Related papers: The Nonconvex Geometry of Linear Inverse Problems

Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…

We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…

In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity…

Similarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large,…

Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

We consider the problem of selective inference after solving a (randomized) convex statistical learning program in the form of a penalized or constrained loss function. Our first main result is a change-of-measure formula that describes…

We study the problem of minimizing the average of a very large number of smooth functions, which is of key importance in training supervised learning models. One of the most celebrated methods in this context is the SAGA algorithm. Despite…

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…

Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph…

In numerical linear algebra, a well-established practice is to choose a norm that exploits the structure of the problem at hand in order to optimize accuracy or computational complexity. In numerical polynomial algebra, a single norm…

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…

In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from…

Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…

A wide range of graph learning tasks, such as structure discovery, temporal graph analysis, and combinatorial optimization, focus on inferring graph structures from data, rather than making predictions on given graphs. However, the…

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…