Related papers: Limits to classification performance by relating K…

Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different probability distributions. In this work, we give an information-theoretic analysis of the…

A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit…

The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence -- a family of divergences that includes the…

In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…

Causal discovery from observational data underpins applications in finance, climate modeling, and machine learning. Constraint-based causal discovery reduces structure learning to a sequence of conditional independence (CI) tests, where…

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…

A widespread approach in machine learning to evaluate the quality of a classifier is to cross -- classify predicted and actual decision classes in a confusion matrix, also called error matrix. A classification tool which does not assume…

There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…

Knowing if a model will generalize to data 'in the wild' is crucial for safe deployment. To this end, we study model disagreement notions that consider the full predictive distribution - specifically disagreement based on Hellinger…

In this paper, we provide new theoretical results on the generalization properties of learning algorithms for multiclass classification problems. The originality of our work is that we propose to use the confusion matrix of a classifier as…

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…

A variety of different performance metrics are commonly used in the machine learning literature for the evaluation of classification systems. Some of the most common ones for measuring quality of hard decisions are standard and balanced…

We consider model-based reinforcement learning in finite Markov De- cision Processes (MDPs), focussing on so-called optimistic strategies. In MDPs, optimism can be implemented by carrying out extended value it- erations under a constraint…

Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…

An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the "classical" case of…

Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for…

The Kullback-Leibler divergence, the Kullback-Leibler variation, and the Bernstein "norm" are used to quantify discrepancies among probability distributions in likelihood models such as nonparametric maximum likelihood and nonparametric…

We examine the estimation of the Kullback-Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate continuous distributions. Our starting point is the maximum entropy principle for Shannon entropy: among all…

In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…