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With the development of Artificial Intelligence, numerous real-world tasks have been accomplished using technology integrated with deep learning. To achieve optimal performance, deep neural networks typically require large volumes of data…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference…

Recently, diffusion models (DMs) have made significant strides in high-quality image generation. However, the multi-step denoising process often results in considerable computational overhead, impeding deployment on resource-constrained…

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…

In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…

This article proposes a new approach to modeling high-dimensional time series by treating a $p$-dimensional time series as a nonsingular linear transformation of certain common factors and idiosyncratic components. Unlike the approximate…

Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…

This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…

Generative diffusion models have emerged as a powerful tool for high-quality image synthesis, yet their iterative nature demands significant computational resources. This paper proposes an efficient time step sampling method based on an…

Spatiotemporal data analysis is pivotal across various domains, such as transportation, meteorology, and healthcare. The data collected in real-world scenarios are often incomplete due to device malfunctions and network errors.…

In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to…

Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…

The rapidly increasing complexity of (mainly wireless) ad-hoc networks stresses the need of reliable distributed estimation of several variables of interest. The widely used centralized approach, in which the network nodes communicate their…

Many policies hinge on a continuous variable exceeding a threshold, prompting strategic behavior by agents to stay on the favorable side. This creates density discontinuities at cutoffs, evident in contexts like taxable income, corporate…

High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Autoregressive neural networks within the temporal point process (TPP) framework have become the standard for modeling continuous-time event data. Even though these models can expressively capture event sequences in a one-step-ahead…