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We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d samples. While there have been recent results for specific graph classes, these involve…
Recently, a novel coded compressed sensing (CCS) approach was proposed in [1] for dealing with the scalability problem for large sensing matrices in massive machine-type communications. The approach is to divide the compressed sensing (CS)…
Most explainable AI (XAI) frameworks are limited in their expressiveness, summarizing complex feature effects as single scalar values \phi_i. This approach answers "what" features are important but fails to reveal "how" they interact.…
We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…
Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in data analysis. The PCA direction is a linear combination of all features with nonzero loadings -- this impedes interpretability. Sparse PCA…
Given a random $n \times n$ symmetric matrix $\boldsymbol W$ drawn from the Gaussian orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the maximum value of the quadratic form $\boldsymbol x^\top \boldsymbol…
We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…
The increasing heterogeneity of high-performance computing (HPC) systems and the transition to exascale architectures require systematic and reproducible performance evaluation across diverse workloads. While continuous integration (CI)…
In this paper, we propose a scalable and highly efficient index structure for the reachability problem over graphs. We build on the well-known node interval labeling scheme where the set of vertices reachable from a particular node is…
For supervised classification problems involving design, control, other practical purposes, users are not only interested in finding a highly accurate classifier, but they also demand that the obtained classifier be easily interpretable.…
Hierarchical Classification (HC) is a supervised learning problem where unlabeled instances are classified into a taxonomy of classes. Several methods that utilize the hierarchical structure have been developed to improve the HC…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…
Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and…
We demonstrate that techniques of Weihrauch complexity can be used to get easy and elegant proofs of known and new results on initial value problems. Our main result is that solving continuous initial value problems is Weihrauch equivalent…
Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string over S. A "secondary index" for x answers alphabet range queries of the form: Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in [a_l;…
Let $\Lambda=\{\Lambda_0,\Lambda_1,\Lambda_2,\ldots\}$ be the point process that describes the edge scaling limit of either (i) "regular" beta-ensembles with inverse temperature $\beta>0$, or (ii) the top eigenvalues of Wishart or Gaussian…
Designing an embedding retrieval system requires navigating a complex design space of conflicting trade-offs between efficiency and effectiveness. This work structures these decisions as a vertical traversal of the system design stack. We…
A work of Sorensen is rewritten here to include nontrivial types at the infinite places. This extends results of K. Ribet and R. Taylor on level-raising for algebraic modular forms on D^{\times}, where D is a definite quaternion algebra…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…