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The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
Recent breakthroughs in high-resolution imaging of biomolecules in solution with cryo-electron microscopy (cryo-EM) have unlocked new doors for the reconstruction of molecular volumes, thereby promising further advances in biology,…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
After a quick review of the framework for phenomenological analyses of supersymmetry, we summarize current limits on supersymmetric particle masses and discuss strategies for their searches at the Fermilab Tevatron and the LHC. We also…
In signal detection problems, one is usually faced with the task of searching a parameter space for peaks in the likelihood function which indicate the presence of a signal. Random searches have proven to be very efficient as well as easy…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
Keyword-based search in text-rich multi-dimensional datasets facilitates many novel applications and tools. In this paper, we consider objects that are tagged with keywords and are embedded in a vector space. For these datasets, we study…
Space-filling designs such as scrambled-Hammersley, Latin Hypercube Sampling and Jittered Sampling have been proposed for fully parallel hyperparameter search, and were shown to be more effective than random or grid search. In this paper,…
We present a novel approach to template matching that is efficient, can handle partial occlusions, and comes with provable performance guarantees. A key component of the method is a reduction that transforms the problem of searching a…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the…
The paper presents a comprehensive performance evaluation of some heuristic search algorithms in the context of autonomous systems and robotics. The objective of the study is to evaluate and compare the performance of different search…
Traditional retrieval methods have been essential for assessing document similarity but struggle with capturing semantic nuances. Despite advancements in latent semantic analysis (LSA) and deep learning, achieving comprehensive semantic…
We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the…
We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…