From the Publisher:
This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts, the book examines techniques for modelling probability density functions and the properties and merits of the multi-layer perceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100 exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.

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Neural networks for pattern recognition

This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.

/pdf/a-simple-positive-semi-definite-heteroskedasticity-and-1h9nwsy8i5.pdf

A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix

Structural equation modeling (SEM) has become a quasi-standard in marketing and management research when it comes to analyzing the cause-effect relations between latent constructs. For most researchers, SEM is equivalent to carrying out covariance-based SEM (CB-SEM). While marketing researchers have a basic understanding of CB-SEM, most of them are only barely familiar with the other useful approach to SEM-partial least squares SEM (PLS-SEM). The current paper reviews PLS-SEM and its algorithm, and provides an overview of when it can be most appropriately applied, indicating its potential and limitations for future research. The authors conclude that PLS-SEM path modeling, if appropriately applied, is indeed a "silver bullet" for estimating causal models in many theoretical models and empirical data situations.

PLS-SEM: Indeed a Silver Bullet

Generalized Additive Models.

Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data d/sub i/=f(t/sub i/)+/spl sigma/z/sub i/, i=0, ..., n-1,t/sub i/=i/n, where the z/sub i/ are independent and identically distributed standard Gaussian random variables. The reconstruction f/spl circ/*/sub n/ is defined in the wavelet domain by translating all the empirical wavelet coefficients of d toward 0 by an amount /spl sigma//spl middot//spl radic/(2log (n)/n). The authors prove two results about this type of estimator. [Smooth]: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: the estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes. These two properties are unprecedented in several ways. The present proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model. >

De-noising by soft-thresholding

https://imedea.uib-csic.es/master/cambioglobal/Modulo_V_cod101615/Theory/lit_support/pca_wold.pdf

Principal component analysis

https://libpls.net/publication/PLS_basic_2001.pdf

PLS-regression: a basic tool of chemometrics

By means of factor analysis (FA) or principal components analysis (PCA) a matrix Y with the elements y ik is approximated by the model Here the parameters α, β and θ express the systematic part of the data yik, “signal,” and the residuals ∊ ik express the “random” part, “noise.” When applying FA or PCA to a matrix of real data obtained, for example, by characterizing N chemical mixtures by M measured variables, one major problem is the estimation of the rank A of the matrix Y, i.e. the estimation of how much of the data y ik is “signal” and how much is “noise.” Cross validation can be used to approach this problem. The matrix Y is partitioned and the rank A is determined so as to maximize the predictive properties of model (I) when the parameters are estimated on one part of the matrix Y and the prediction tested on another part of the matrix Y.

Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models

The use of partial least squares (PLS) for handling collinearities among the independent variables X in multiple regression is discussed. Consecutive estimates $({\text{rank }}1,2,\cdots )$ are obtained using the residuals from previous rank as a new dependent variable y. The PLS method is equivalent to the conjugate gradient method used in Numerical Analysis for related problems.To estimate the “optimal” rank, cross validation is used. Jackknife estimates of the standard errors are thereby obtained with no extra computation.The PLS method is compared with ridge regression and principal components regression on a chemical example of modelling the relation between the measured biological activity and variables describing the chemical structure of a set of substituted phenethylamines.

The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses

A generic preprocessing method for multivariate data, called orthogonal projections to latent structures (O-PLS), is described. O-PLS removes variation from X (descriptor variables) that is not correlated to Y (property variables, e.g. yield, cost or toxicity). In mathematical terms this is equivalent to removing systematic variation in X that is orthogonal to Y. In an earlier paper, Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175-185) described orthogonal signal correction (OSC). In this paper a method with the same objective but with different means is described. The proposed O-PLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in X is removed, making interpretation of the resulting PLS model easier and with the additional benefit that the non-correlated variation itself can be analyzed further. As an example, near-infrared (NIR) reflectance spectra of wood chips were analyzed. Applying O-PLS resulted in reduced model complexity with preserved prediction ability, effective removal of non-correlated variation in X and, not least, improved interpretational ability of both correlated and non-correlated variation in the NIR spectra.

Svante Wold

Papers

Principal component analysis

PLS-regression: a basic tool of chemometrics

Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models

The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses

Orthogonal projections to latent structures (O-PLS)