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Information criteria are an appropriate and widely used tool for solving model selection problems. However, different ways to use them exist, each leading to a more or less precise approximation of the sought model. In this paper, we mainly…

A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the `right' model…

We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…

We introduce a Parametric Information Maximization (PIM) model for the Generalized Category Discovery (GCD) problem. Specifically, we propose a bi-level optimization formulation, which explores a parameterized family of objective functions,…

The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…

State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the…

Accurate model selection is a fundamental requirement for statistical analysis. In many real-world applications of graphical modelling, correct model structure identification is the ultimate objective. Standard model validation procedures…

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…

Selecting an optimal subset of features or instances under an information theoretic criterion has become an effective preprocessing strategy for reducing data complexity while preserving essential information. This study investigates two…

Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…

This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…

Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear…

We consider the problem of evaluating representations of data for use in solving a downstream task. We propose to measure the quality of a representation by the complexity of learning a predictor on top of the representation that achieves…

Coding, which targets compressing and reconstructing data, and intelligence, often regarded at an abstract computational level as being centered around model learning and prediction, interweave recently to give birth to a series of…

Several tasks in information retrieval (IR) rely on assumptions regarding the distribution of some property (such as term frequency) in the data being processed. This thesis argues that such distributional assumptions can lead to incorrect…

The quantity of event logs available is increasing rapidly, be they produced by industrial processes, computing systems, or life tracking, for instance. It is thus important to design effective ways to uncover the information they contain.…

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal…

Machine learning continues to grow in popularity in academia, in industry, and is increasingly used in other fields. However, most of the common metrics used to evaluate even simple binary classification models have shortcomings that are…

This paper considers the problem of approximating a density when it can be evaluated up to a normalizing constant at a limited number of points. We call this problem the Boltzmann approximation (BA) problem. The BA problem is ubiquitous in…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…