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Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…

We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on…

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector…

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…

This paper presents a novel hybrid model that integrates long-short-term memory (LSTM) networks and Graph Neural Networks (GNNs) to significantly enhance the accuracy of stock market predictions. The LSTM component adeptly captures temporal…

The time it takes for a classifier to make an accurate prediction can be crucial in many behaviour recognition problems. For example, an autonomous vehicle should detect hazardous pedestrian behaviour early enough for it to take appropriate…

The stock market is a crucial component of the financial system, but predicting the movement of stock prices is challenging due to the dynamic and intricate relations arising from various aspects such as economic indicators, financial…

We introduce a new approach for decoupling trends (drift) and changepoints (shifts) in time series. Our locally adaptive model-based approach for robustly decoupling combines Bayesian trend filtering and machine learning based…

The econometric challenge of finding sparse mean reverting portfolios based on a subset of a large number of assets is well known. Many current state-of-the-art approaches fall into the field of co-integration theory, where the problem is…

Estimation of origin-destination (OD) demand plays a key role in successful transportation studies. In this paper, we consider the estimation of time-varying day-to-day OD flows given data on traffic volumes in a transportation network for…

To address the complexity of financial time series, this paper proposes a forecasting model combining sliding window and variational mode decomposition (VMD) methods. Historical stock prices and relevant market indicators are used to…

Joint models (JMs) for longitudinal and time-to-event data are an important class of biostatistical models in health and medical research. When the study population consists of heterogeneous subgroups, the standard JM may be inadequate and…

Multi-step stock index forecasting is vital in finance for informed decision-making. Current forecasting methods on this task frequently produce unsatisfactory results due to the inherent data randomness and instability, thereby…

We develop a framework for derivative Gaussian process latent variable models (DGP-LVMs) that can handle multi-dimensional output data using modified derivative covariance functions. The modifications account for complexities in the…

Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…

Forecasting future stock trends remains challenging for academia and industry due to stochastic inter-stock dynamics and hierarchical intra-stock dynamics influencing stock prices. In recent years, graph neural networks have achieved…

We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. Thus far, GLMs are difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using…

We introduce three adaptive time series learning methods, called Dynamic Model Selection (DMS), Adaptive Ensemble (AE), and Dynamic Asset Allocation (DAA). The methods respectively handle model selection, ensembling, and contextual…

Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…