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Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…

The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty…

Model selection is central to statistics, and many learning problems can be formulated as model selection problems. In this paper, we treat the problem of selecting a maximum entropy model given various feature subsets and their moments, as…

In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional…

Multiple Description Coding (MDC) is an error-resilient source coding method designed for transmission over noisy channels. We present a novel MDC scheme employing a neural network based on implicit neural representation. This involves…

Information theoretic criteria (ITC) have been widely adopted in engineering and statistics for selecting, among an ordered set of candidate models, the one that better fits the observed sample data. The selected model minimizes a penalized…

The Minimum Description Length (MDL) principle is solidly based on a provably ideal method of inference using Kolmogorov complexity. We test how the theory behaves in practice on a general problem in model selection: that of learning the…

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which…

This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a…

The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which…

Model selection based on classical information criteria, such as BIC, is generally computationally demanding, but its properties are well studied. On the other hand, model selection based on parameter shrinkage by $\ell_1$-type penalties is…

A major challenge in designing efficient statistical supervised learning algorithms is finding representations that perform well not only on available training samples but also on unseen data. While the study of representation learning has…

Artificial Intelligence (AI) has achieved remarkable success in specialized tasks but struggles with efficient skill acquisition and generalization. The Abstraction and Reasoning Corpus (ARC) benchmark evaluates intelligence based on…

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the…

This paper introduces a new method for model selection and more generally hyperparameter selection in machine learning. Minimum description length (MDL) is an established method for model selection, which is however not directly aimed at…

We study distributed estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we…

Non-concave penalized maximum likelihood methods, such as the Bridge, the SCAD, and the MCP, are widely used because they not only do parameter estimation and variable selection simultaneously but also have a high efficiency as compared to…

Model order selection (MOS) in linear regression models is a widely studied problem in signal processing. Techniques based on information theoretic criteria (ITC) are algorithms of choice in MOS problems. This article proposes a novel…

Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a…

We have recently proposed a new information-based approach to model selection, the Frequentist Information Criterion (FIC), that reconciles information-based and frequentist inference. The purpose of this current paper is to provide a…