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Gaussian Bayesian networks (a.k.a. linear Gaussian structural equation models) are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian…

Hessian based measures of flatness, such as the trace, Frobenius and spectral norms, have been argued, used and shown to relate to generalisation. In this paper we demonstrate that for feed forward neural networks under the cross entropy…

Real-world datasets exhibit imbalances of varying types and degrees. Several techniques based on re-weighting and margin adjustment of loss are often used to enhance the performance of neural networks, particularly on minority classes. In…

Gaussian mixture models are a popular tool for model-based clustering, and mixtures of factor analyzers are Gaussian mixture models having parsimonious factor covariance structure for mixture components. There are several recent extensions…

Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies of a fixed density kernel and obtain explicit results for…

Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a…

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…

The elusive nature of gradient-based optimization in neural networks is tied to their loss landscape geometry, which is poorly understood. However recent work has brought solid evidence that there is essentially no loss barrier between the…

Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework…

Overparameterized models fail to generalize well in the presence of data imbalance even when combined with traditional techniques for mitigating imbalances. This paper focuses on imbalanced classification datasets, in which a small subset…

The estimation of the generalization error of classifiers often relies on a validation set. Such a set is hardly available in few-shot learning scenarios, a highly disregarded shortcoming in the field. In these scenarios, it is common to…

A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…

We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…

Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated…

One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em…

The mechanisms by which certain training interventions, such as increasing learning rates and applying batch normalization, improve the generalization of deep networks remains a mystery. Prior works have speculated that "flatter" solutions…

We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., $\textit{deep constrained clustering}$ (DCC) -- has proven effective for incorporating weak supervision into massive data…

Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been…