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Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by…
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),…
The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…
Motivated by the problem of inferring the graph structure of functional connectivity networks from multi-level functional magnetic resonance imaging data, we develop a valid inference framework for high-dimensional graphical models that…
In this work, we consider learning sparse models in large scale settings, where the number of samples and the feature dimension can grow as large as millions or billions. Two immediate issues occur under such challenging scenario: (i)…
Mathematical modelling, particularly through approaches such as structured sparse support vector machines (SS-SVM), plays a crucial role in processing data with complex feature structures, yet efficient algorithms for distributed…
Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large $K$) under a high-dimensional (large $p$) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…
Network theory has proven invaluable in unraveling complex protein interactions. Previous studies have employed statistical methods rooted in network theory, including the Gaussian graphical model, to infer networks among proteins,…
Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…
There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating…
We present a Lagrangian model of galaxy clustering bias in which we train a neural net using the local properties of the smoothed initial density field to predict the late-time mass-weighted halo field. By fitting the mass-weighted halo…
A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…
Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
Hashing learns compact binary codes to store and retrieve massive data efficiently. Particularly, unsupervised deep hashing is supported by powerful deep neural networks and has the desirable advantage of label independence. It is a…