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We study the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the…
This manuscript presents an advanced framework for Bayesian learning by incorporating action and state-dependent signal variances into decision-making models. This framework is pivotal in understanding complex data-feedback loops and…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR…
We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…
Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location…
This paper proposes a fast two-stage variational Bayesian (VB) algorithm to estimate unrestricted panel spatial autoregressive models. Using Dirichlet-Laplace priors, we are able to uncover the spatial relationships between cross-sectional…
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…
Most sensor calibrations rely on the linearity and steadiness of their response characteristics, but practical sensors are nonlinear, and their response drifts with time, restricting their choices for adoption. To broaden the realm of…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
Some challenging problems in tracking multiple objects include the time-dependent cardinality, unordered measurements and object parameter labeling. In this paper, we employ Bayesian Bayesian nonparametric methods to address these…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
The time it takes for a classifier to make an accurate prediction can be crucial in many behaviour recognition problems. For example, an autonomous vehicle should detect hazardous pedestrian behaviour early enough for it to take appropriate…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…
Robot introspection, as opposed to anomaly detection typical in process monitoring, helps a robot understand what it is doing at all times. A robot should be able to identify its actions not only when failure or novelty occurs, but also as…