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Robust learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While probably approximately correct (PAC) Semantics…
Let $V$ be any vector space of multivariate degree-$d$ homogeneous polynomials with co-dimension at most $k$, and $S$ be the set of points where all polynomials in $V$ {\em nearly} vanish. We establish a qualitatively optimal upper bound on…
We consider principled alternatives to unsupervised learning in data mining by situating the learning task in the context of the subsequent analysis task. Specifically, we consider a query-answering (hypothesis-testing) task: In the…
We propose a new approach to address the text classification problems when learning with partial labels is beneficial. Instead of offering each training sample a set of candidate labels, we assign negative-oriented labels to the ambiguous…
Partial-label learning is a popular weakly supervised learning setting that allows each training example to be annotated with a set of candidate labels. Previous studies on partial-label learning only focused on the classification setting…
In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…
In this paper, we analyze the convergence %semi-convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of…
How to design fair and (computationally) efficient voting rules is a central challenge in Computational Social Choice. In this paper, we aim at designing efficient algorithms for computing most equitable rules for large classes of…
A locally testable semigroup S is a semigroup with the property that for some nonnegative integer k, called the order or level of local testability, two words u and v in some set of generators for semigroup S are equal in the semigroup if…
We consider polynomial optimization problems on Cartesian products of basic compact semialgebraic sets. The solution of such problems can be approximated as closely as desired by hierarchies of semidefinite programming relaxations, based on…
Weakly supervised text classification methods typically train a deep neural classifier based on pseudo-labels. The quality of pseudo-labels is crucial to final performance but they are inevitably noisy due to their heuristic nature, so…
Binary classification from positive-only samples is a variant of PAC learning where the learner receives i.i.d. positive samples and aims to learn a classifier with low error. Previous work by Natarajan, Gereb-Graus, and Shvaytser…
Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since…
We study distribution-free property testing and learning problems where the unknown probability distribution is a product distribution over $\mathbb{R}^d$. For many important classes of functions, such as intersections of halfspaces,…
We show that the class of strongly connected graphical models with treewidth at most k can be properly efficiently PAC-learnt with respect to the Kullback-Leibler Divergence. Previous approaches to this problem, such as those of Chow ([1]),…
This paper investigates the problem of safety certification for black-box discrete-time stochastic systems, where both the system dynamics and disturbance distributions are unknown, and only sampled data are available. Under such limited…
In the realm of cross-modal retrieval, seamlessly integrating diverse modalities within multimedia remains a formidable challenge, especially given the complexities introduced by noisy correspondence learning (NCL). Such noise often stems…
We consider the well-studied problem of learning intersections of halfspaces under the Gaussian distribution in the challenging \emph{agnostic learning} model. Recent work of Diakonikolas et al. (2021) shows that any Statistical Query (SQ)…
The notions of cutwidth and pathwidth of digraphs play a central role in the containment theory for tournaments, or more generally semi-complete digraphs, developed in a recent series of papers by Chudnovsky, Fradkin, Kim, Scott, and…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…