然函数，可以使用梯度上升法或者其他优化算法来求解。

Logistic Regression的优点之一是模型简单且易于解释。

由于模型的输出可以解释为概率，因此可以根据设定的阈值来进行分类预测。

此外，Logistic Regression对异常值和噪声有较好的鲁棒性，可以在一定程度上避免过拟合问题。

然而，Logistic Regression也有一些限制。

首先，它只能处理二分类问题，对于多分类问题需要进行扩展。

logistic regression逻辑回归算法 -回复

logistic regression逻辑回归算法-回复什么是逻辑回归算法（Logistic Regression Algorithm）？逻辑回归算法是一种广泛应用于机器学习和统计学领域的经典算法，用于建立分类模型。

它适用于用于预测二元分类问题的情况，即目标变量只有两个可能的输出。

逻辑回归通过将线性回归模型的输出转换为0和1之间的概率，从而实现分类。

逻辑回归算法的基本原理是将输入特征的加权和通过一个被称为"逻辑函数"或"sigmoid函数"的非线性函数进行转换。

这个函数可以将任何实数映射到[0,1]区间上的一个值。

逻辑函数常见的形式是：sigmoid(z) = \frac{1}{1 + e^{-z}}其中，z是线性回归模型的输出，由输入特征的加权和计算得到。

这个转换将使得输出可以被视为属于某个类别的概率。

逻辑回归算法的训练过程主要通过最大似然估计来确定模型的参数。

最大似然估计的目标是最大化给定数据样本的输出发生概率的乘积。

根据逻辑回归模型的假设，每个数据样本的输出概率可以由逻辑函数来表示。

因此，似然函数可以由所有数据样本的输出概率乘积来表示。

为了最大化似然函数，可以使用梯度下降法或牛顿法等优化算法来更新模型的参数，使得似然函数取得最大值。

这些优化算法会根据似然函数的梯度信息来调整参数的值，直至达到最优解。

在训练完成后，逻辑回归模型可以用于预测新的未知数据样本的类别。

通过计算输入特征的加权和，并将其输入逻辑函数中，可以得到一个概率值。

通常，概率值大于一个阈值（通常是0.5），模型将判定该数据样本属于正类别；反之则属于负类别。

逻辑回归算法具有许多优点。

首先，它的训练速度相对较快，尤其适用于大规模数据集。

其次，逻辑回归可以提供一个明确的概率值，而不仅仅是简单地判定一个样本属于哪个类别。

此外，逻辑回归模型也比较易于解释和理解。

然而，逻辑回归模型也有一些限制。

例如，它只适用于线性可分的数据集，因为它只能通过线性方式从输入特征中提取信息。

SequentialLogisticRegression

Methods -- Subjects
The 219 mother-infant dyads recruited for this study were part of a larger cohort recruited in waves over four years, beginning in 1990 as part of the Capella Project, a twenty year longitudinal study funded by NIH.
Examples of commonly understood protective factors include individual verbal communication skills, the capacity for empathy, problem solving skills, frustration tolerance, the presence of multiple and consistent caregivers, access to health care and social services, and the concrete, social, and affective support of family and friends.
It is easy to conduct the analysis using a statistical software package.
Overview of Study
Children grow up within the context of personality, family, neighborhood, and society.
Data used in the current analysis were collected over a period of approximately 4-5 years.

logistic regression算法

Algorithm introduction
Logistic regression
David
History
Logistic regression was developed by statistician David in 1958. The binary logistic model is used to estimate the probability of a binary response based on one or more independent variables. Logistic regression is a linear model for classification rather than regression.
Introduction
The model of logistic regression, however, is based on quite different assumptions (about the relationship between dependent and independent variables) from those of linear regression. In particular the key differences of these two models can be seen in the following two features of logistic regression. First, the conditional distribution is a Bernoulli distribution rather than a Gaussian distribution. Second, the predicted values are probabilities and are therefore restricted to (0,1) through the logistic distribution function because logistic regression predicts the probability of particular outcomes.

单因素逻辑回归英文名词

单因素逻辑回归英文名词When dealing with data analysis, one common technique we use is simple logistic regression. It's a statistical method that helps us understand the relationship between a binary outcome and a single predictor variable. In other words, it answers the question, "how likely is this event to happen based on one factor?" The simplicity of this approach makes it a great starting point for many researchers and analysts.The beauty of logistic regression lies in its ability to handle categorical outcomes. Unlike linear regression, which predicts continuous variables, logistic regression predicts probabilities of occurrence. This is especially useful when dealing with things like "yes/no" questions or binary outcomes.One of the coolest things about this method is that it provides us with an odds ratio. This ratio tells us how much the odds of an event change with each unit increase inthe predictor variable. So not only can we say that factor X is associated with an increase in the outcome, but we can also quantify exactly how much of an increase it is.Another aspect I love about logistic regression is its flexibility. While it's called "simple" here, we can easily extend it to include multiple predictor variables using multivariate logistic regression. This gives us the ability to capture complex relationships between many different factors and an outcome, making it a powerful tool in our data analysis arsenal.In summary, single-factor logistic regression is a straightforward yet powerful technique that allows us to understand the relationship between a binary outcome and a single predictor variable. Its simplicity, ability to handle categorical outcomes, provision of odds ratios, and flexibility make it a go-to method for many analysts and researchers.。

单因素logistic回归英文缩写

单因素logistic回归英文缩写English:"Single-factor logistic regression is abbreviated as SFLR. It is a statistical method used to model the relationship between a binary dependent variable and one independent variable. In SFLR, the dependent variable is categorical with two outcomes, usually coded as 0 and 1, representing, for example, failure and success or presence and absence. The independent variable can be continuous, categorical, or dichotomous. The logistic regression model estimates the probability of the occurrence of one of the outcomes based on the values of the independent variable. It calculates the odds ratio, which represents the odds of one outcome relative to the other. The logistic function, also known as the sigmoid function, transforms the linear combination of the independent variables into probabilities. SFLR is widely used in various fields such as medicine, epidemiology, and social sciences for predicting binary outcomes and understanding the factors influencing them."中文翻译:"单因素logistic回归的英文缩写是SFLR。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

1
Migratory Logistic Regression for Learning Concept Drift Between Two Data Sets with Application to UXO Sensing
Xuejun Liao and Lawrence Carin Department of Electrical and Computer Engineering Duke University Durham, NC 27708-0291, USA {xjlia
N
L(yi , ζ (xi )),
i=1
with
(x, y ) ∼ T (x, y )
(1)
The empirical loss is known to approach the true loss when N → ∞. A learning algorithm based on the empirical loss minimization in (1) implicitly assumes that the future test instances are also drawn from T (x, y ). It is this assumption that assures that the classiﬁer generalizes to test instances when it is trained to minimize empirical loss on training examples. This assumption, however, is often violated in practice, since training examples and test instances may correspond to different collections of measurements (likely performed at different times under different experimental conditions) and the class memberships of the measurements may also change. These issues can introduce statistical differences between the
1 Traditionally, the (probabilistic) mapping Pr(y |x) is called a concept, and Pr(x) is called a virtual concept (language describing the concept) [2]. For simplicity, usually they are collectively called a concept.
training data. Such training data typically comes from other former bombing sites that have been cleaned, and there is a signiﬁcant issue as to whether such extant labeled sensor data are relevant for a new site under test. The challenge addressed in this paper involves learning the relevance and relationship of existing labeled (training) data for analysis of a new unlabeled or partially labeled data set of interest. This type of problem has signiﬁcant practical relevance for UXO sensing, for which results are presented on measured data, as well as for the aforementioned classes of problems, for which there is uncertainty concerning the appropriateness of existing labeled data for a new set of unlabeled data of interest. To place this problem in a mathematical setting, let T (x, y ) be the probability distribution (or concept, borrowing a term from psychology 1 ) from which test instances (each including a feature vector x and the associated class label y ) are drawn. The goal in classiﬁer design is to minimize a loss function L(y, ζ (x)), which is a quantitative measure for the loss incurred by the classiﬁer when it predicts ζ (x) for x whose true label is y . The minimization is performed for N independent training examples (x, y ) drawn from T (x, y ), leading to the empirical loss minimization [3], [4] min
Abstract— To achieve good generalization in supervised learning, the training and testing examples are usually required to be drawn from the same source distribution. In this paper we propose a method to relax this requirement in the context of logistic regression. Assuming Dp and Da are two sets of examples drawn from two different distributions T and A (called concepts, borrowing a term from psychology), where Da are fully labeled and Dp partially labeled, our objective is to complete the labels of Dp . We introduce an auxiliary variable µ for each example in Da to reﬂect its mismatch with Dp . Under an appropriate constraint the µ’s are estimated as a byproduct, along with the classiﬁer. We also present an active learning approach for selecting the labeled examples in Dp . The proposed algorithm, called migratory logistic regression (MigLogit), is demonstrated successfully on simulated data as well as on real measured data of interest for unexploded ordnance (UXO) cleanup.
I. I NTRODUCTION In supervised classiﬁcation problems, the goal is to design a classiﬁer using the training examples (labeled data) such that the classiﬁer predicts the labels correctly for unlabeled test data. The accuracy of the predictions is signiﬁcantly affected by the quality of the training examples, which are assumed to contain essential information about the test instances for which predictions are desired. A common assumption utilized by learning algorithms is that the training examples and the test instances are drawn from the same source distribution. As a practical example, consider the detection of a concealed entity based on sensor data collected in a non-invasive manner. This problem is of relevance in several practical problems, for example in the medical imaging of potential tumors or other hidden anomalies. In the context of remote sensing, one is often challenged with the problem of detecting and characterizing a concealed (e.g., underground) target based on remotely collected sensor data. In an example that will be considered explicitly in this paper, consider the detection of buried unexploded ordnance (UXO) [1]. An unexploded ordnance is a bomb that did not explode upon impact with the ground, and such items pose great danger if disturbed (excavated) without care. Sensors used for detecting and characterizing UXO include magnetometers and electromagnetic induction [1]. In designing an algorithm for characterization of anomalies detected by such sensors, to determine if a given buried item is UXO or clutter, one typically requires

Migratory Logistic Regression for Learning Concept Drift Between Two Data Sets with Applica

合集下载

Logistic回归(逻辑回归)总结

logistic regression法

逻辑回归

logistic regression算法

第17章Logistic回归分析..

逻辑回归 logistic regression

Maximun likelihood linear regression for speaker adaptation of

logistic回归分析PPT优秀课件

logistic regression原理(一)

用Logistic回归模型预测糖尿病人病情程度毕业论文

R语言英文回归教案Logistic Regression Multinomial Data

机器学习笔记04（LogisticRegression）

logisticregression简介

logistic regression逻辑回归算法 -回复

SequentialLogisticRegression

logistic regression算法

单因素逻辑回归英文名词

单因素logistic回归英文缩写

文档推荐

最新文档