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Complex systems with intricate causal dependencies challenge accurate prediction. Effective modeling requires precise physical process representation, integration of interdependent factors, and incorporation of multi-resolution…

The financial domain presents a complex environment for stock market prediction, characterized by volatile patterns and the influence of multifaceted data sources. Traditional models have leveraged either Convolutional Neural Networks (CNN)…

Insufficient amounts of available training data is a critical challenge for both development and deployment of artificial intelligence and machine learning (AI/ML) models. This paper proposes a unified approach to both synthetic data…

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…

We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

This paper deals with inference and prediction for multiple correlated time series, where one has also the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for the…

Graphical modeling is a widely used tool for analyzing conditional dependencies between variables and traditional methods may struggle to capture shared and distinct structures in multi-group or multi-condition settings. Joint graphical…

More and more stock trading strategies are constructed using deep reinforcement learning (DRL) algorithms, but DRL methods originally widely used in the gaming community are not directly adaptable to financial data with low signal-to-noise…

Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Many modern time-series datasets contain large numbers of output response variables sampled for prolonged periods of time. For example, in neuroscience, the activities of 100s-1000's of neurons are recorded during behaviors and in response…

This analysis derives the maximum likelihood estimator and applies Bayesian inference to model geometric Brownian motion, incorporating jump diffusion to account for sudden market shifts. The Bayesian approach is implemented using Markov…

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…

Time series forecasting is essential for our daily activities and precise modeling of the complex correlations and shared patterns among multiple time series is essential for improving forecasting performance. Spatial-Temporal Graph Neural…

We propose Heterogeneous Swarms, an algorithm to design multi-LLM systems by jointly optimizing model roles and weights. We represent multi-LLM systems as directed acyclic graphs (DAGs) of LLMs with topological message passing for…

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable posterior sampling and decentralized variants enabling…

Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…