Model Selection for Support Vector Machine Classification

We address the problem of model selection for Support Vector Machine (SVM) classification. For fixed functional form of the kernel, model selection amounts to tuning kernel parameters and the slack penalty coefficient $C$. We begin by reviewing a recently developed probabilistic framework for SVM classification. An extension to the case of SVMs with quadratic slack penalties is given and a simple approximation for the evidence is derived, which can be used as a criterion for model selection. We also derive the exact gradients of the evidence in terms of posterior averages and describe how they can be estimated numerically using Hybrid Monte Carlo techniques. Though computationally demanding, the resulting gradient ascent algorithm is a useful baseline tool for probabilistic SVM model selection, since it can locate maxima of the exact (unapproximated) evidence. We then perform extensive experiments on several benchmark data sets. The aim of these experiments is to compare the performance of probabilistic model selection criteria with alternatives based on estimates of the test error, namely the so-called ``span estimate'' and Wahba's Generalized Approximate Cross-Validation (GACV) error. We find that all the ``simple'' model criteria (Laplace evidence approximations, and the Span and GACV error estimates) exhibit multiple local optima with respect to the hyperparameters. While some of these give performance that is competitive with results from other approaches in the literature, a significant fraction lead to rather higher test errors. The results for the evidence gradient ascent method show that also the exact evidence exhibits local optima, but these give test errors which are much less variable and also consistently lower than for the simpler model selection criteria

A sparse multinomial probit model for classification

A recent development in penalized probit modelling using a hierarchical Bayesian approach has led to a sparse binomial (two-class) probit classifier that can be trained via an EM algorithm. A key advantage of the formulation is that no tuning of hyperparameters relating to the penalty is needed thus simplifying the model selection process. The resulting model demonstrates excellent classification performance and a high degree of sparsity when used as a kernel machine. It is, however, restricted to the binary classification problem and can only be used in the multinomial situation via a one-against-all or one-against-many strategy. To overcome this, we apply the idea to the multinomial probit model. This leads to a direct multi-classification approach and is shown to give a sparse solution with accuracy and sparsity comparable with the current state-of-the-art. Comparative numerical benchmark examples are used to demonstrate the method

Hyperparameter Importance Across Datasets

With the advent of automated machine learning, automated hyperparameter optimization methods are by now routinely used in data mining. However, this progress is not yet matched by equal progress on automatic analyses that yield information beyond performance-optimizing hyperparameter settings. In this work, we aim to answer the following two questions: Given an algorithm, what are generally its most important hyperparameters, and what are typically good values for these? We present methodology and a framework to answer these questions based on meta-learning across many datasets. We apply this methodology using the experimental meta-data available on OpenML to determine the most important hyperparameters of support vector machines, random forests and Adaboost, and to infer priors for all their hyperparameters. The results, obtained fully automatically, provide a quantitative basis to focus efforts in both manual algorithm design and in automated hyperparameter optimization. The conducted experiments confirm that the hyperparameters selected by the proposed method are indeed the most important ones and that the obtained priors also lead to statistically significant improvements in hyperparameter optimization.Comment: \c{opyright} 2018. Copyright is held by the owner/author(s). Publication rights licensed to ACM. This is the author's version of the work. It is posted here for your personal use, not for redistribution. The definitive Version of Record was published in Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Minin

Mean field variational Bayesian inference for support vector machine classification

A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with classical SVMs including automatic penalty parameter selection, the ability to handle dependent samples, missing data and variable selection. We demonstrate on simulated and real datasets that our approach is easily extendable to non-standard situations and outperforms the classical SVM approach whilst remaining computationally efficient.Comment: 18 pages, 4 figure

Sparse multinomial kernel discriminant analysis (sMKDA)

Dimensionality reduction via canonical variate analysis (CVA) is important for pattern recognition and has been extended variously to permit more flexibility, e.g. by "kernelizing" the formulation. This can lead to over-fitting, usually ameliorated by regularization. Here, a method for sparse, multinomial kernel discriminant analysis (sMKDA) is proposed, using a sparse basis to control complexity. It is based on the connection between CVA and least-squares, and uses forward selection via orthogonal least-squares to approximate a basis, generalizing a similar approach for binomial problems. Classification can be performed directly via minimum Mahalanobis distance in the canonical variates. sMKDA achieves state-of-the-art performance in terms of accuracy and sparseness on 11 benchmark datasets