Modern advances in computing power have greatly widened scientists' scope in gathering and investigating information from many variables, information which might have been ignored in the past. Yet to effectively scan a large pool of variables is not an easy task, although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics. In this article, we propose a novel data-analytic tool, sliced inverse regression (SIR), for reducing the dimension of the input variable x without going through any parametric or nonparametric model-fitting process. This method explores the simplicity of the inverse view of regression; that is, instead of regressing the univariate output variable y against the multivariate x, we regress x against y. Forward regression and inverse regression are connected by a theorem that motivates this method. The theoretical properties of SIR are investigated under a model of the form, y = f(β 1 x, …, β K x, e), where the β k 's are the unknown...

/pdf/sliced-inverse-regression-for-dimension-reduction-rmlfwdlpoe.pdf

Sliced Inverse Regression for Dimension Reduction

Ouvragedestine aux etudiants de 2e cycle Sommaire: METHODES FACTORIELLES: Analyse generale, decomposition aux valeurs singulieres; Analyse en Composantes Principales; Analyse des correspondances; Analyse des correspondances multiples; QUELQUES METHODES DE CLASSIFICATION: Agregation autour des centres mobiles; Classification hierarchique; Classification mixte et description statistique des classes; Complementarite entre analyse factorielle et classificationLIENS AVEC LES METHODES EXPLICATIVES USUELLES, METHODES DERIVEES: Analyse canonique; Regression multiple, modele lineaire; Analyse factorielle discriminante; Modeles log-lineaires; Segmentation; Structures de graphe, analyses locales; Tableaux multiples, groupes de variables VALIDITE ET PORTEE DES RESULTATS: Signification des valeurs propres et des taux d'inertie; Stabilite des axes, des formes, des classes 

/pdf/statistique-exploratoire-multidimensionnelle-4075iaw080.pdf

Statistique exploratoire multidimensionnelle

In this paper (expanded from an invited talk at AISEC 2010), we discuss an emerging field of study: adversarial machine learning---the study of effective machine learning techniques against an adversarial opponent. In this paper, we: give a taxonomy for classifying attacks against online machine learning algorithms; discuss application-specific factors that limit an adversary's capabilities; introduce two models for modeling an adversary's capabilities; explore the limits of an adversary's knowledge about the algorithm, feature space, training, and input data; explore vulnerabilities in machine learning algorithms; discuss countermeasures against attacks; introduce the evasion challenge; and discuss privacy-preserving learning techniques.

/pdf/adversarial-machine-learning-56wpx170q1.pdf

Adversarial machine learning

We introduce a new method for robust principal component analysis (PCA). Classical PCA is based on the empirical covariance matrix of the data and hence is highly sensitive to outlying observations. Two robust approaches have been developed to date. The first approach is based on the eigenvectors of a robust scatter matrix such as the minimum covariance determinant or an S-estimator and is limited to relatively low-dimensional data. The second approach is based on projection pursuit and can handle high-dimensional data. Here we propose the ROBPCA approach, which combines projection pursuit ideas with robust scatter matrix estimation. ROBPCA yields more accurate estimates at noncontaminated datasets and more robust estimates at contaminated data. ROBPCA can be computed rapidly, and is able to detect exact-fit situations. As a by-product, ROBPCA produces a diagnostic plot that displays and classifies the outliers. We apply the algorithm to several datasets from chemometrics and engineering.

ROBPCA: A New Approach to Robust Principal Component Analysis

Prefaces Introduction What Is Computational Statistics? An Overview of the Book Probability Concepts Introduction Probability Conditional Probability and Independence Expectation Common Distributions Sampling Concepts Introduction Sampling Terminology and Concepts Sampling Distributions Parameter Estimation Empirical Distribution Function Generating Random Variables Introduction General Techniques for Generating Random Variables Generating Continuous Random Variables Generating Discrete Random Variables Exploratory Data Analysis Introduction Exploring Univariate Data Exploring Bivariate and Trivariate Data Exploring Multidimensional Data Finding Structure Introduction Projecting Data Principal Component Analysis Projection Pursuit EDA Independent Component Analysis Grand Tour Nonlinear Dimensionality Reduction Monte Carlo Methods for Inferential Statistics Introduction Classical Inferential Statistics Monte Carlo Methods for Inferential Statistics Bootstrap Methods Data Partitioning Introduction Cross-Validation Jackknife Better Bootstrap Confidence Intervals Jackknife-after-Bootstrap Probability Density Estimation Introduction Histograms Kernel Density Estimation Finite Mixtures Generating Random Variables Supervised Learning Introduction Bayes' Decision Theory Evaluating the Classifier Classification Trees Combining Classifiers Unsupervised Learning Introduction Measures of Distance Hierarchical Clustering K-Means Clustering Model-Based Clustering Assessing Cluster Results Parametric Models Introduction Spline Regression Models Logistic Regression Generalized Linear Models Nonparametric models Introduction Some Smoothing Methods Kernel Methods Smoothing Splines Nonparametric Regression-Other Details Regression Trees Additive Models Markov Chain Monte Carlo Methods Introduction Background Metropolis-Hastings Algorithms The Gibbs Sampler Convergence Monitoring Spatial Statistics Introduction Visualizing Spatial Point Processes Exploring First-Order and Second-Order Properties Modeling Spatial Point Processes Simulating Spatial Point Processes Appendix A: Introduction to Matlab What Is MATLAB? Getting Help in MATLAB File and Workspace Management Punctuation in MATLAB Arithmetic Operators Data Constructs in MATLAB Script Files and Functions Control Flow Simple Plotting Contact Information Appendix B: Projection Pursuit Indexes Indexes MATLAB Source Code Appendix C: Matlab Statistics Toolbox Appendix D: Computational Statistics Toolbox Appendix E: Exploratory Data Analysis Toolboxes Introduction EDA Toolbox EDA GUI Toolbox Appendix F: Data Sets Appendix G: NOTATION References INDEX MATLAB Code, Further Reading, and Exercises appear at the end of each chapter.

https://www.jstatsoft.org/article/view/v011b06/v11b06.pdf

Computational Statistics Handbook with MATLAB

This article proposes and discusses a type of new robust estimators for covariance/correlation matrices and principal components via projection-pursuit techniques. The most attractive advantage of the new procedures is that they are of both rotational equivariance and high breakdown point. Besides, they are qualitatively robust and consistent at elliptic underlying distributions. The Monte Carlo study shows that the best of the new estimators compare favorably with other robust methods. They provide as good a performance as M-estimators and somewhat better empirical breakdown properties.

Zhonglian Chen

Papers

Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo

A Line Search SQP-type Method with Bi-object Strategy for Nonlinear Semidefinite Programming