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Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…

The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…

New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…

We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability…

We consider the level-sets of continuous Gaussian fields on $\mathbb{R}^d$ above a certain level $-\ell\in \mathbb{R}$, which defines a percolation model as $\ell$ varies. We assume that the covariance kernel satisfies certain regularity,…

Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for…

This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification…

Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…

Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…

Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…

We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that, under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The…

While generalized linear mixed models are a fundamental tool in applied statistics, many specifications, such as those involving categorical factors with many levels or interaction terms, can be computationally challenging to estimate due…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

A family of parsimonious ultrametric mixture models with the Manly transformation is developed for clustering high-dimensional and asymmetric data. Advances in Gaussian mixture modeling sufficiently handle high-dimensional data but struggle…

The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…

We establish the sharpness of the phase transition for a wide class of Gaussian percolation models, on $\mathbb{Z}^d$ or $\mathbb{R}^d$, $d \ge 2$, with correlations decaying at least algebraically with exponent $\alpha > 0$, including the…

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However,…

Important insights towards the explainability of neural networks reside in the characteristics of their decision boundaries. In this work, we borrow tools from the field of adversarial robustness, and propose a new perspective that relates…

Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge…