Related papers: Sparse Gaussian Graphical Models with Discrete Opt…
Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clustering structure of the concentration matrix is enforced to…
State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However,…
The sparse representation of graphs has shown great potential for accelerating the computation of graph applications (e.g., Social Networks, Knowledge Graphs) on traditional computing architectures (CPU, GPU, or TPU). But the exploration of…
Time-series datasets are central in machine learning with applications in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs),…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
This paper suggests a nonparametric scheme to find the sparse solution of the underdetermined system of linear equations in the presence of unknown impulsive or non-Gaussian noise. This approach is robust against any variations of the noise…
We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…
A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…
We give a simple, multiplicative-weight update algorithm for learning undirected graphical models or Markov random fields (MRFs). The approach is new, and for the well-studied case of Ising models or Boltzmann machines, we obtain an…
Sparse variable selection improves interpretability and generalization in high-dimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…