Related papers: Sharp mean-field analysis of permutation mixtures …

Using the Fundamental-Measure Density Functional Theory, we have studied theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting…

We investigate the existence of a fundamental computation-information gap for the problem of clustering a mixture of isotropic Gaussian in the high-dimensional regime, where the ambient dimension $p$ is larger than the number $n$ of points.…

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…

Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…

Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…

The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…

Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing…

This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…

Permutation of any two hidden units yields invariant properties in typical deep generative neural networks. This permutation symmetry plays an important role in understanding the computation performance of a broad class of neural networks…

Count data with complex features arise in many disciplines, including ecology, agriculture, criminology, medicine, and public health. Zero inflation, spatial dependence, and non-equidispersion are common features in count data. There are…

We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the…

Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…

A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

This work establishes a framework of near-field communication under different array geometries of extremely large-scale multiple-input multiple-output (XL-MIMO). We first formulate the near-field spatial non-stationary channel model which…