Probabilistic Methodology and Techniques for Artefact Conception and Development

The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art

Score Function Features for Discriminative Learning: Matrix and Tensor Framework

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.Comment: 29 page

Deep Gaussian Mixture Models

Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers of latent variables, where, at each layer, the variables follow a mixture of Gaussian distributions. Thus, the deep mixture model consists of a set of nested mixtures of linear models, which globally provide a nonlinear model able to describe the data in a very flexible way. In order to avoid overparameterized solutions, dimension reduction by factor models can be applied at each layer of the architecture thus resulting in deep mixtures of factor analysers.Comment: 19 pages, 4 figure

A robust approach to model-based classification based on trimming and constraints

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations, namely outliers and data with incorrect labels, can strongly undermine the classifier performance, especially if the training size is small. The present work introduces a robust modification to the Model-Based Classification framework, employing impartial trimming and constraints on the ratio between the maximum and the minimum eigenvalue of the group scatter matrices. The proposed method effectively handles noise presence in both response and exploratory variables, providing reliable classification even when dealing with contaminated datasets. A robust information criterion is proposed for model selection. Experiments on real and simulated data, artificially adulterated, are provided to underline the benefits of the proposed method