相关论文: Harmonic Exponential Families on Manifolds

Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of…

The use of heteronuclear models are often viewed as ways to improve the predictive ability and parameter transferability of advanced association models, such as those derived from the Statistical Associating Fluid Theory (SAFT). Indeed,…

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster.…

Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without…

What if there is a teacher who knows the learning goal and wants to design good training data for a machine learner? We propose an optimal teaching framework aimed at learners who employ Bayesian models. Our framework is expressed as an…

We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…

The Mat{\'e}rn family of isotropic covariance functions has been central to the theoretical development and application of statistical models for geospatial data. For global data defined over the whole sphere representing planet Earth, the…

There has recently been a concerted effort to derive mechanisms in vision and machine learning systems to offer uncertainty estimates of the predictions they make. Clearly, there are enormous benefits to a system that is not only accurate…

Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in…

A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits…

Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding…

In this paper, we present an algorithm for the fitting of a location-scale variant of the canonical fundamental skew t (CFUST) distribution, a superclass of the restricted and unrestricted skew t-distributions. In recent years, a few…

We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing…

Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…

The family of circular distributions based on non-negative trigonometric sums (NNTS), developed by Fern\'andez-Dur\'an (2004), is highly flexible for modeling datasets exhibiting multimodality and/or skewness. In this article, we extend the…

We propose a new algorithm for finding an unknown number of geometric models, e.g., homographies. The problem is formalized as finding dominant model instances progressively without forming crisp point-to-model assignments. Dominant…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

The ability to store continuous variables in the state of a biological system (e.g. a neural network) is critical for many behaviours. Most models for implementing such a memory manifold require hand-crafted symmetries in the interactions…

Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…

The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems,…