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The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…
Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…
This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this…
Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…
A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation…
In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
Complex, multivariable systems are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…