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Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a…

Various brain functions that are necessary to maintain life activities materialize through the interaction of countless neurons. Therefore, it is important to analyze functional neuronal network. To elucidate the mechanism of brain…

The classical approach to non-linear regression in physics, is to take a mathematical model describing the functional dependence of the dependent variable from a set of independent variables, and then, using non-linear fitting algorithms,…

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…

Modern generative models are roughly divided into two main categories: (1) models that can produce high-quality random samples, but cannot estimate the exact density of new data points and (2) those that provide exact density estimation, at…

Recurrent neural networks (RNNs) are powerful models for processing time-series data, but it remains challenging to understand how they function. Improving this understanding is of substantial interest to both the machine learning and…

When governed by underlying low-dimensional dynamics, the interdependence of simultaneously recorded population of neurons can be explained by a small number of shared factors, or a low-dimensional trajectory. Recovering these latent…

The modeling and prediction of the ultrafast nonlinear dynamics in the optical fiber are essential for the studies of laser design, experimental optimization, and other fundamental applications. The traditional propagation modeling method…

Trajectory data generation is an important domain that characterizes the generative process of mobility data. Traditional methods heavily rely on predefined heuristics and distributions and are weak in learning unknown mechanisms. Inspired…

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…

Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces…

The increasing prevalence of Large Language Models (LMs) in critical applications highlights the need for controlled language generation strategies that are not only computationally efficient but that also enjoy performance guarantees. To…

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…

We present a model that can automatically learn alignments between high-dimensional data in an unsupervised manner. Our proposed method casts alignment learning in a framework where both alignment and data are modelled simultaneously.…

As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…

A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent…

When deploying deep learning models to a device, it is traditionally assumed that available computational resources (compute, memory, and power) remain static. However, real-world computing systems do not always provide stable resource…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

This paper introduces a new latent variable generative model able to handle high dimensional longitudinal data and relying on variational inference. The time dependency between the observations of an input sequence is modelled using…