Related papers: A universal framework for learning the elliptical …
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…
We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…
In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of…
Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…
Universal Multimodal Retrieval (UMR) aims to enable search across various modalities using a unified model, where queries and candidates can consist of pure text, images, or a combination of both. Previous work has attempted to adopt…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to…
Mixtures of experts (MoE) models provide a flexible framework for modelling heterogeneity in data for regression and model-based clustering and classification. MoE models for regression are typically based on the Gaussian assumption for the…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality…
The key issue in importance sampling is the choice of the alternative sampling distribution, which is often chosen from the exponential tilt family of the underlying distribution. However, when the problem exhibits certain kind of…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
Deep metric learning (DML) has received much attention in deep learning due to its wide applications in computer vision. Previous studies have focused on designing complicated losses and hard example mining methods, which are mostly…
This work introduces a family of univariate constrained mixtures of generalized normal distributions (CMGND) where the location, scale, and shape parameters can be constrained to be equal across any subset of mixture components. An…
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…
We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…
We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…