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Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…

Confronted with the challenge of identifying the most suitable metric to validate the merits of newly proposed models, the decision-making process is anything but straightforward. Given that comparing rankings introduces its own set of…

Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$,…

Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common…

Proper confidence calibration of deep neural networks is essential for reliable predictions in safety-critical tasks. Miscalibration can lead to model over-confidence and/or under-confidence; i.e., the model's confidence in its prediction…

Comparing the internal representations of neural networks is a central goal in both neuroscience and machine learning. Standard alignment metrics operate on raw neural activations, implicitly assuming that similar representations produce…

In classification tasks, the long-tailed minority classes usually offer the predictions that are most important. Yet these classes consistently exhibit low accuracies, whereas a few high-performing classes dominate the game. We pursue a…

In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes…

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

Recently, deep learning models have achieved great success in computer vision applications, relying on large-scale class-balanced datasets. However, imbalanced class distributions still limit the wide applicability of these models due to…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

This paper derives fundamental limits on the performance of compressive classification when the source is a mixture of Gaussians. It provides an asymptotic analysis of a Bhattacharya based upper bound on the misclassification probability…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

Not all data in a typical training set help with generalization; some samples can be overly ambiguous or outrightly mislabeled. This paper introduces a new method to identify such samples and mitigate their impact when training neural…

Class imbalance poses a significant challenge in classification tasks, where traditional approaches often lead to biased models and unreliable predictions. Undersampling and oversampling techniques have been commonly employed to address…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Open-world link prediction supports the knowledge representation and link prediction of new entities, enhancing the practical value of knowledge graphs in real-world applications. However, as research deepens, the performance improvements…

The crux of semi-supervised semantic segmentation is to assign adequate pseudo-labels to the pixels of unlabeled images. A common practice is to select the highly confident predictions as the pseudo ground-truth, but it leads to a problem…

Two major uncertainties, dataset bias and adversarial examples, prevail in state-of-the-art AI algorithms with deep neural networks. In this paper, we present an intuitive explanation for these issues as well as an interpretation of the…