Related papers: Refined Statistical Bounds for Classification Erro…

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

Machine learning algorithms are increasingly used to inform critical decisions. There is a growing concern about bias, that algorithms may produce uneven outcomes for individuals in different demographic groups. In this work, we measure…

We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the…

The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…

Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework,…

Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of…

We study learning algorithms when there is a mismatch between the distributions of the training and test datasets of a learning algorithm. The effect of this mismatch on the generalization error and model misspecification are quantified.…

Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…

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…

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…

We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL…

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…

There is a fundamental limitation in the prediction performance that a machine learning model can achieve due to the inevitable uncertainty of the prediction target. In classification problems, this can be characterized by the Bayes error,…

Article discusses the application of Kullback-Leibler divergence to the recognition of speech signals and suggests three algorithms implementing this divergence criterion: correlation algorithm, spectral algorithm and filter algorithm.…

Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…

This paper considers reparameterization invariant Bayesian point estimates and credible regions of model parameters for scientific inference and communication. The effect of intrinsic loss function choice in Bayesian intrinsic estimates and…

Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cram\'er-Rao bound…

We provide a rigorous analysis of training by variational inference (VI) of Bayesian neural networks in the two-layer and infinite-width case. We consider a regression problem with a regularized evidence lower bound (ELBO) which is…

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…