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We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…
Demanding sparsity in estimated models has become a routine practice in statistics. In many situations, we wish to require that the sparsity patterns attained honor certain problem-specific constraints. Hierarchical sparse modeling (HSM)…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…
Increased amount of vehicular traffic on roads is a significant issue. High amount of vehicular traffic creates traffic congestion, unwanted delays, pollution, money loss, health issues, accidents, emergency vehicle passage and traffic…
Deep neural networks achieve state-of-the-art performance in a variety of tasks by extracting a rich set of features from unstructured data, however this performance is closely tied to model size. Modern techniques for inducing sparsity and…
Graphs have become pervasive tools to represent information and datasets with irregular support. However, in many cases, the underlying graph is either unavailable or naively obtained, calling for more advanced methods to its estimation.…
L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation for the calibration parameters is urgently needed. To alleviate the computational burden, we…
In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…
In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for…
Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is…
Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging…
To operate effectively in the real world, agents should be able to act from high-dimensional raw sensory input such as images and achieve diverse goals across long time-horizons. Current deep reinforcement and imitation learning methods can…
This article explores the estimation of precision matrices in high-dimensional Gaussian graphical models. We address the challenge of improving the accuracy of maximum likelihood-based precision estimation through penalization.…
Longitudinal analysis is important in many disciplines, such as the study of behavioral transitions in social science. Only very recently, feature selection has drawn adequate attention in the context of longitudinal modeling. Standard…