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We study gradient flow on the multi-index regression problem for high-dimensional Gaussian data. Multi-index functions consist of a composition of an unknown low-rank linear projection and an arbitrary unknown, low-dimensional link…
In this paper, we develop an approach to modeling high-dimensional networks with a large number of nodes arranged in a hierarchical and modular structure. We propose a novel multi-scale factor analysis (MSFA) model which partitions the…
In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…
Neuroscience models commonly have a high number of degrees of freedom and only specific regions within the parameter space are able to produce dynamics of interest. This makes the development of tools and strategies to efficiently find…
The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the…
Smoothed model checking based on Gaussian process classification provides a powerful approach for statistical model checking of parametric continuous time Markov chain models. The method constructs a model for the functional dependence of…
Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent…
In this study, we propose a novel approach to uncover subgroup-specific and subgroup-common latent factors addressing the challenges posed by the heterogeneity of neurological and mental disorders, which hinder disease understanding,…
This paper introduces a novel system identification and tracking method for PieceWise Smooth (PWS) nonlinear stochastic hybrid systems. We are able to correctly identify and track challenging problems with diverse dynamics and low…
In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of…
Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring…
Probabilistic topic models are popular unsupervised learning methods, including probabilistic latent semantic indexing (pLSI) and latent Dirichlet allocation (LDA). By now, their training is implemented on general purpose computers (GPCs),…
Ubiquitous linear Gaussian exploratory tools such as principle component analysis (PCA) and factor analysis (FA) remain widely used as tools for: exploratory analysis, pre-processing, data visualization and related tasks. However, due to…
Sequential modelling of high-dimensional data is an important problem that appears in many domains including model-based reinforcement learning and dynamics identification for control. Latent variable models applied to sequential data…
Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…
Multimodal learning aims to discover the relationship between multiple modalities. It has become an important research topic due to extensive multimodal applications such as cross-modal retrieval. This paper attempts to address the modality…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
In a common experimental setting, the behaviour of a noisy dynamical system is monitored in response to manipulations of one or more control parameters. Here, we introduce a structured model to describe parametric changes in qualitative…