相关论文: Diffusion Approximations for Online Principal Comp…

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

We introduce Orchid, a unified latent diffusion model that learns a joint appearance-geometry prior to generate color, depth, and surface normal images in a single diffusion process. This unified approach is more efficient and coherent than…

In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…

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,…

We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…

In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…

We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…

Diffusion Transformers (DiTs) have demonstrated exceptional performance in high-fidelity image and video generation. To reduce their substantial computational costs, feature caching techniques have been proposed to accelerate inference by…

Online optimization has gained increasing interest due to its capability of tracking real-world streaming data. Although online optimization methods have been widely studied in the setting of frequentist statistics, few works have…

Distributed online convex optimization (D-OCO) is a powerful paradigm for modeling distributed scenarios with streaming data. However, the communication cost between local learners and the central server is substantial in large-scale…

Existing high-dimensional online learning methods often face the challenge that their error bounds, or per-batch sample sizes, diverge as the number of data batches increases. To address this issue, we propose an asynchronous decomposition…

We consider the problem of distributed online optimization, with a group of learners connected via a dynamic communication graph. The goal of the learners is to track the global minimizer of a sum of time-varying loss functions in a…

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…

We consider a semi-discrete finite element approximation for a system consisting of the evolution of a planar curve evolving by forced curve shortening flow inside a given bounded domain $\Omega \subset \mathbb{R}^2$, such that the curve…

Online prediction methods are typically presented as serial algorithms running on a single processor. However, in the age of web-scale prediction problems, it is increasingly common to encounter situations where a single processor cannot…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based…

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Edgeworth type expansions of third order for transition densities are proved. This is done for time horizons that converge to 0. For this purpose we…

Diffusion models are a class of generative models that have been recently used for speech enhancement with remarkable success but are computationally expensive at inference time. Therefore, these models are impractical for processing…