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Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. 15 to…

State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…

Structured state-space models (SSMs) have been developed to offer more persistent memory retention than traditional recurrent neural networks, while maintaining real-time inference capabilities and addressing the time-complexity limitations…

A novel State-Space Neural Network with Ordered variance (SSNNO) is presented in which the state variables are ordered in decreasing variance. A systematic way of model order reduction with SSNNO is proposed, which leads to a Reduced order…

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and…

The rapid growth of online network platforms generates large-scale network data and it poses great challenges for statistical analysis using the spatial autoregression (SAR) model. In this work, we develop a novel distributed estimation and…

Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…

The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…

Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly…

We present a novel family of language model (LM) estimation techniques named Sparse Non-negative Matrix (SNM) estimation. A first set of experiments empirically evaluating it on the One Billion Word Benchmark shows that SNM $n$-gram LMs…

The need to recognise long-term dependencies in sequential data such as video streams has made Long Short-Term Memory (LSTM) networks a prominent Artificial Intelligence model for many emerging applications. However, the high computational…

State space models (SSMs) are a flexible approach to modeling complex time series. However, inference in SSMs is often computationally prohibitive for long time series. Stochastic gradient MCMC (SGMCMC) is a popular method for scalable…

Synthetic likelihood (SL) is a strategy for parameter inference when the likelihood function is analytically or computationally intractable. In SL, the likelihood function of the data is replaced by a multivariate Gaussian density over…

Bayesian neural networks offer better estimates of model uncertainty compared to frequentist networks. However, inference involving Bayesian models requires multiple instantiations or sampling of the network parameters, requiring…

Deep neural networks (DNN) has received increasing attention in machine learning applications in the last several years. Recently, a non-asymptotic error bound has been developed to measure the performance of the fully connected DNN…

Event cameras unlock new frontiers that were previously unthinkable with standard frame-based cameras. One notable example is low-latency motion estimation (optical flow), which is critical for many real-time applications. In such…

For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…

Time series analysis by state-space models is widely used in forecasting and extracting unobservable components like level, slope, and seasonality, along with explanatory variables. However, their reliance on traditional Kalman filtering…