Related papers: Estimating a difference between Kullback-Leibler r…
This paper investigates the expected excess risk of in-context learning (ICL) for multiclass classification. We formalize each task as a sequence of labeled examples followed by a query input; a pretrained model then estimates the query's…
This paper studies the problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance. The system state and the unknown covariance are jointly estimated in the framework of…
Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been…
The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the…
Generalized $k$-means can be incorporated with any similarity or dissimilarity measure for clustering. By choosing the dissimilarity measure as the well known likelihood ratio or $F$-statistic, this work proposes a method based on…
Meta-analytic methods tend to take all-or-nothing approaches to study-level heterogeneity, assuming all studies are heterogeneous or homogeneous, leading to inefficiency and/or bias in estimation and inference. In this paper, we develop a…
This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter…
Machine Learning (ML) models are often complex and difficult to interpret due to their 'black-box' characteristics. Interpretability of a ML model is usually defined as the degree to which a human can understand the cause of decisions…
The performance of machine learning classification algorithms are evaluated by estimating metrics, often from the confusion matrix, using training data and cross-validation. However, these do not prove that the best possible performance has…
In this article, we develop a modern perspective on Akaike's Information Criterion and Mallows' Cp for model selection. Despite the diff erences in their respective motivation, they are equivalent in the special case of Gaussian linear…
We go through the process of crafting a robust and numerically stable online algorithm for the computation of the Watanabe-Akaike information criteria (WAIC). We implement this algorithm in the NIMBLE software. The implementation is…
Wide conditions are provided to guarantee asymptotic unbiasedness and L^2-consistency of the introduced estimates of the Kullback-Leibler divergence for probability measures in R^d having densities w.r.t. the Lebesgue measure. These…
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…
Indirect comparisons of treatment-specific outcomes across separate studies often inform decision-making in the absence of head-to-head randomized comparisons. Differences in baseline characteristics between study populations may introduce…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
Model-based component-wise gradient boosting is a popular tool for data-driven variable selection. In order to improve its prediction and selection qualities even further, several modifications of the original algorithm have been developed,…
This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
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…
Interest in targeted disease prevention has stimulated development of models that assign risks to individuals, using their personal covariates. We need to evaluate these models, and to quantify the gains achieved by expanding a model with…