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Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these…
Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…
Interest in the study and analysis of dynamic processes in the social, behavioral, and health sciences has burgeoned in recent years due to the increased availability of intensive longitudinal data. However, how best to model and account…
Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous…
At online retail platforms, detecting fraudulent accounts and transactions is crucial to improve customer experience, minimize loss, and avoid unauthorized transactions. Despite the variety of different models for deep learning on graphs,…
Graph Networks (GNs) enable the fusion of prior knowledge and relational reasoning with flexible function approximations. In this work, a general GN-based model is proposed which takes full advantage of the relational modeling capabilities…
We introduce MGP-VAE (Multi-disentangled-features Gaussian Processes Variational AutoEncoder), a variational autoencoder which uses Gaussian processes (GP) to model the latent space for the unsupervised learning of disentangled…
We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the…
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…
In the realm of heterogeneous mixed autonomy, vehicles experience dynamic spatial correlations and nonlinear temporal interactions in a complex, non-Euclidean space. These complexities pose significant challenges to traditional…
This paper focuses on spatiotemporal (ST) traffic prediction using graph neural networks (GNNs). Given that ST data comprises non-stationary and complex temporal patterns, interpreting and predicting such trends is inherently challenging.…
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…
While a wide range of interpretable generative procedures for graphs exist, matching observed graph topologies with such procedures and choices for its parameters remains an open problem. Devising generative models that closely reproduce…
Spatial-temporal graph representations play a crucial role in urban sensing applications, including traffic analysis, human mobility behavior modeling, and citywide crime prediction. However, a key challenge lies in the noisy and sparse…
Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data. However, most SR methods prioritize minimizing prediction error over identifying the governing…
The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), $H_q$, for various values of the parameter $q$. Using $H_q$, we introduce a new visual methodology to…
Recent work in graph models has found that probabilistic hyperedge replacement grammars (HRGs) can be extracted from graphs and used to generate new random graphs with graph properties and substructures close to the original. In this paper,…
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…
This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables…
Multi-view learning has progressed rapidly in recent years. Although many previous studies assume that each instance appears in all views, it is common in real-world applications for instances to be missing from some views, resulting in…