Related papers: Efficient and principled score estimation with Nys…

The goal of nonparametric regression is to recover an underlying regression function from noisy observations, under the assumption that the regression function belongs to a pre-specified infinite dimensional function space. In the online…

This paper proposes an efficient approach to learning disentangled representations with causal mechanisms based on the difference of conditional probabilities in original and new distributions. We approximate the difference with models'…

The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along…

This article initiates the study of a basic question about model pruning. Given a vector $s$ of importance scores assigned to model components, how many of the scored components could be discarded without sacrificing performance? We propose…

Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family…

We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids…

Bayesian Likelihood-Free Inference (LFI) approaches allow to obtain posterior distributions for stochastic models with intractable likelihood, by relying on model simulations. In Approximate Bayesian Computation (ABC), a popular LFI method,…

Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by…

Score matching is an alternative to maximum likelihood (ML) for estimating a probability distribution parametrized up to a constant of proportionality. By fitting the ''score'' of the distribution, it sidesteps the need to compute this…

In this work, we investigated the application of score-based gradient learning in discriminative and generative classification settings. Score function can be used to characterize data distribution as an alternative to density. It can be…

We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…

The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…

Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency, and subjective human factors. We developed a novel data-driven geological feature detection…

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied…

Recently, Zhang et al. have proposed the Diffusion Exponential Integrator Sampler (DEIS) for fast generation of samples from Diffusion Models. It leverages the semi-linear nature of the probability flow ordinary differential equation (ODE)…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…