ValidationofEMMS_base_省略_mannsimulations

BERT（Bidirectional Encoder Representations from Transformers）是一种基于Transformer架构的预训练语言模型，由Google在2018年提出。

它是一种革命性的模型，因为它允许双向（双向）处理上下文，这使得它在理解和生成自然语言方面表现得非常出色。

BERT-base-uncased是BERT的一种变体，它是基于未加大写的英文文本进行预训练的。

在本文中，我们将对BERT-base-uncased模型进行解读，深入探讨它的原理、训练方法和应用领域，希望能让读者对这一领域有更深入的了解。

1. BERT-base-uncased模型原理BERT-base-uncased模型的核心原理是Transformer架构。

Transformer是一种基于自注意力机制（self-attention）的模型，它能够并行计算输入序列中不同位置的信息，极大地提高了处理长距离依赖关系的能力。

在BERT中，这种能力被充分利用，使得模型能够在预训练阶段捕捉到丰富的语言表示。

2. BERT-base-uncased模型训练方法BERT-base-uncased模型的训练方法是使用无标签的语料库进行大规模的无监督预训练。

在预训练阶段，模型被要求通过Masked Language Model（MLM）和Next Sentence Prediction（NSP）两个任务学习语言表示。

MLM任务要求模型预测被掩盖的单词，从而训练模型对上下文信息进行编码；NSP任务要求模型判断两个句子是否是相邻的，从而训练模型对文本关系进行建模。

3. BERT-base-uncased模型应用领域由于其出色的性能，BERT-base-uncased模型已经在多个自然语言处理领域取得了突出的成绩。

在文本分类、命名实体识别、问答系统等任务中，BERT-base-uncased模型都展现出了强大的表现力和泛化能力。

深度学习神经网络逼近非线性函数深度研究神经网络是一种强大的机器研究模型，被广泛应用于各个领域，包括图像识别、自然语言处理等。

它通过多层神经元来建模复杂的非线性函数关系，可以实现对非线性函数的逼近。

神经网络基础神经网络由输入层、隐藏层和输出层组成。

输入层接收输入数据，隐藏层负责对输入进行加工和提取特征，输出层则生成最终的预测结果。

每个神经元在隐藏层和输出层都会进行激活函数的运算，将线性变换后的结果转化为非线性的输出。

非线性函数逼近深度研究神经网络能够逼近非线性函数的原因在于其多层结构。

每一层的神经元都可以研究到不同级别的特征表示，通过多层的组合与堆叠，神经网络能够模拟和逼近非常复杂的非线性函数。

激活函数的重要性激活函数是神经网络中非常重要的组成部分，它引入了非线性因素，使得神经网络能够处理非线性问题。

常见的激活函数有Sigmoid函数、ReLU函数等，它们可以将线性变换的结果映射到非线性的输出，增强神经网络的表达能力。

深度研究的训练深度研究神经网络的训练过程通常使用反向传播算法。

该算法通过计算实际输出与期望输出之间的误差，然后根据误差调整神经网络的权重和偏置，以逐渐提高网络的预测准确性。

通过反复迭代训练，神经网络可以逐渐优化和逼近目标非线性函数。

应用领域深度研究神经网络广泛应用于图像识别、语音识别、自然语言处理等领域。

例如，在图像识别中，神经网络可以通过研究大量图像样本来识别物体、人脸等；在自然语言处理中，神经网络可以对文本进行分类、情感分析等任务。

深度研究神经网络的强大逼近能力使得它在这些领域具有很高的应用价值。

结论深度学习神经网络通过多层神经元和非线性激活函数的组合，能够逼近非线性函数。

它是一种强大的机器学习模型，在各个领域都有广泛的应用。

随着深度学习技术的不断发展，我们相信神经网络将会在更多领域展现出强大的能力和应用前景。

Package‘hdImpute’August7,2023Type PackageTitle A Batch Process for High Dimensional ImputationVersion0.2.1BugReports https:///pdwaggoner/hdImpute/issuesMaintainer Philip Waggoner<*************************>Description A correlation-based batch process for fast,accurate imputation forhigh dimensional missing data problems via chained random forests.See Waggoner(2023)<doi:10.1007/s00180-023-01325-9>for more on'hdImpute',Stekhoven and Bühlmann(2012)<doi:10.1093/bioinformatics/btr597>for more on'missForest', and Mayer(2022)<https:///mayer79/missRanger>for more on'missRanger'. License MIT+file LICENSEEncoding UTF-8Imports missRanger,plyr,purrr,magrittr,tibble,dplyr,tidyselect,tidyr,cliSuggests testthat(>=3.0.0),knitr,rmarkdown,usethis,missForest,tidyverseVignetteBuilder knitrRoxygenNote7.2.3Config/testthat/edition3URL https:///pdwaggoner/hdImputeNeedsCompilation noAuthor Philip Waggoner[aut,cre]Repository CRANDate/Publication2023-08-0721:20:02UTCR topics documented:check_feature_na (2)check_row_na (2)12check_row_na feature_cor (3)flatten_mat (4)hdImpute (4)impute_batches (5)mad (6)Index8 check_feature_na Find features with(specified amount of)missingnessDescriptionFind features with(specified amount of)missingnessUsagecheck_feature_na(data,threshold)Argumentsdata A data frame or tibble.threshold Missingness threshold in a given column/feature as a proportion bounded be-tween0and1.Default set to sensitive level at1e-04.ValueA vector of column/feature names that contain missingness greater than threshold.Examples##Not run:check_feature_na(data=any_data_frame,threshold=1e-04)##End(Not run)check_row_na Find number of and which rows contain any missingnessDescriptionFind number of and which rows contain any missingnessUsagecheck_row_na(data,which)feature_cor3Argumentsdata A data frame or tibble.which Logical.Should a list be returned with the row numbers corresponding to each row with missingness?Default set to FALSE.ValueEither an integer value corresponding to the number of rows in data with any missingness(if which =FALSE),or a tibble containing:1)number of rows in data with any missingness,and2)a list of which rows/row numbers contain missingness(if which=TRUE).Examples##Not run:check_row_na(data=any_data_frame,which=FALSE)##End(Not run)feature_cor High dimensional imputation via batch processed chained randomforests Build correlation matrixDescriptionHigh dimensional imputation via batch processed chained random forests Build correlation matrixUsagefeature_cor(data,return_cor)Argumentsdata A data frame or tibble.return_cor Logical.Should the correlation matrix be printed?Default set to FALSE.ValueA cross-feature correlation matrixReferencesWaggoner,P.D.(2023).A batch process for high dimensional putational Statistics, 1-22.doi:<10.1007/s00180-023-01325-9>van Buuren S,Groothuis-Oudshoorn K(2011)."mice:Multivariate Imputation by Chained Equa-tions in R."Journal of Statistical Software,45(3),1-67.doi:<10.18637/jss.v045.i03>4hdImputeExamples##Not run:feature_cor(data=data,return_cor=FALSE)##End(Not run)flatten_mat Flatten and arrange cor matrix to be dfDescriptionFlatten and arrange cor matrix to be dfUsageflatten_mat(cor_mat,return_mat)Argumentscor_mat A correlation matrix output from running feature_cor()return_mat Logical.Should theflattened matrix be printed?Default set to FALSE.ValueA vector of correlation-based ranked featuresExamples##Not run:flatten_mat(cor_mat=cor_mat,return_mat=FALSE)##End(Not run)hdImpute Complete hdImpute process:correlation matrix,flatten,rank,createbatches,impute,joinDescriptionComplete hdImpute process:correlation matrix,flatten,rank,create batches,impute,joinUsagehdImpute(data,batch,pmm_k,n_trees,seed,save)impute_batches5Argumentsdata Original data frame or tibble(with missing values)batch Numeric.Batch size.pmm_k Integer.Number of neighbors considered in imputation.Default set at5.n_trees Integer.Number of trees used in imputation.Default set at15.seed Integer.Seed to be set for reproducibility.save Should the list of individual imputed batches be saved as.rdsfile to working directory?Default set to FALSE.DetailsStep1.group data by dividing the row_number()by batch size(batch,number of batches set by user)using integer division.Step2.pass through group_split()to return a list.Step3.impute each batch individually and time.Step4.generate completed(unlisted/joined)imputed data frame ValueA completed,imputed data setReferencesWaggoner,P.D.(2023).A batch process for high dimensional putational Statistics, 1-22.doi:<10.1007/s00180-023-01325-9>Stekhoven,D.J.,&Bühlmann,P.(2012).MissForest—non-parametric missing value imputation for mixed-type data.Bioinformatics,28(1),112-118.doi:<10.1093/bioinformatics/btr597> Examples##Not run:impute_batches(data=data,batch=2,pmm_k=5,n_trees=15,seed=123,save=FALSE)##End(Not run)impute_batches Impute batches and return completed data frameDescriptionImpute batches and return completed data frameUsageimpute_batches(data,features,batch,pmm_k,n_trees,seed,save)6mad Argumentsdata Original data frame or tibble(with missing values)features Correlation-based vector of ranked features output from running flatten_mat() batch Numeric.Batch size.pmm_k Integer.Number of neighbors considered in imputation.Default at5.n_trees Integer.Number of trees used in imputation.Default at15.seed Integer.Seed to be set for reproducibility.save Should the list of individual imputed batches be saved as.rdsfile to working directory?Default set to FALSE.DetailsStep1.group data by dividing the row_number()by batch size(batch,number of batches set by user)using integer division.Step2.pass through group_split()to return a list.Step3.impute each batch individually and time.Step4.generate completed(unlisted/joined)imputed data frame ValueA completed,imputed data setReferencesWaggoner,P.D.(2023).A batch process for high dimensional putational Statistics, 1-22.doi:<10.1007/s00180-023-01325-9>Stekhoven,D.J.,&Bühlmann,P.(2012).MissForest—non-parametric missing value imputation for mixed-type data.Bioinformatics,28(1),112-118.doi:<10.1093/bioinformatics/btr597> Examples##Not run:impute_batches(data=data,features=flat_mat,batch=2,pmm_k=5,n_trees=15,seed=123,save=FALSE)##End(Not run)mad Compute variable-wise mean absolute differences(MAD)betweenoriginal and imputed dataframes.DescriptionCompute variable-wise mean absolute differences(MAD)between original and imputed dataframes.mad7Usagemad(original,imputed,round)Argumentsoriginal A data frame or tibble with original values.imputed A data frame or tibble that has been imputed/completed.round Integer.Number of places to round MAD scores.Default set to3.Value‘mad_scores‘as‘p‘x2tibble.One row for each variable in original,from1to‘p‘.Two columns:first is variable names(‘var‘)and second is associated MAD score(‘mad‘)as percentages for each variable.Examples##Not run:mad(original=original_data,imputed=imputed_data,round=3)##End(Not run)Indexcheck_feature_na,2check_row_na,2feature_cor,3flatten_mat,4hdImpute,4impute_batches,5mad,68。

validation实现原理在机器学习中，训练模型的主要目标是通过数据来获得一个能够泛化到新数据的模型。

为了确保模型的泛化能力，需要将数据集划分为训练集和验证集。

具体地说，数据集通常被划分为三个部分：训练集、验证集和测试集。

训练集用于训练模型，验证集用于选择模型的超参数或进行模型选择，而测试集则用于评估模型的性能。

在训练过程中，模型会根据训练集的数据进行参数更新，不断优化模型的拟合能力。

然而，如果模型在训练集上过分拟合，可能会导致对新数据的泛化能力很差。

为了避免这种情况，要在训练过程中通过验证集来监控模型的性能。

验证集的主要作用是用于选择模型的超参数或进行模型选择。

通过在验证集上评估不同超参数或不同模型的性能，可以选择出最佳的模型。

常见的方法包括交叉验证、留出法和自助采样等。

交叉验证是一种常用的验证方法，它将训练集进一步划分为K个不重叠的子集，然后使用K-1个子集作为训练集，剩下的子集作为验证集。

这样可以对K个模型进行训练和验证，得到它们的性能指标。

最后，可以通过平均或选择最优的性能指标来选择最佳的模型或最佳的超参数。

留出法是另一种常用的验证方法，它将数据集划分为训练集和验证集两部分，通常将数据集的一定比例留出作为验证集。

然后使用训练集进行模型训练，使用验证集评估模型的性能。

自助采样是一种基于有放回抽样的方法，它通过在训练集中随机有放回地选择样本，构建多个训练集。

然后将这些训练集分别用于模型训练和模型验证，最后通过平均或选择最优的性能指标来选择最佳的模型或最佳的超参数。

总之，验证的实现原理是通过划分数据集为训练集和验证集，监控模型在验证集上的性能指标，例如准确率、精确率、召回率等，以选择最佳的模型或最佳的超参数。

常用的方法包括交叉验证、留出法和自助采样等。

在深度学习模型训练中，无法计算分离步骤1的初始残差往往是一个重要的问题。

深度学习模型通过多层神经网络进行训练，每一层的输出都会作为下一层的输入，而在每一层的输出和输入之间都存在着残差，即当前层的输出和上一层的输入之间的差异。

无法计算分离步骤1的初始残差意味着在模型训练的初始阶段，无法有效地计算残差，这可能会导致模型的训练过程出现问题，甚至无法收敛到理想的结果。

这个问题的产生通常与模型的初始化、数据的预处理、激活函数的选择等因素有关。

在实际应用中，我们需要对这些因素进行全面评估，以确保模型能够正确地计算分离步骤1的初始残差，并顺利进行训练。

对于模型的初始化，我们需要选择合适的初始化方法，以确保模型在初始阶段就能够接近最优解。

常见的初始化方法包括随机初始化、Xavier初始化、He初始化等。

针对不同类型的神经网络结构和激活函数，合适的初始化方法也会有所不同。

在选择初始化方法时，我们需要考虑到模型的具体结构和激活函数的选择，以避免无法计算分离步骤1的初始残差。

数据的预处理也是影响模型训练的重要因素之一。

在进行数据的预处理时，我们需要考虑到数据的分布情况、标准化、归一化等因素，以确保训练数据能够更好地适应模型的训练过程。

如果数据的预处理不当，就可能会导致模型无法有效地计算初始残差，从而影响模型的训练效果。

激活函数的选择也是影响模型训练的重要因素之一。

不同的激活函数对于模型的训练效果有着不同的影响，如果选择不当，就可能会导致模型无法有效地计算初始残差。

在选择激活函数时，我们需要考虑到它的非线性特性、导数的性质等因素，以确保模型能够正确地计算初始残差。

在深度学习模型训练中，无法计算分离步骤1的初始残差是一个影响模型训练效果的重要问题。

为了解决这个问题，我们需要对模型的初始化、数据的预处理、激活函数的选择等因素进行全面评估，并据此进行相应的调整和优化，以确保模型能够顺利进行训练，并收敛到理想的结果。

个人观点上，我认为解决无法计算分离步骤1的初始残差问题需要综合考虑模型结构、数据特性和训练参数等多个方面的因素。

7 Westferry Circus ● Canary Wharf ● London E14 4HB ● United KingdomTelephone +44 (0)20 7418 8400 Facsimile +44 (0)20 7418 861321 July 2011EMEA/CHMP/EWP/192217/2009 Committee for Medicinal Products for Human Use (CHMP)Guideline on bioanalytical method validationDraft agreed by the Efficacy Working PartySeptember 2009 Adoption by CHMP for release for consultation 19 November 2009 End of consultation (deadline for comments)31 May 2010 Agreed by Pharmacokinetics Working Party (PKWP)June 2011 Adoption by CHMP21 July 2011 Date for coming into effect1 February 2012Keywords CHMP, EMEA, Guideline, validation, bioanalytical method, analysesGuideline on bioanalytical method validationTable of contents1. Introduction (background) (3)2. Scope (3)3. Legal basis (3)4. Method validation (4)4.1. Full validation of an analytical method (4)4.1.1. Selectivity (5)4.1.2. Carry-over (5)4.1.3. Lower limit of quantification (6)4.1.4. Calibration curve (6)4.1.5. Accuracy (7)4.1.6. Precision (7)4.1.7. Dilution integrity (8)4.1.8. Matrix effect (8)4.1.9. Stability (9)4.2. Partial validation (10)4.3. Cross validation (10)5. Analysis of study samples (10)5.1. Analytical run (11)5.2. Acceptance criteria of an analytical run (11)5.3. Calibration range (12)5.4. Reanalysis of study samples (12)5.5. Integration (13)6. Incurred samples reanalysis (13)7. Ligand binding assays (14)7.1.1. Full validation (14)7.2. Partial validation and cross-validation (17)7.3. Analysis of study samples (17)7.3.1. Analytical run (17)7.3.2. .Acceptance criteria for study sample analysis (17)7.3.3. Incurred samples reanalysis (18)8. Reports (18)8.1. Validation report (18)8.2. Analytical report (19)Definitions (20)Executive summaryThis guideline defines key elements necessary for the validation of bioanalytical methods. The guideline focuses on the validation of the bioanalytical methods generating quantitative concentration data used for pharmacokinetic and toxicokinetic parameter determinations. Guidance and criteria are given on the application of these validated methods in the routine analysis of study samples from animal and human studies.1. Introduction (background)Measurement of drug concentrations in biological matrices (such as serum, plasma, blood, urine, and saliva) is an important aspect of medicinal product development. Such data may be required to support applications for new actives substances and generics as well as variations to authorised drug products. The results of animal toxicokinetic studies and of clinical trials, including bioequivalence studies are used to make critical decisions supporting the safety and efficacy of a medicinal drug substance or product. It is therefore paramount that the applied bioanalytical methods used are well characterised, fully validated and documented to a satisfactory standard in order to yield reliable results.Acceptance criteria wider than those defined in this guideline may be used in special situations. This should be prospectively defined based on the intended use of the method.2. ScopeThis guideline provides recommendations for the validation of bioanalytical methods applied to measure drug concentrations in biological matrices obtained in animal toxicokinetic studies and all phases of clinical trials. As ligand binding assays differ substantially from chromatographic analytical methods, separate validation recommendations for ligand binding assays are provided.In addition, specific aspects for the analysis of study samples will be addressed.Furthermore, this guideline will describe when partial validation or cross validation should be carried out in addition to the full validation of an analytical method.Methods used for determining quantitative concentrations of biomarkers used in assessing pharmacodynamic endpoints are out of the scope of this guideline.3. Legal basisThis guideline has to be read in conjunction with the introduction and general principles (4) and Part I and II of the Annex I to Directive 2001/83 as amended. It applies to Marketing Authorisation Applications for human medicinal products submitted in accordance with the Directive 2001/83/EC as amended, and Regulation (EC) No. 726/2004, in which the analysis of drug concentrations in a biological matrix is part of the application.The validation of bioanalytical methods and the analysis of study samples for clinical trials in humans should be performed following the principles of Good Clinical Practice (GCP). Further guidance that will help clinical laboratories develop and maintain quality systems which will comply with relevant European Union Directives, national regulations and associated guidance documents can be found in the “Reflection Paper for Laboratories That Perform The Analysis Or Evaluation Of Clinical Trial Samples.” (EMA/INS/GCP/532137/2010).Non-clinical (pharmaco-toxicological) studies submitted in a marketing authorisation application shall be carried out in conformity with the provisions related to Good Laboratory Practice, Directive2004/10/EC on the harmonisation of laws, regulations and administrative provisions relating to the application of the principles of good laboratory practice and the verification of their applications for tests on chemical substances and Directive 2004/9/EC on the inspection and verification of good laboratory practice (GLP). Normally, the validation of bioanalytical methods used in non-clinical pharmacotoxicological studies that are carried out in conformity with the provisions related to Good Laboratory Practice should be performed following the Principles of Good Laboratory Practice. Aspects of method validation not performed according to GLP should be clearly identified and their potential impact on the validation status of the method indicated. Methods used in pre-clinical studies not required to be performed to GLP should be fit for purpose but not necessarily developed in a GLP facility.4. Method validation4.1. Full validation of an analytical methodA full method validation should be performed for any analytical method whether new or based upon literature.The main objective of method validation is to demonstrate the reliability of a particular method for the determination of an analyte concentration in a specific biological matrix, such as blood, serum, plasma, urine, or saliva. Moreover, if an anticoagulant is used, validation should be performed using the same anticoagulant as for the study samples. Generally a full validation should be performed for each species and matrix concerned.In some cases, it may be problematic for validation purposes to obtain an identical matrix compared to the matrix of the study samples. A suitable alternative matrix may be used, e.g. synthetically prepared cerebrospinal fluid, if justified.The main characteristics of a bioanalytical method that are essential to ensure the acceptability of the performance and the reliability of analytical results are: selectivity, lower limit of quantification, the response function and calibration range (calibration curve performance), accuracy, precision, matrix effects, stability of the analyte(s) in the biological matrix and stability of the analyte(s) and of the internal standard in the stock and working solutions and in extracts under the entire period of storage and processing conditions.Usually one analyte or drug has to be determined, but on occasions it may be appropriate to measure more than one analyte. This may involve two different drugs, but can also involve a parent drug with its metabolites, or the enantiomers or isomers of a drug. In these cases the principles of validation and analysis apply to all analytes of interest.Reference standardsDuring method validation and analysis of study samples, a blank biological matrix will be spiked with the analyte(s) of interest using solutions of reference standard(s) to prepare calibration standards, quality control samples and stability samples. In addition, suitable internal standard(s) (IS) can be added during sample processing in chromatographic methods.It is important that the quality of the reference standard and IS is ensured, as the quality (purity) may affect the outcome of the analysis, and therefore the outcome of the study data. Therefore the reference standards used during the validation and study sample analysis should be obtained from an authentic and traceable source. Suitable reference standards, include certified standards such ascompendial standards (EPCRS, USP, WHO), commercially available standards, or sufficiently characterised standards prepared in-house or by an external non-commercial organisation. A certificate of analysis is required to ensure purity and provide information on storage conditions, expiration date and batch number of the reference standard.The use of certified standards is not needed for IS, as long as the suitability for use is demonstrated, e.g. lack of analytical interference is shown for the substance itself or any impurities thereof. A certificate of analysis is not required.When mass-spectrometry (MS) detection is used in the bioanalytical method, a stable isotope-labelled IS is recommended to be used whenever possible. However, it is essential that the labelled standard is of the highest isotope purity and that no isotope exchange reaction occurs. The presence of any unlabelled analyte should be checked and if relative amounts of unlabelled analyte are detected the potential influence has to be evaluated during method validation.4.1.1. SelectivityThe analytical method should be able to differentiate the analyte(s) of interest and IS from endogenous components in the matrix or other components in the sample. Selectivity should be proved using at least 6 individual sources of the appropriate blank matrix, which are individually analysed and evaluated for interference. Use of fewer sources is acceptable in case of rare matrices. Normally, absence of interfering components is accepted where the response is less than 20% of the lower limit of quantification for the analyte and 5% for the internal standard.It may also be necessary to investigate the extent of any interference caused by metabolites of the drug(s), interference from degradation products formed during sample preparation, and interference from possible co-administered medications. Co-medications normally used in the subject population studied which may potentially interfere should be taken into account at the stage of method validation, or on a study specific and compound specific base.The possibility of back-conversion of a metabolite into parent analyte during the successive steps of the analysis (including extraction procedures or in the MS source) should also be evaluated, when relevant (i.e. potentially unstable metabolites e.g. acidic metabolites to ester, unstable N-oxides or glucuronide metabolites, lactone-ring structures). The extent of back-conversion should be established and the impact on the study results discussed. It is acknowledged that this evaluation will not be possible early during drug development of a new chemical entity when the metabolism is not yet evaluated. However, it is expected that this issue is taken into account and a partial validation is performed if relevant as further knowledge regarding metabolism of the active substance is gained during drug development.It is recognized that in some cases it is very difficult to obtain the metabolites of interest. Alternatively, back-conversion of a metabolite can be checked by applying incurred sample reanalysis. However, in this case potential back conversion during sample processing cannot be ruled out.4.1.2. Carry-overCarry-over should be addressed and minimised during method development. During validation carry-over should be assessed by injecting blank samples after a high concentration sample or calibration standard at the upper limit of quantification. Carry over in the blank sample following the high concentration standard should not be greater than 20% of the lower limit of quantification (LLOQ; see below) and 5% for the internal standard. If it appears that carry-over is unavoidable, study samples should not be randomised. Specific measures should be considered, tested during the validation andapplied during the analysis of the study samples, so that it does not affect accuracy and precision. This could include the injection of blank samples after samples with an expected high concentration, before the analysis of the next study sample.4.1.3. Lower limit of quantificationThe lower limit of quantification (LLOQ) is the lowest concentration of analyte in a sample which can be quantified reliably, with an acceptable accuracy and precision. The LLOQ is considered being the lowest calibration standard (see Accuracy and Precision). In addition, the analyte signal of the LLOQ sample should be at least 5 times the signal of a blank sample. The LLOQ should be adapted to expected concentrations and to the aim of the study. As an example, for bioequivalence studies the LLOQ should be not higher than 5% of the Cmax, while such a low LLOQ may be not necessary for exploratory pharmacokinetic studies.4.1.4. Calibration curveThe response of the instrument with regard to the concentration of analyte should be known, and should be evaluated over a specified concentration range. The calibration standards should be prepared in the same matrix as the matrix of the intended study samples by spiking the blank matrix with known concentrations of the analyte. There should be one calibration curve for each analyte studied in the method validation and for each analytical run.Ideally, before carrying out the validation of the analytical method it should be known what concentration range is expected. This range should be covered by the calibration curve range, defined by the LLOQ being the lowest calibration standard and the upper limit of quantification (ULOQ), being the highest calibration standard. The range should be established to allow adequate description of the pharmacokinetics of the analyte of interest.A minimum of six calibration concentration levels should be used, in addition to the blank sample (processed matrix sample without analyte and without IS) and a zero sample (processed matrix with IS). Each calibration standard can be analysed in replicate.A relationship which can simply and adequately describe the response of the instrument with regard to the concentration of analyte should be applied. The blank and zero samples should not be taken into consideration to calculate the calibration curve parameters.The calibration curve parameters should be reported (slope and intercept in case of linear fit). In addition, the back calculated concentrations of the calibration standards should be presented together with the calculated mean accuracy values (see definition of Accuracy below). All the available (or acceptable) curves obtained during validation, with a minimum of 3 should be reported.The back calculated concentrations of the calibration standards should be within ±15% of the nominal value, except for the LLOQ for which it should be within ±20%. At least 75% of the calibration standards, with a minimum of six calibration standard levels, must fulfil this criterion. In case replicates are used, the criteria (within ±15% or ±20% for LLOQ) should also be fulfilled for at least 50% of the calibration standards tested per concentration level. In case a calibration standard does not comply with these criteria, this calibration standard sample should be rejected, and the calibration curve without this calibration standard should be re-evaluated, including regression analysis. In case all replicates of the LLOQ or the ULOQ calibration standard are rejected then the batch should be rejected from the validation, the possible source of the failure be determined and the method revised (if necessary). If the next validation batch also fails, then the method should be revised before restarting validation.Although the calibration curve should preferably be prepared using freshly spiked samples, it is allowed to use previously prepared and stored calibration samples, if supported by appropriate stability data.4.1.5. AccuracyThe accuracy of an analytical method describes the closeness of the determined value obtained by the method to the nominal concentration of the analyte (expressed in percentage). Accuracy should be assessed on samples spiked with known amounts of the analyte, the quality control samples (QC samples). The QC samples should be spiked independently from the calibration standards, using separately prepared stock solutions, unless the nominal concentration(s) of the stock solutions have been established.The QC samples are analysed against the calibration curve, and the obtained concentrations are compared with the nominal value. The accuracy should be reported as percent of the nominal value. Accuracy should be evaluated for the values of the QC samples obtained within a single run (the within run accuracy) and in different runs (the between-run accuracy).To enable evaluation of any trends over time within one run, it is recommended to demonstrate accuracy and precision of QC samples over at least one of the runs in a size equivalent to a prospective analytical run of study samples.Within-run accuracyWithin-run accuracy should be determined by analysing in a single run a minimum of 5 samples per level at a minimum of 4 concentration levels which are covering the calibration curve range: the LLOQ, within three times the LLOQ (low QC), around 50% of the calibration curve range (medium QC), and at least at 75% of the upper calibration curve range (high QC). The mean concentration should be within 15% of the nominal values for the QC samples, except for the LLOQ which should be within 20% of the nominal value.Between –run accuracyFor the validation of the between-run accuracy, LLOQ, low, medium and high QC samples from at least three runs analysed on at least two different days should be evaluated. The mean concentration should be within 15% of the nominal values for the QC samples, except for the LLOQ which should be within 20% of the nominal value.Reported method validation data and the determination of accuracy and precision should include all results obtained except those cases where errors are obvious and documented.4.1.6. PrecisionThe precision of the analytical method describes the closeness of repeated individual measures of analyte. Precision is expressed as the coefficient of variation (CV). Precision should be demonstrated for the LLOQ, low, medium and high QC samples, within a single run and between different runs, i.e. using the same runs and data as for the demonstration of accuracy.Within-run precisionFor the validation of the within-run precision, there should be a minimum of five samples per concentration level at LLOQ, low, medium and high QC samples in a single run. The within-run CV value should not exceed 15% for the QC samples, except for the LLOQ which should not exceed 20%.Between –run precisionFor the validation of the between-run precision, LLOQ, low, medium and high QC samples from at least three runs analysed on at least two different days should be evaluated. The between-run CV value should not exceed 15% for the QC samples, except for the LLOQ which should not exceed 20%.4.1.7. Dilution integrityDilution of samples should not affect the accuracy and precision. If applicable, dilution integrity should be demonstrated by spiking the matrix with an analyte concentration above the ULOQ and diluting this sample with blank matrix (at least five determinations per dilution factor). Accuracy and precision should be within the set criteria, i.e. within ±15%. Dilution integrity should cover the dilution applied to the study samples.Evaluation of dilution integrity may be covered by partial validation. Use of another matrix may be acceptable, as long as it has been demonstrated that this does not affect precision and accuracy.4.1.8. Matrix effectMatrix effects should be investigated when using mass spectrometric methods, using at least 6 lots of blank matrix from individual donors. Pooled matrix should not be used.For each analyte and the IS, the matrix factor (MF) should be calculated for each lot of matrix, by calculating the ratio of the peak area in the presence of matrix (measured by analysing blank matrix spiked after extraction with analyte), to the peak area in absence of matrix (pure solution of the analyte). The IS normalised MF should also be calculated by dividing the MF of the analyte by the MF of the IS. The CV of the IS-normalised MF calculated from the 6 lots of matrix should not be greater than 15 %. This determination should be done at a low and at a high level of concentration (maximum of 3 times the LLOQ and close to the ULOQ).If this approach cannot be used, for instance in the case of on-line sample preparation, the variability of the response from lot to lot should be assessed by analysing at least 6 lots of matrix, spiked at a low and at a high level of concentration (maximum of 3 times the LLOQ and close to the ULOQ). The validation report should include the peak areas of the analyte and of the IS and the calculated concentration for each individual sample. The overall CV calculated for the concentration should not be greater than 15 %.If the matrix is difficult to obtain, less than 6 different lots of matrix may be used, but this should be justified. However, matrix effects should still be investigated.If a formulation for injection to be administered to the subjects or animals contains excipients known to be responsible for matrix effects, for instance polyethylene glycol or polysorbate, matrix effects should be studied with matrix containing these excipients, in addition to blank matrix. The matrix used for this evaluation should be obtained from subjects or animals administered the excipient, unless it has been demonstrated that the excipient is not metabolised or transformed in-vivo. The effect of the excipients can be studied by the determination of the MF or by a dilution study of a study sample with a high concentration with blank matrix not containing the excipient.In addition to the normal matrix it is recommended to investigate matrix effects on other samples e.g. haemolysed and hyperlipidaemic plasma samples. If samples from special populations (such as renally or hepatically impaired populations) are to be analysed it is also recommended to study matrix effects using matrix from such populations.4.1.9. StabilityEvaluation of stability should be carried out to ensure that every step taken during sample preparation and sample analysis, as well as the storage conditions used do not affect the concentration of the analyte.Stability should be ensured for every step in the analytical method, meaning that the conditions applied to the stability tests, such as sample matrix, anticoagulant, container materials, storage and analytical conditions should be similar to those used for the actual study samples. Reference to data published in the literature is not considered sufficient.Stability of the analyte in the studied matrix is evaluated using low and high QC samples (blank matrix spiked with analyte at a concentration of a maximum of 3 times the LLOQ and close to the ULOQ) which are analysed immediately after preparation and after the applied storage conditions that are to be evaluated. The QC samples are analysed against a calibration curve, obtained from freshly spiked calibration standards, and the obtained concentrations are compared to the nominal concentrations. The mean concentration at each level should be within ±15% of the nominal concentration.Stability of the stock and working solutions should be tested with an appropriate dilution, taking into consideration the linearity and measuring range of the detector.Stability studies should investigate the different storage conditions over time periods that equal or exceed those applied to the actual study samples.The following stability tests should be evaluated:•stability of the stock solution and working solutions of the analyte and internal standard,•freeze and thaw stability of the analyte in the matrix from freezer storage conditions to room temperature or sample processing temperature,•short term stability of the analyte in matrix at room temperature or sample processing temperature,•long term stability of the analyte in matrix stored in the freezer,In addition the following tests should be performed if applicable:•stability of the processed sample at room temperature or under the storage conditions to be used during the study (dry extract or in the injection phase),•on-instrument/ autosampler stability of the processed sample at injector or autosampler temperature.Regarding the freeze and thaw stability: The QC samples are stored and frozen in the freezer at the intended temperature and thereafter thawed at room or processing temperature. After complete thawing, samples are refrozen again applying the same conditions. At each cycle, samples should be frozen for at least 12 hours before they are thawed. The number of cycles in the freeze-thaw stability should equal or exceed that of the freeze/thaw cycles of study samples.Regarding long term stability of the analyte in matrix stored in the freezer: The QC samples should be stored in the freezer under the same storage conditions and at least for the same duration as the study samples. For small molecules it is considered acceptable to apply a bracketing approach, i.e. in case stability has been proved for instance at -70°C and -20°C, it is not necessary to investigate the stability at temperatures in between. For large molecules (such as peptides and proteins) stability should be studied at each temperature at which study samples will be stored. Study samples may be used in addition to QC samples, but the exclusive use of study samples is not considered sufficient asthe nominal concentrations of those samples is not known. The results of the evaluation of long term stability should be available before the study report is issued.Regarding the stability of stock and working solutions: It is not needed to study the stability at each concentration level of working solutions and a bracketing approach can be used. It is not needed to study the stability of stable-isotope labelled internal standards if it is demonstrated that no isotope exchange reactions occur under the same conditions as the stability of the analyte was demonstrated.In case of a multi-analyte study and specific for bioequivalence studies, attention should be paid to stability of the analytes in the matrix containing all the analytes.Sufficient attention should be paid to the stability of the analyte in the sampled matrix directly after blood sampling of subjects and further preparation before storage, to ensure that the obtained concentrations by the analytical method reflect the concentrations of the analyte in the subject at the moment of sampling. A demonstration of this stability may be needed on a case-by-case basis, depending on the structure of the analyte.4.2. Partial validationIn situations where minor changes are made to an analytical method that has already been validated, a full validation may not be necessary, depending on the nature of the applied changes. Changes for which a partial validation may be needed include transfer of the bioanalytical method to another laboratory, change in equipment, calibration concentration range, limited sample volume, another matrix or species, change in anticoagulant, sample processing procedure, storage conditions etc. All modifications should be reported and the scope of revalidation or partial validation justified.Partial validation can range from as little as the determination of the within-run precision and accuracy, to an almost full validation.4.3. Cross validationWhere data are obtained from different methods within and across studies or when data are obtained within a study from different laboratories, applying the same method, comparison of those data is needed and a cross validation of the applied analytical methods should be carried out. Differences in sample preparation or the use of another analytical method may result in different outcomes between the study sites. Cross validation should be performed in advance of study samples being analysed if possible. For the cross validation, the same set of QC samples or study samples should be analysed by both analytical methods. For QC samples, the obtained mean accuracy by the different methods should be within 15% and may be wider, if justified. For study samples, the difference between the two values obtained should be within 20% of the mean for at least 67% of the repeats. The outcome of the cross validation is critical in determining whether the obtained data are reliable and whether they can be compared and used.5. Analysis of study samplesAfter full validation of the analytical method, analysis of study or subject samples can be carried out. Before start of the analysis of the study samples the performance of the bioanalytical method should have been verified.The study samples, QC samples and calibration standards should be processed in accordance with the validated analytical method to ensure the acceptability of the analytical run.。

硕士学位论文组合体航天器质量特性辨识和自适应姿态控制COMBINED SPACECRAFT MASS PROPERTY IDENTIFICATION AND ADAPTIVE ATTITUDECONTROL马婉玉哈尔滨工业大学2018年6月国内图书分类号：V448.2 学校代码：10213 国际图书分类号：629.7 密级：公开工程硕士学位论文组合体航天器质量特性辨识和自适应姿态控制硕士研究生：马婉玉导师：马广富教授申请学位：工程硕士学科：控制工程所在单位：控制科学与工程系答辩日期：2018年6月授予学位单位：哈尔滨工业大学Classified Index: V448.2U.D.C: 629.7Dissertation for the Master Degree in EngineeringCOMBINED SPACECRAFT MASS PROPERTY IDENTIFICATION AND ADAPTIVE ATTITUDECONTROLCandidate：MA WanyuSupervisor：Prof. MA GuangfuAcademic Degree Applied for：Master of Engineering Speciality：Control Engineering Affiliation：Department of Control Science andEngineeringDate of Defence：June, 2018Degree-Conferring-Institution：Harbin Institute of Technology摘要随着科技的发展，各个国家发展航天技术的力度越来越大，航天任务也变得日益多样复杂，其中在轨服务任务由于其具有极高的学术价值和经济价值已得到国内外学者的广泛关注。

在轨服务航天器在执行任务的过程中，很多情况下会抓捕非合作目标，即质量特性与运动状态均未知的目标航天器，这会为服务航天器的控制系统带来巨大挑战，因此辨识组合体航天器的质量特性是执行控制任务的必要前提。

目录第一部分 (3)第二部分 (12)Letter A (12)Letter B (14)Letter C (15)Letter D (17)Letter E (19)Letter F (20)Letter G (21)Letter H (22)Letter I (23)Letter K (24)Letter L (24)Letter M (26)Letter N (27)Letter O (29)Letter P (29)Letter R (31)Letter S (32)Letter T (35)Letter U (36)Letter W (37)Letter Z (37)第三部分 (37)A (37)B (38)C (38)D (40)E (40)F (41)G (41)H (42)L (42)J (43)L (43)M (43)N (44)O (44)P (44)Q (45)R (46)S (46)U (47)V (48)第一部分[ ] intensity 强度[ ] Regression 回归[ ] Loss function 损失函数[ ] non-convex 非凸函数[ ] neural network 神经网络[ ] supervised learning 监督学习[ ] regression problem 回归问题处理的是连续的问题[ ] classification problem 分类问题处理的问题是离散的而不是连续的回归问题和分类问题的区别应该在于回归问题的结果是连续的，分类问题的结果是离散的。

[ ]discreet value 离散值[ ] support vector machines 支持向量机,用来处理分类算法中输入的维度不单一的情况（甚至输入维度为无穷）[ ] learning theory 学习理论[ ] learning algorithms 学习算法[ ] unsupervised learning 无监督学习[ ] gradient descent 梯度下降[ ] linear regression 线性回归[ ] Neural Network 神经网络[ ] gradient descent 梯度下降监督学习的一种算法，用来拟合的算法[ ] normal equations[ ] linear algebra 线性代数原谅我英语不太好[ ] superscript上标[ ] exponentiation 指数[ ] training set 训练集合[ ] training example 训练样本[ ] hypothesis 假设，用来表示学习算法的输出，叫我们不要太纠结H的意思，因为这只是历史的惯例[ ] LMS algorithm “least mean squares” 最小二乘法算法[ ] batch gradient descent 批量梯度下降，因为每次都会计算最小拟合的方差，所以运算慢[ ] constantly gradient descent 字幕组翻译成“随机梯度下降” 我怎么觉得是“常量梯度下降”也就是梯度下降的运算次数不变，一般比批量梯度下降速度快，但是通常不是那么准确[ ] iterative algorithm 迭代算法[ ] partial derivative 偏导数[ ] contour 等高线[ ] quadratic function 二元函数[ ] locally weighted regression局部加权回归[ ] underfitting欠拟合[ ] overfitting 过拟合[ ] non-parametric learning algorithms 无参数学习算法[ ] parametric learning algorithm 参数学习算法[ ] other[ ] activation 激活值[ ] activation function 激活函数[ ] additive noise 加性噪声[ ] autoencoder 自编码器[ ] Autoencoders 自编码算法[ ] average firing rate 平均激活率[ ] average sum-of-squares error 均方差[ ] backpropagation 后向传播[ ] basis 基[ ] basis feature vectors 特征基向量[50 ] batch gradient ascent 批量梯度上升法[ ] Bayesian regularization method 贝叶斯规则化方法[ ] Bernoulli random variable 伯努利随机变量[ ] bias term 偏置项[ ] binary classfication 二元分类[ ] class labels 类型标记[ ] concatenation 级联[ ] conjugate gradient 共轭梯度[ ] contiguous groups 联通区域[ ] convex optimization software 凸优化软件[ ] convolution 卷积[ ] cost function 代价函数[ ] covariance matrix 协方差矩阵[ ] DC component 直流分量[ ] decorrelation 去相关[ ] degeneracy 退化[ ] demensionality reduction 降维[ ] derivative 导函数[ ] diagonal 对角线[ ] diffusion of gradients 梯度的弥散[ ] eigenvalue 特征值[ ] eigenvector 特征向量[ ] error term 残差[ ] feature matrix 特征矩阵[ ] feature standardization 特征标准化[ ] feedforward architectures 前馈结构算法[ ] feedforward neural network 前馈神经网络[ ] feedforward pass 前馈传导[ ] fine-tuned 微调[ ] first-order feature 一阶特征[ ] forward pass 前向传导[ ] forward propagation 前向传播[ ] Gaussian prior 高斯先验概率[ ] generative model 生成模型[ ] gradient descent 梯度下降[ ] Greedy layer-wise training 逐层贪婪训练方法[ ] grouping matrix 分组矩阵[ ] Hadamard product 阿达马乘积[ ] Hessian matrix Hessian 矩阵[ ] hidden layer 隐含层[ ] hidden units 隐藏神经元[ ] Hierarchical grouping 层次型分组[ ] higher-order features 更高阶特征[ ] highly non-convex optimization problem 高度非凸的优化问题[ ] histogram 直方图[ ] hyperbolic tangent 双曲正切函数[ ] hypothesis 估值，假设[ ] identity activation function 恒等激励函数[ ] IID 独立同分布[ ] illumination 照明[100 ] inactive 抑制[ ] independent component analysis 独立成份分析[ ] input domains 输入域[ ] input layer 输入层[ ] intensity 亮度/灰度[ ] intercept term 截距[ ] KL divergence 相对熵[ ] KL divergence KL分散度[ ] k-Means K-均值[ ] learning rate 学习速率[ ] least squares 最小二乘法[ ] linear correspondence 线性响应[ ] linear superposition 线性叠加[ ] line-search algorithm 线搜索算法[ ] local mean subtraction 局部均值消减[ ] local optima 局部最优解[ ] logistic regression 逻辑回归[ ] loss function 损失函数[ ] low-pass filtering 低通滤波[ ] magnitude 幅值[ ] MAP 极大后验估计[ ] maximum likelihood estimation 极大似然估计[ ] mean 平均值[ ] MFCC Mel 倒频系数[ ] multi-class classification 多元分类[ ] neural networks 神经网络[ ] neuron 神经元[ ] Newton’s method 牛顿法[ ] non-convex function 非凸函数[ ] non-linear feature 非线性特征[ ] norm 范式[ ] norm bounded 有界范数[ ] norm constrained 范数约束[ ] normalization 归一化[ ] numerical roundoff errors 数值舍入误差[ ] numerically checking 数值检验[ ] numerically reliable 数值计算上稳定[ ] object detection 物体检测[ ] objective function 目标函数[ ] off-by-one error 缺位错误[ ] orthogonalization 正交化[ ] output layer 输出层[ ] overall cost function 总体代价函数[ ] over-complete basis 超完备基[ ] over-fitting 过拟合[ ] parts of objects 目标的部件[ ] part-whole decompostion 部分-整体分解[ ] PCA 主元分析[ ] penalty term 惩罚因子[ ] per-example mean subtraction 逐样本均值消减[150 ] pooling 池化[ ] pretrain 预训练[ ] principal components analysis 主成份分析[ ] quadratic constraints 二次约束[ ] RBMs 受限Boltzman机[ ] reconstruction based models 基于重构的模型[ ] reconstruction cost 重建代价[ ] reconstruction term 重构项[ ] redundant 冗余[ ] reflection matrix 反射矩阵[ ] regularization 正则化[ ] regularization term 正则化项[ ] rescaling 缩放[ ] robust 鲁棒性[ ] run 行程[ ] second-order feature 二阶特征[ ] sigmoid activation function S型激励函数[ ] significant digits 有效数字[ ] singular value 奇异值[ ] singular vector 奇异向量[ ] smoothed L1 penalty 平滑的L1范数惩罚[ ] Smoothed topographic L1 sparsity penalty 平滑地形L1稀疏惩罚函数[ ] smoothing 平滑[ ] Softmax Regresson Softmax回归[ ] sorted in decreasing order 降序排列[ ] source features 源特征[ ] sparse autoencoder 消减归一化[ ] Sparsity 稀疏性[ ] sparsity parameter 稀疏性参数[ ] sparsity penalty 稀疏惩罚[ ] square function 平方函数[ ] squared-error 方差[ ] stationary 平稳性（不变性）[ ] stationary stochastic process 平稳随机过程[ ] step-size 步长值[ ] supervised learning 监督学习[ ] symmetric positive semi-definite matrix 对称半正定矩阵[ ] symmetry breaking 对称失效[ ] tanh function 双曲正切函数[ ] the average activation 平均活跃度[ ] the derivative checking method 梯度验证方法[ ] the empirical distribution 经验分布函数[ ] the energy function 能量函数[ ] the Lagrange dual 拉格朗日对偶函数[ ] the log likelihood 对数似然函数[ ] the pixel intensity value 像素灰度值[ ] the rate of convergence 收敛速度[ ] topographic cost term 拓扑代价项[ ] topographic ordered 拓扑秩序[ ] transformation 变换[200 ] translation invariant 平移不变性[ ] trivial answer 平凡解[ ] under-complete basis 不完备基[ ] unrolling 组合扩展[ ] unsupervised learning 无监督学习[ ] variance 方差[ ] vecotrized implementation 向量化实现[ ] vectorization 矢量化[ ] visual cortex 视觉皮层[ ] weight decay 权重衰减[ ] weighted average 加权平均值[ ] whitening 白化[ ] zero-mean 均值为零第二部分Letter A[ ] Accumulated error backpropagation 累积误差逆传播[ ] Activation Function 激活函数[ ] Adaptive Resonance Theory/ART 自适应谐振理论[ ] Addictive model 加性学习[ ] Adversarial Networks 对抗网络[ ] Affine Layer 仿射层[ ] Affinity matrix 亲和矩阵[ ] Agent 代理/ 智能体[ ] Algorithm 算法[ ] Alpha-beta pruning α-β剪枝[ ] Anomaly detection 异常检测[ ] Approximation 近似[ ] Area Under ROC Curve／AUC Roc 曲线下面积[ ] Artificial General Intelligence/AGI 通用人工智能[ ] Artificial Intelligence/AI 人工智能[ ] Association analysis 关联分析[ ] Attention mechanism 注意力机制[ ] Attribute conditional independence assumption 属性条件独立性假设[ ] Attribute space 属性空间[ ] Attribute value 属性值[ ] Autoencoder 自编码器[ ] Automatic speech recognition 自动语音识别[ ] Automatic summarization 自动摘要[ ] Average gradient 平均梯度[ ] Average-Pooling 平均池化Letter B[ ] Backpropagation Through Time 通过时间的反向传播[ ] Backpropagation/BP 反向传播[ ] Base learner 基学习器[ ] Base learning algorithm 基学习算法[ ] Batch Normalization/BN 批量归一化[ ] Bayes decision rule 贝叶斯判定准则[250 ] Bayes Model Averaging／BMA 贝叶斯模型平均[ ] Bayes optimal classifier 贝叶斯最优分类器[ ] Bayesian decision theory 贝叶斯决策论[ ] Bayesian network 贝叶斯网络[ ] Between-class scatter matrix 类间散度矩阵[ ] Bias 偏置/ 偏差[ ] Bias-variance decomposition 偏差-方差分解[ ] Bias-Variance Dilemma 偏差–方差困境[ ] Bi-directional Long-Short Term Memory/Bi-LSTM 双向长短期记忆[ ] Binary classification 二分类[ ] Binomial test 二项检验[ ] Bi-partition 二分法[ ] Boltzmann machine 玻尔兹曼机[ ] Bootstrap sampling 自助采样法／可重复采样／有放回采样[ ] Bootstrapping 自助法[ ] Break-Event Point／BEP 平衡点Letter C[ ] Calibration 校准[ ] Cascade-Correlation 级联相关[ ] Categorical attribute 离散属性[ ] Class-conditional probability 类条件概率[ ] Classification and regression tree/CART 分类与回归树[ ] Classifier 分类器[ ] Class-imbalance 类别不平衡[ ] Closed -form 闭式[ ] Cluster 簇/类/集群[ ] Cluster analysis 聚类分析[ ] Clustering 聚类[ ] Clustering ensemble 聚类集成[ ] Co-adapting 共适应[ ] Coding matrix 编码矩阵[ ] COLT 国际学习理论会议[ ] Committee-based learning 基于委员会的学习[ ] Competitive learning 竞争型学习[ ] Component learner 组件学习器[ ] Comprehensibility 可解释性[ ] Computation Cost 计算成本[ ] Computational Linguistics 计算语言学[ ] Computer vision 计算机视觉[ ] Concept drift 概念漂移[ ] Concept Learning System /CLS 概念学习系统[ ] Conditional entropy 条件熵[ ] Conditional mutual information 条件互信息[ ] Conditional Probability Table／CPT 条件概率表[ ] Conditional random field/CRF 条件随机场[ ] Conditional risk 条件风险[ ] Confidence 置信度[ ] Confusion matrix 混淆矩阵[300 ] Connection weight 连接权[ ] Connectionism 连结主义[ ] Consistency 一致性／相合性[ ] Contingency table 列联表[ ] Continuous attribute 连续属性[ ] Convergence 收敛[ ] Conversational agent 会话智能体[ ] Convex quadratic programming 凸二次规划[ ] Convexity 凸性[ ] Convolutional neural network/CNN 卷积神经网络[ ] Co-occurrence 同现[ ] Correlation coefficient 相关系数[ ] Cosine similarity 余弦相似度[ ] Cost curve 成本曲线[ ] Cost Function 成本函数[ ] Cost matrix 成本矩阵[ ] Cost-sensitive 成本敏感[ ] Cross entropy 交叉熵[ ] Cross validation 交叉验证[ ] Crowdsourcing 众包[ ] Curse of dimensionality 维数灾难[ ] Cut point 截断点[ ] Cutting plane algorithm 割平面法Letter D[ ] Data mining 数据挖掘[ ] Data set 数据集[ ] Decision Boundary 决策边界[ ] Decision stump 决策树桩[ ] Decision tree 决策树／判定树[ ] Deduction 演绎[ ] Deep Belief Network 深度信念网络[ ] Deep Convolutional Generative Adversarial Network/DCGAN 深度卷积生成对抗网络[ ] Deep learning 深度学习[ ] Deep neural network/DNN 深度神经网络[ ] Deep Q-Learning 深度Q 学习[ ] Deep Q-Network 深度Q 网络[ ] Density estimation 密度估计[ ] Density-based clustering 密度聚类[ ] Differentiable neural computer 可微分神经计算机[ ] Dimensionality reduction algorithm 降维算法[ ] Directed edge 有向边[ ] Disagreement measure 不合度量[ ] Discriminative model 判别模型[ ] Discriminator 判别器[ ] Distance measure 距离度量[ ] Distance metric learning 距离度量学习[ ] Distribution 分布[ ] Divergence 散度[350 ] Diversity measure 多样性度量／差异性度量[ ] Domain adaption 领域自适应[ ] Downsampling 下采样[ ] D-separation （Directed separation）有向分离[ ] Dual problem 对偶问题[ ] Dummy node 哑结点[ ] Dynamic Fusion 动态融合[ ] Dynamic programming 动态规划Letter E[ ] Eigenvalue decomposition 特征值分解[ ] Embedding 嵌入[ ] Emotional analysis 情绪分析[ ] Empirical conditional entropy 经验条件熵[ ] Empirical entropy 经验熵[ ] Empirical error 经验误差[ ] Empirical risk 经验风险[ ] End-to-End 端到端[ ] Energy-based model 基于能量的模型[ ] Ensemble learning 集成学习[ ] Ensemble pruning 集成修剪[ ] Error Correcting Output Codes／ECOC 纠错输出码[ ] Error rate 错误率[ ] Error-ambiguity decomposition 误差-分歧分解[ ] Euclidean distance 欧氏距离[ ] Evolutionary computation 演化计算[ ] Expectation-Maximization 期望最大化[ ] Expected loss 期望损失[ ] Exploding Gradient Problem 梯度爆炸问题[ ] Exponential loss function 指数损失函数[ ] Extreme Learning Machine/ELM 超限学习机Letter F[ ] Factorization 因子分解[ ] False negative 假负类[ ] False positive 假正类[ ] False Positive Rate/FPR 假正例率[ ] Feature engineering 特征工程[ ] Feature selection 特征选择[ ] Feature vector 特征向量[ ] Featured Learning 特征学习[ ] Feedforward Neural Networks/FNN 前馈神经网络[ ] Fine-tuning 微调[ ] Flipping output 翻转法[ ] Fluctuation 震荡[ ] Forward stagewise algorithm 前向分步算法[ ] Frequentist 频率主义学派[ ] Full-rank matrix 满秩矩阵[400 ] Functional neuron 功能神经元Letter G[ ] Gain ratio 增益率[ ] Game theory 博弈论[ ] Gaussian kernel function 高斯核函数[ ] Gaussian Mixture Model 高斯混合模型[ ] General Problem Solving 通用问题求解[ ] Generalization 泛化[ ] Generalization error 泛化误差[ ] Generalization error bound 泛化误差上界[ ] Generalized Lagrange function 广义拉格朗日函数[ ] Generalized linear model 广义线性模型[ ] Generalized Rayleigh quotient 广义瑞利商[ ] Generative Adversarial Networks/GAN 生成对抗网络[ ] Generative Model 生成模型[ ] Generator 生成器[ ] Genetic Algorithm/GA 遗传算法[ ] Gibbs sampling 吉布斯采样[ ] Gini index 基尼指数[ ] Global minimum 全局最小[ ] Global Optimization 全局优化[ ] Gradient boosting 梯度提升[ ] Gradient Descent 梯度下降[ ] Graph theory 图论[ ] Ground-truth 真相／真实Letter H[ ] Hard margin 硬间隔[ ] Hard voting 硬投票[ ] Harmonic mean 调和平均[ ] Hesse matrix 海塞矩阵[ ] Hidden dynamic model 隐动态模型[ ] Hidden layer 隐藏层[ ] Hidden Markov Model/HMM 隐马尔可夫模型[ ] Hierarchical clustering 层次聚类[ ] Hilbert space 希尔伯特空间[ ] Hinge loss function 合页损失函数[ ] Hold-out 留出法[ ] Homogeneous 同质[ ] Hybrid computing 混合计算[ ] Hyperparameter 超参数[ ] Hypothesis 假设[ ] Hypothesis test 假设验证Letter I[ ] ICML 国际机器学习会议[450 ] Improved iterative scaling/IIS 改进的迭代尺度法[ ] Incremental learning 增量学习[ ] Independent and identically distributed/i.i.d. 独立同分布[ ] Independent Component Analysis/ICA 独立成分分析[ ] Indicator function 指示函数[ ] Individual learner 个体学习器[ ] Induction 归纳[ ] Inductive bias 归纳偏好[ ] Inductive learning 归纳学习[ ] Inductive Logic Programming／ILP 归纳逻辑程序设计[ ] Information entropy 信息熵[ ] Information gain 信息增益[ ] Input layer 输入层[ ] Insensitive loss 不敏感损失[ ] Inter-cluster similarity 簇间相似度[ ] International Conference for Machine Learning/ICML 国际机器学习大会[ ] Intra-cluster similarity 簇内相似度[ ] Intrinsic value 固有值[ ] Isometric Mapping/Isomap 等度量映射[ ] Isotonic regression 等分回归[ ] Iterative Dichotomiser 迭代二分器Letter K[ ] Kernel method 核方法[ ] Kernel trick 核技巧[ ] Kernelized Linear Discriminant Analysis／KLDA 核线性判别分析[ ] K-fold cross validation k 折交叉验证／k 倍交叉验证[ ] K-Means Clustering K –均值聚类[ ] K-Nearest Neighbours Algorithm/KNN K近邻算法[ ] Knowledge base 知识库[ ] Knowledge Representation 知识表征Letter L[ ] Label space 标记空间[ ] Lagrange duality 拉格朗日对偶性[ ] Lagrange multiplier 拉格朗日乘子[ ] Laplace smoothing 拉普拉斯平滑[ ] Laplacian correction 拉普拉斯修正[ ] Latent Dirichlet Allocation 隐狄利克雷分布[ ] Latent semantic analysis 潜在语义分析[ ] Latent variable 隐变量[ ] Lazy learning 懒惰学习[ ] Learner 学习器[ ] Learning by analogy 类比学习[ ] Learning rate 学习率[ ] Learning Vector Quantization/LVQ 学习向量量化[ ] Least squares regression tree 最小二乘回归树[ ] Leave-One-Out/LOO 留一法[500 ] linear chain conditional random field 线性链条件随机场[ ] Linear Discriminant Analysis／LDA 线性判别分析[ ] Linear model 线性模型[ ] Linear Regression 线性回归[ ] Link function 联系函数[ ] Local Markov property 局部马尔可夫性[ ] Local minimum 局部最小[ ] Log likelihood 对数似然[ ] Log odds／logit 对数几率[ ] Logistic Regression Logistic 回归[ ] Log-likelihood 对数似然[ ] Log-linear regression 对数线性回归[ ] Long-Short Term Memory/LSTM 长短期记忆[ ] Loss function 损失函数Letter M[ ] Machine translation/MT 机器翻译[ ] Macron-P 宏查准率[ ] Macron-R 宏查全率[ ] Majority voting 绝对多数投票法[ ] Manifold assumption 流形假设[ ] Manifold learning 流形学习[ ] Margin theory 间隔理论[ ] Marginal distribution 边际分布[ ] Marginal independence 边际独立性[ ] Marginalization 边际化[ ] Markov Chain Monte Carlo/MCMC 马尔可夫链蒙特卡罗方法[ ] Markov Random Field 马尔可夫随机场[ ] Maximal clique 最大团[ ] Maximum Likelihood Estimation/MLE 极大似然估计／极大似然法[ ] Maximum margin 最大间隔[ ] Maximum weighted spanning tree 最大带权生成树[ ] Max-Pooling 最大池化[ ] Mean squared error 均方误差[ ] Meta-learner 元学习器[ ] Metric learning 度量学习[ ] Micro-P 微查准率[ ] Micro-R 微查全率[ ] Minimal Description Length/MDL 最小描述长度[ ] Minimax game 极小极大博弈[ ] Misclassification cost 误分类成本[ ] Mixture of experts 混合专家[ ] Momentum 动量[ ] Moral graph 道德图／端正图[ ] Multi-class classification 多分类[ ] Multi-document summarization 多文档摘要[ ] Multi-layer feedforward neural networks 多层前馈神经网络[ ] Multilayer Perceptron/MLP 多层感知器[ ] Multimodal learning 多模态学习[550 ] Multiple Dimensional Scaling 多维缩放[ ] Multiple linear regression 多元线性回归[ ] Multi-response Linear Regression ／MLR 多响应线性回归[ ] Mutual information 互信息Letter N[ ] Naive bayes 朴素贝叶斯[ ] Naive Bayes Classifier 朴素贝叶斯分类器[ ] Named entity recognition 命名实体识别[ ] Nash equilibrium 纳什均衡[ ] Natural language generation/NLG 自然语言生成[ ] Natural language processing 自然语言处理[ ] Negative class 负类[ ] Negative correlation 负相关法[ ] Negative Log Likelihood 负对数似然[ ] Neighbourhood Component Analysis/NCA 近邻成分分析[ ] Neural Machine Translation 神经机器翻译[ ] Neural Turing Machine 神经图灵机[ ] Newton method 牛顿法[ ] NIPS 国际神经信息处理系统会议[ ] No Free Lunch Theorem／NFL 没有免费的午餐定理[ ] Noise-contrastive estimation 噪音对比估计[ ] Nominal attribute 列名属性[ ] Non-convex optimization 非凸优化[ ] Nonlinear model 非线性模型[ ] Non-metric distance 非度量距离[ ] Non-negative matrix factorization 非负矩阵分解[ ] Non-ordinal attribute 无序属性[ ] Non-Saturating Game 非饱和博弈[ ] Norm 范数[ ] Normalization 归一化[ ] Nuclear norm 核范数[ ] Numerical attribute 数值属性Letter O[ ] Objective function 目标函数[ ] Oblique decision tree 斜决策树[ ] Occam’s razor 奥卡姆剃刀[ ] Odds 几率[ ] Off-Policy 离策略[ ] One shot learning 一次性学习[ ] One-Dependent Estimator／ODE 独依赖估计[ ] On-Policy 在策略[ ] Ordinal attribute 有序属性[ ] Out-of-bag estimate 包外估计[ ] Output layer 输出层[ ] Output smearing 输出调制法[ ] Overfitting 过拟合／过配[600 ] Oversampling 过采样Letter P[ ] Paired t-test 成对t 检验[ ] Pairwise 成对型[ ] Pairwise Markov property 成对马尔可夫性[ ] Parameter 参数[ ] Parameter estimation 参数估计[ ] Parameter tuning 调参[ ] Parse tree 解析树[ ] Particle Swarm Optimization/PSO 粒子群优化算法[ ] Part-of-speech tagging 词性标注[ ] Perceptron 感知机[ ] Performance measure 性能度量[ ] Plug and Play Generative Network 即插即用生成网络[ ] Plurality voting 相对多数投票法[ ] Polarity detection 极性检测[ ] Polynomial kernel function 多项式核函数[ ] Pooling 池化[ ] Positive class 正类[ ] Positive definite matrix 正定矩阵[ ] Post-hoc test 后续检验[ ] Post-pruning 后剪枝[ ] potential function 势函数[ ] Precision 查准率／准确率[ ] Prepruning 预剪枝[ ] Principal component analysis/PCA 主成分分析[ ] Principle of multiple explanations 多释原则[ ] Prior 先验[ ] Probability Graphical Model 概率图模型[ ] Proximal Gradient Descent/PGD 近端梯度下降[ ] Pruning 剪枝[ ] Pseudo-label 伪标记[ ] Letter Q[ ] Quantized Neural Network 量子化神经网络[ ] Quantum computer 量子计算机[ ] Quantum Computing 量子计算[ ] Quasi Newton method 拟牛顿法Letter R[ ] Radial Basis Function／RBF 径向基函数[ ] Random Forest Algorithm 随机森林算法[ ] Random walk 随机漫步[ ] Recall 查全率／召回率[ ] Receiver Operating Characteristic/ROC 受试者工作特征[ ] Rectified Linear Unit/ReLU 线性修正单元[650 ] Recurrent Neural Network 循环神经网络[ ] Recursive neural network 递归神经网络[ ] Reference model 参考模型[ ] Regression 回归[ ] Regularization 正则化[ ] Reinforcement learning/RL 强化学习[ ] Representation learning 表征学习[ ] Representer theorem 表示定理[ ] reproducing kernel Hilbert space/RKHS 再生核希尔伯特空间[ ] Re-sampling 重采样法[ ] Rescaling 再缩放[ ] Residual Mapping 残差映射[ ] Residual Network 残差网络[ ] Restricted Boltzmann Machine/RBM 受限玻尔兹曼机[ ] Restricted Isometry Property/RIP 限定等距性[ ] Re-weighting 重赋权法[ ] Robustness 稳健性/鲁棒性[ ] Root node 根结点[ ] Rule Engine 规则引擎[ ] Rule learning 规则学习Letter S[ ] Saddle point 鞍点[ ] Sample space 样本空间[ ] Sampling 采样[ ] Score function 评分函数[ ] Self-Driving 自动驾驶[ ] Self-Organizing Map／SOM 自组织映射[ ] Semi-naive Bayes classifiers 半朴素贝叶斯分类器[ ] Semi-Supervised Learning 半监督学习[ ] semi-Supervised Support Vector Machine 半监督支持向量机[ ] Sentiment analysis 情感分析[ ] Separating hyperplane 分离超平面[ ] Sigmoid function Sigmoid 函数[ ] Similarity measure 相似度度量[ ] Simulated annealing 模拟退火[ ] Simultaneous localization and mapping 同步定位与地图构建[ ] Singular Value Decomposition 奇异值分解[ ] Slack variables 松弛变量[ ] Smoothing 平滑[ ] Soft margin 软间隔[ ] Soft margin maximization 软间隔最大化[ ] Soft voting 软投票[ ] Sparse representation 稀疏表征[ ] Sparsity 稀疏性[ ] Specialization 特化[ ] Spectral Clustering 谱聚类[ ] Speech Recognition 语音识别[ ] Splitting variable 切分变量[700 ] Squashing function 挤压函数[ ] Stability-plasticity dilemma 可塑性-稳定性困境[ ] Statistical learning 统计学习[ ] Status feature function 状态特征函[ ] Stochastic gradient descent 随机梯度下降[ ] Stratified sampling 分层采样[ ] Structural risk 结构风险[ ] Structural risk minimization/SRM 结构风险最小化[ ] Subspace 子空间[ ] Supervised learning 监督学习／有导师学习[ ] support vector expansion 支持向量展式[ ] Support Vector Machine/SVM 支持向量机[ ] Surrogat loss 替代损失[ ] Surrogate function 替代函数[ ] Symbolic learning 符号学习[ ] Symbolism 符号主义[ ] Synset 同义词集Letter T[ ] T-Distribution Stochastic Neighbour Embedding/t-SNE T –分布随机近邻嵌入[ ] Tensor 张量[ ] Tensor Processing Units/TPU 张量处理单元[ ] The least square method 最小二乘法[ ] Threshold 阈值[ ] Threshold logic unit 阈值逻辑单元[ ] Threshold-moving 阈值移动[ ] Time Step 时间步骤[ ] Tokenization 标记化[ ] Training error 训练误差[ ] Training instance 训练示例／训练例[ ] Transductive learning 直推学习[ ] Transfer learning 迁移学习[ ] Treebank 树库[ ] Tria-by-error 试错法[ ] True negative 真负类[ ] True positive 真正类[ ] True Positive Rate/TPR 真正例率[ ] Turing Machine 图灵机[ ] Twice-learning 二次学习Letter U[ ] Underfitting 欠拟合／欠配[ ] Undersampling 欠采样[ ] Understandability 可理解性[ ] Unequal cost 非均等代价[ ] Unit-step function 单位阶跃函数[ ] Univariate decision tree 单变量决策树[ ] Unsupervised learning 无监督学习／无导师学习[ ] Unsupervised layer-wise training 无监督逐层训练[ ] Upsampling 上采样Letter V[ ] Vanishing Gradient Problem 梯度消失问题[ ] Variational inference 变分推断[ ] VC Theory VC维理论[ ] Version space 版本空间[ ] Viterbi algorithm 维特比算法[760 ] Von Neumann architecture 冯· 诺伊曼架构Letter W[ ] Wasserstein GAN/WGAN Wasserstein生成对抗网络[ ] Weak learner 弱学习器[ ] Weight 权重[ ] Weight sharing 权共享[ ] Weighted voting 加权投票法[ ] Within-class scatter matrix 类内散度矩阵[ ] Word embedding 词嵌入[ ] Word sense disambiguation 词义消歧Letter Z[ ] Zero-data learning 零数据学习[ ] Zero-shot learning 零次学习第三部分A[ ] approximations近似值[ ] arbitrary随意的[ ] affine仿射的[ ] arbitrary任意的[ ] amino acid氨基酸[ ] amenable经得起检验的[ ] axiom公理，原则[ ] abstract提取[ ] architecture架构，体系结构；建造业[ ] absolute绝对的[ ] arsenal军火库[ ] assignment分配[ ] algebra线性代数[ ] asymptotically无症状的[ ] appropriate恰当的B[ ] bias偏差[ ] brevity简短，简洁；短暂[800 ] broader广泛[ ] briefly简短的[ ] batch批量C[ ] convergence 收敛，集中到一点[ ] convex凸的[ ] contours轮廓[ ] constraint约束[ ] constant常理[ ] commercial商务的[ ] complementarity补充[ ] coordinate ascent同等级上升[ ] clipping剪下物；剪报；修剪[ ] component分量；部件[ ] continuous连续的[ ] covariance协方差[ ] canonical正规的，正则的[ ] concave非凸的[ ] corresponds相符合；相当；通信[ ] corollary推论[ ] concrete具体的事物，实在的东西[ ] cross validation交叉验证[ ] correlation相互关系[ ] convention约定[ ] cluster一簇[ ] centroids 质心，形心[ ] converge收敛[ ] computationally计算(机)的[ ] calculus计算D[ ] derive获得，取得[ ] dual二元的[ ] duality二元性；二象性；对偶性[ ] derivation求导；得到；起源[ ] denote预示，表示，是…的标志；意味着，[逻]指称[ ] divergence 散度；发散性[ ] dimension尺度，规格；维数[ ] dot小圆点[ ] distortion变形[ ] density概率密度函数[ ] discrete离散的[ ] discriminative有识别能力的[ ] diagonal对角[ ] dispersion分散，散开[ ] determinant决定因素[849 ] disjoint不相交的E[ ] encounter遇到[ ] ellipses椭圆[ ] equality等式[ ] extra额外的[ ] empirical经验；观察[ ] ennmerate例举，计数[ ] exceed超过，越出[ ] expectation期望[ ] efficient生效的[ ] endow赋予[ ] explicitly清楚的[ ] exponential family指数家族[ ] equivalently等价的F[ ] feasible可行的[ ] forary初次尝试[ ] finite有限的，限定的[ ] forgo摒弃，放弃[ ] fliter过滤[ ] frequentist最常发生的[ ] forward search前向式搜索[ ] formalize使定形G[ ] generalized归纳的[ ] generalization概括，归纳；普遍化；判断（根据不足）[ ] guarantee保证；抵押品[ ] generate形成，产生[ ] geometric margins几何边界[ ] gap裂口[ ] generative生产的；有生产力的H[ ] heuristic启发式的；启发法；启发程序[ ] hone怀恋；磨[ ] hyperplane超平面L[ ] initial最初的[ ] implement执行[ ] intuitive凭直觉获知的[ ] incremental增加的[900 ] intercept截距[ ] intuitious直觉[ ] instantiation例子[ ] indicator指示物，指示器[ ] interative重复的，迭代的[ ] integral积分[ ] identical相等的；完全相同的[ ] indicate表示，指出[ ] invariance不变性，恒定性[ ] impose把…强加于[ ] intermediate中间的[ ] interpretation解释，翻译J[ ] joint distribution联合概率L[ ] lieu替代[ ] logarithmic对数的，用对数表示的[ ] latent潜在的[ ] Leave-one-out cross validation留一法交叉验证M[ ] magnitude巨大[ ] mapping绘图，制图；映射[ ] matrix矩阵[ ] mutual相互的，共同的[ ] monotonically单调的[ ] minor较小的，次要的[ ] multinomial多项的[ ] multi-class classification二分类问题N[ ] nasty讨厌的[ ] notation标志，注释[ ] naïve朴素的O[ ] obtain得到[ ] oscillate摆动[ ] optimization problem最优化问题[ ] objective function目标函数[ ] optimal最理想的[ ] orthogonal(矢量，矩阵等)正交的[ ] orientation方向[ ] ordinary普通的[ ] occasionally偶然的P[ ] partial derivative偏导数[ ] property性质[ ] proportional成比例的[ ] primal原始的，最初的[ ] permit允许[ ] pseudocode伪代码[ ] permissible可允许的[ ] polynomial多项式[ ] preliminary预备[ ] precision精度[ ] perturbation 不安，扰乱[ ] poist假定，设想[ ] positive semi-definite半正定的[ ] parentheses圆括号[ ] posterior probability后验概率[ ] plementarity补充[ ] pictorially图像的[ ] parameterize确定…的参数[ ] poisson distribution柏松分布[ ] pertinent相关的Q[ ] quadratic二次的[ ] quantity量，数量；分量[ ] query疑问的R[ ] regularization使系统化；调整[ ] reoptimize重新优化[ ] restrict限制；限定；约束[ ] reminiscent回忆往事的；提醒的；使人联想…的（of）[ ] remark注意[ ] random variable随机变量[ ] respect考虑[ ] respectively各自的；分别的[ ] redundant过多的；冗余的S[ ] susceptible敏感的[ ] stochastic可能的；随机的[ ] symmetric对称的[ ] sophisticated复杂的[ ] spurious假的；伪造的[ ] subtract减去；减法器[ ] simultaneously同时发生地；同步地[ ] suffice满足[ ] scarce稀有的，难得的[ ] split分解，分离[ ] subset子集[ ] statistic统计量[ ] successive iteratious连续的迭代[ ] scale标度[ ] sort of有几分的[ ] squares平方T[ ] trajectory轨迹[ ] temporarily暂时的[ ] terminology专用名词[ ] tolerance容忍；公差[ ] thumb翻阅[ ] threshold阈，临界[ ] theorem定理[ ] tangent正弦U[ ] unit-length vector单位向量V[ ] valid有效的，正确的[ ] variance方差[ ] variable变量；变元[ ] vocabulary词汇[ ] valued经估价的；宝贵的[ ] W [1038 ] wrapper包装。

厄米多项式正交归一证明在数学中，厄米多项式指的是一种正交多项式，其定义为：H_n(x) = (-1)^n e^(x^2) (d^n/dx^n) e^(-x^2)其中，d^n/dx^n表示对x求n阶导数。

厄米多项式的正交归一条件可以表示为：∫_{-∞}^{∞} H_n(x) H_m(x) e^(-x^2) dx = √π 2^n n! δ_{nm}其中，∫表示积分，δ_{nm}表示Kronecker delta符号，即当n=m时，δ_{nm}=1，否则δ_{nm}=0。

该条件表明厄米多项式是在权函数为e^(-x^2)的情况下正交归一的。

厄米多项式的正交归一条件可以通过数学归纳法进行证明。

首先，当n=m时，有：∫_{-∞}^{∞} H_n(x) H_m(x) e^(-x^2) dx = ∫_{-∞}^{∞} H_n(x)^2 e^(-x^2) dx由于H_n(x)的定义中包含了e^(-x^2)，因此可以使用Leibniz公式对其进行求导，得到：d/dx (e^(x^2) H_n(x)) = 2x e^(x^2) H_n(x) - e^(x^2)H_n-1(x)因此，有：x H_n(x) = 1/2 (H_n+1(x) - H_n-1(x))将其代入上式中，可得：∫_{-∞}^{∞} H_n(x)^2 e^(-x^2) dx = √π 2^n n!接下来，假设当n=m-1时，上述条件成立。

则有：∫_{-∞}^{∞} H_n(x) H_m(x) e^(-x^2) dx = 0因此，有：∫_{-∞}^{∞} H_n(x) H_m(x+2x) e^(-x^2) dx = 0使用Leibniz公式，可得：H_m(x+2x) = 2m H_m-1(x) - 2x H_m-1(x)因此，有：∫_{-∞}^{∞} H_n(x) H_m(x+2x) e^(-x^2) dx = 2m ∫_{-∞}^{∞} H_n(x) H_m-1(x) e^(-x^2) dx根据归纳假设，可知∫_{-∞}^{∞} H_n(x) H_m-1(x) e^(-x^2) dx = 0 (当n<m-1时)，∫_{-∞}^{∞} H_n(x) H_m-1(x) e^(-x^2) dx = √π 2^(m-1) (m-1)! (当n=m-1时)。

多元高斯混合模型em算法工况-概述说明以及解释1.引言1.1 概述在编写文章的概述部分时，需要对主题进行简要介绍，并提供相关背景信息。

这里是关于多元高斯混合模型（Gaussian Mixture Model, GMM）及其在工况（engineering conditions）中的应用的概述。

多元高斯混合模型是一种常见的统计模型，它是由多个高斯分布组成的概率密度函数的线性组合。

在实际问题中，很多数据的分布无法被单个高斯分布完全描述，而是由多个高斯分布混合而成。

多元高斯混合模型通过将这些高斯分布加权组合，能够更好地近似复杂数据的分布情况。

EM算法是一种常用于估计多元高斯混合模型参数的迭代算法。

通过EM算法，我们可以根据观测数据来估计出模型中每个高斯分布的均值、协方差和权重等参数，从而得到最优的模型拟合结果。

EM算法的基本思想是通过交替迭代的方式，通过E步骤计算隐变量（即数据来自于哪个高斯分布），再通过M步骤更新模型参数，不断优化模型，直到收敛到最优解。

在工况中，多元高斯混合模型及EM算法的应用非常广泛。

工况通常涉及到多个不同的条件和变量，而且这些条件和变量之间往往存在复杂的关联关系。

通过使用多元高斯混合模型，可以更好地对这些变量的分布进行建模和描述，进而提供更准确的分析和预测结果。

无论是在工程领域的故障诊断、质量控制还是金融领域的风险分析等应用场景中，多元高斯混合模型都发挥着重要的作用。

总而言之，本文将针对多元高斯混合模型及其在工况中的应用展开详细探讨。

通过介绍多元高斯混合模型的基本原理和EM算法的实现方式，以及探讨其在工况中的应用案例，旨在提供一种全面的分析方法和工具，以帮助读者更好地理解和应用该模型解决实际问题。

1.2文章结构文章结构部分的内容可以包括以下内容：本文将从以下几个方面进行论述：多元高斯混合模型、EM算法以及它们在工况中的应用。

首先，我们将介绍多元高斯混合模型的基本概念和原理。

通过对多元高斯分布和混合模型的介绍，读者将了解到多元高斯混合模型在数据建模和聚类分析中的重要性及应用场景。