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The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are…

Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling…

We study the random loop model with crosses and bars on sparse random graphs. Our main objective is to prove the existence of macroscopic loops, in the sense that a loop visits a positive proportion of the vertices. We develop a…

We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map $\mathcal{M}:\mathbb{R}^d\rightarrow \mathbb{R}$, which assigns to every point in space a real…

We study the classical Election problem in anonymous net- works, where solutions can rely on the use of random bits, which may be either shared or unshared among nodes. We provide a complete char- acterization of the conditions under which…

Let $A$ be a square matrix with a given structure (e.g. real matrix, sparsity pattern, Toeplitz structure, etc.) and assume that it is unstable, i.e. at least one of its eigenvalues lies in the complex right half-plane. The problem of…

Sparse models require less memory for storage and enable a faster inference by reducing the necessary number of FLOPs. This is relevant both for time-critical and on-device computations using neural networks. The stabilized lottery ticket…

Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…

This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with…

This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…

We consider rooted subgraphs in random graphs, i.e., extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three connecting two given vertices. In 1989, Spencer gave sufficient…

The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…

Recent work on deep neural network pruning has shown there exist sparse subnetworks that achieve equal or improved accuracy, training time, and loss using fewer network parameters when compared to their dense counterparts. Orthogonal to…

Learning algorithms that divide the data into batches are prevalent in many machine-learning applications, typically offering useful trade-offs between computational efficiency and performance. In this paper, we examine the benefits of…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…

In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…

Let f:=(f^1,\...,f^n) be a sparse random polynomial system. This means that each f^i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussian probability distribution of arbitrary variance. We express…

Bootstrapping can produce confidence levels for hypotheses about quadratic regression models - such as whether the U-shape is inverted, and the location of optima. The method has several advantages over conventional methods: it provides…

The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…