A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination

By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks

Speaker verification using sequence discriminant support vector machines

This paper presents a text-independent speaker verification system using support vector machines (SVMs) with score-space kernels. Score-space kernels generalize Fisher kernels and are based on underlying generative models such as Gaussian mixture models (GMMs). This approach provides direct discrimination between whole sequences, in contrast with the frame-level approaches at the heart of most current systems. The resultant SVMs have a very high dimensionality since it is related to the number of parameters in the underlying generative model. To address problems that arise in the resultant optimization we introduce a technique called spherical normalization that preconditions the Hessian matrix. We have performed speaker verification experiments using the PolyVar database. The SVM system presented here reduces the relative error rates by 34% compared to a GMM likelihood ratio system

Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring

Hybrid Models with Deep and Invertible Features

We propose a neural hybrid model consisting of a linear model defined on a set of features computed by a deep, invertible transformation (i.e. a normalizing flow). An attractive property of our model is that both p(features), the density of the features, and p(targets | features), the predictive distribution, can be computed exactly in a single feed-forward pass. We show that our hybrid model, despite the invertibility constraints, achieves similar accuracy to purely predictive models. Moreover the generative component remains a good model of the input features despite the hybrid optimization objective. This offers additional capabilities such as detection of out-of-distribution inputs and enabling semi-supervised learning. The availability of the exact joint density p(targets, features) also allows us to compute many quantities readily, making our hybrid model a useful building block for downstream applications of probabilistic deep learning.Comment: ICML 201