Related papers: Minimax Optimality of Score-based Diffusion Models…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of…
We study the problem of high-dimensional sparse mean estimation in the presence of an $\epsilon$-fraction of adversarial outliers. Prior work obtained sample and computationally efficient algorithms for this task for identity-covariance…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by…
We consider nonparametric inference of finite dimensional, potentially non-pathwise differentiable target parameters. In a nonparametric model, some examples of such parameters that are always non pathwise differentiable target parameters…
Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a…
Score-based diffusion models have significantly advanced generative deep learning for image processing. Measurement conditioned models have also been applied to inverse problems such as CT reconstruction. However, the conventional approach,…
We introduce a framework for designing efficient diffusion models for $d$-dimensional symmetric-space Riemannian manifolds, including the torus, sphere, special orthogonal group and unitary group. Existing manifold diffusion models often…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
Recent work has explored a range of model families for human motion generation, including Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and diffusion-based models. Despite their differences, many methods rely on…
We consider the problem of inference for projection parameters in linear regression with increasing dimensions. This problem has been studied under a variety of assumptions in the literature. The classical asymptotic normality result for…
Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We…