Related papers: Exploiting ideal-sparsity in the generalized momen…
Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
Let A be an M by N matrix (M < N) which is an instance of a real random Gaussian ensemble. In compressed sensing we are interested in finding the sparsest solution to the system of equations A x = y for a given y. In general, whenever the…
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while…
We consider the problem of learning the underlying graph of a sparse Ising model with $p$ nodes from $n$ i.i.d. samples. The most recent and best performing approaches combine an empirical loss (the logistic regression loss or the…
Many problems require the selection of a subset of variables from a full set of optimization variables. The computational complexity of an exhaustive search over all possible subsets of variables is, however, prohibitively expensive,…
Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study…
Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…
Nonnegative Matrix Factorization (NMF) is a widely applied technique in the fields of machine learning and data mining. Graph Regularized Non-negative Matrix Factorization (GNMF) is an extension of NMF that incorporates graph regularization…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Many modern data analysis algorithms either assume that or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimensionality reduction.…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved non convex…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
We develop a principled way of identifying probability distributions whose independent and identically distributed (iid) realizations are compressible, i.e., can be well-approximated as sparse. We focus on Gaussian random underdetermined…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions.…