Related papers: Learning general Gaussian mixtures with efficient …
Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…
Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…
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…
How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usually used to train diffusion models is the score function of…
In this note, we consider the problem of robust learning mixtures of linear regressions. We connect mixtures of linear regressions and mixtures of Gaussians with a simple thresholding, so that a quasi-polynomial time algorithm can be…
How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also…
Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…
Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise…
Feature selection can facilitate the learning of mixtures of discrete random variables as they arise, e.g. in crowdsourcing tasks. Intuitively, not all workers are equally reliable but, if the less reliable ones could be eliminated, then…
We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to…
Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient…
Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…
Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
We consider the sparse moment problem of learning a $k$-spike mixture in high-dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous…
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…
This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…
GNSS localization is an important part of today's autonomous systems, although it suffers from non-Gaussian errors caused by non-line-of-sight effects. Recent methods are able to mitigate these effects by including the corresponding…
Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…