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Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling in genome-wide association studies. These two approaches make very different assumptions, so are…

A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian…

Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…

Precise and timely forecasting of blood glucose levels is essential for effective diabetes management. While extensive research has been conducted on Type 1 diabetes mellitus, Type 2 diabetes mellitus (T2DM) presents unique challenges due…

In the paper we compare the modelling ability of discrete-time multivariate Stochastic Volatility models to describe the conditional correlations between stock index returns. We consider four trivariate SV models, which differ in the…

This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…

The continuous expansion of the urban construction scale has recently contributed to the demand for the dynamics of traffic intersections that are managed, making adaptive modellings become a hot topic. Existing deep learning methods are…

We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime. We prove limit theorems for the trajectories of summary statistics (i.e., finite-dimensional functions) of SGD as the…

The importance of unspanned macroeconomic variables for Dynamic Term Structure Models has been intensively discussed in the literature. To our best knowledge the earlier studies considered only linear interactions between the economy and…

In recent years, advancements in deep learning have spurred the development of numerous models for Long-term Time Series Forecasting (LTSF). However, most existing approaches struggle to fully capture the complex and structured dependencies…

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an…

The Gaussian Process with a deep kernel is an extension of the classic GP regression model and this extended model usually constructs a new kernel function by deploying deep learning techniques like long short-term memory networks. A…

In this paper, we study time-varying graphical models based on data measured over a temporal grid. Such models are motivated by the needs to describe and understand evolving interacting relationships among a set of random variables in many…

In this tutorial, we provide a hands-on guideline on how to implement complex Dynamic Latent Class Structural Equation Models (DLCSEM) in the Bayesian software JAGS. We provide building blocks starting with simple Confirmatory Factor and…

Driven by the critical needs of biomanufacturing 4.0, we introduce a probabilistic knowledge graph hybrid model characterizing the risk- and science-based understanding of bioprocess mechanisms. It can faithfully capture the important…

Large Language Models (LLMs) have recently gained popularity in stock trading for their ability to process multimodal financial data. However, most existing methods focus on single-stock trading and lack the capacity to reason over multiple…

Distributed Deep Learning (DDL) is essential for large-scale Deep Learning (DL) training. Synchronous Stochastic Gradient Descent (SSGD) 1 is the de facto DDL optimization method. Using a sufficiently large batch size is critical to…

Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how…

Advances in deep neural network (DNN) architectures have enabled new prediction techniques for stock market data. Unlike other multivariate time-series data, stock markets show two unique characteristics: (i) \emph{multi-order dynamics}, as…