Related papers: Sample Complexity Bounds for Score-Matching: Causa…

This paper studies the binary classification of unbounded data from ${\mathbb R}^d$ generated under Gaussian Mixture Models (GMMs) using deep ReLU neural networks. We obtain $\unicode{x2013}$ for the first time $\unicode{x2013}$…

Score-based generative models (SGMs) need to approximate the scores $\nabla \log p_t$ of the intermediate distributions as well as the final distribution $p_T$ of the forward process. The theoretical underpinnings of the effects of these…

Recovering the structure of causal graphical models from observational data is an essential yet challenging task for causal discovery in scientific scenarios. Domain-specific causal discovery usually relies on expert validation or prior…

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…

Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in \cite{wu2022score}. We analyze the performance of this…

Diffusion models, today's leading image generative models, estimate the score function, i.e. the gradient of the log probability of (perturbed) data samples, without direct access to the underlying probability distribution. This work…

In the algorithm Intersort, Chevalley et al. (2024) proposed a score-based method to discover the causal order of variables in a Directed Acyclic Graph (DAG) model, leveraging interventional data to outperform existing methods. However, as…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often…

Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…

A statistical model for segmentation and word discovery in continuous speech is presented. An incremental unsupervised learning algorithm to infer word boundaries based on this model is described. Results of empirical tests showing that the…

Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive…

The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…

Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct low-dimensional…

We introduce a new approach to functional causal modeling from observational data, called Causal Generative Neural Networks (CGNN). CGNN leverages the power of neural networks to learn a generative model of the joint distribution of the…

Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…

Many benchmarks for automated causal inference evaluate a system's performance based on a single numerical output, such as an Average Treatment Effect (ATE). This approach conflates two distinct steps in causal analysis: identification -…

In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…