What are the differences between Bayesian classifiers and mutual-information classifiers?

Information Bottleneck as Optimisation Method for SSVEP-Based BCI

In this study, the information bottleneck method is proposed as an optimisation method for steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI). The information bottleneck is an information-theoretic optimisation method for solving problems with a trade-off between preserving meaningful information and compression. Its main practical application in machine learning is in representation learning or feature extraction. In this study, we use the information bottleneck to find optimal classification rule for a BCI. This is a novel application for the information bottleneck. This approach is particularly suitable for BCIs since the information bottleneck optimises the amount of information transferred by the BCI. Steady-state visual evoked potential-based BCIs often classify targets using very simple rules like choosing the class corresponding to the largest feature value. We call this classifier the arg max classifier. It is unlikely that this approach is optimal, and in this study, we propose a classification method specifically designed to optimise the performance measure of BCIs. This approach gives an advantage over standard machine learning methods, which aim to optimise different measures. The performance of the proposed algorithm is tested on two publicly available datasets in offline experiments. We use the standard power spectral density analysis (PSDA) and canonical correlation analysis (CCA) feature extraction methods on one dataset and show that the current approach outperforms most of the related studies on this dataset. On the second dataset, we use the task-related component analysis (TRCA) method and demonstrate that the proposed method outperforms the standard argmax classification rule in terms of information transfer rate when using a small number of classes. To our knowledge, this is the first time the information bottleneck is used in the context of SSVEP-based BCIs. The approach is unique in the sense that optimisation is done over the space of classification functions. It potentially improves the performance of BCIs and makes it easier to calibrate the system for different subjects.

Parameter Identifiability in Statistical Machine Learning: A Review

This review examines the relevance of parameter identifiability for statistical models used in machine learning. In addition to defining main concepts, we address several issues of identifiability closely related to machine learning, showing the advantages and disadvantages of state-of-the-art research and demonstrating recent progress. First, we review criteria for determining the parameter structure of models from the literature. This has three related issues: parameter identifiability, parameter redundancy, and reparameterization. Second, we review the deep influence of identifiability on various aspects of machine learning from theoretical and application viewpoints. In addition to illustrating the utility and influence of identifiability, we emphasize the interplay among identifiability theory, machine learning, mathematical statistics, information theory, optimization theory, information geometry, Riemann geometry, symbolic computation, Bayesian inference, algebraic geometry, and others. Finally, we present a new perspective together with the associated challenges.

A Semidefinite Programming Based Search Strategy for Feature Selection with Mutual Information Measure

Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem there are two main issues that need to be addressed: (i) Finding an appropriate measure function than can be fairly fast and robustly computed for high-dimensional data. (ii) A search strategy to optimize the measure over the subset space in a reasonable amount of time. In this article mutual information between features and class labels is considered to be the measure function. Two series expansions for mutual information are proposed, and it is shown that most heuristic criteria suggested in the literature are truncated approximations of these expansions. It is well-known that searching the whole subset space is an NP-hard problem. Here, instead of the conventional sequential search algorithms, we suggest a parallel search strategy based on semidefinite programming (SDP) that can search through the subset space in polynomial time. By exploiting the similarities between the proposed algorithm and an instance of the maximum-cut problem in graph theory, the approximation ratio of this algorithm is derived and is compared with the approximation ratio of the backward elimination method. The experiments show that it can be misleading to judge the quality of a measure solely based on the classification accuracy, without taking the effect of the non-optimum search strategy into account.