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Graph embeddings are scalable and performant node representations in a graph. Fast Random Projections (FastRP) is claimed to be thousands of times faster to generate embeddings compared to random walk-based algorithms like DeepWalk and Node2Vec, while ...

For any n ∈ ℕ and d = o(loglog(n)), we prove that there is a Boolean function F on n bits and a value γ = 2^−Θ(d) such that F can be computed by a uniform depth-(d + 1) AC⁰ circuit with O(n) wires, but F cannot be computed by any depth-d TC⁰ circuit ...

We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized dimensionality reduction ...

We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension p grows proportionally to the number of observations n. Despite a number of prior work studying this problem, whether there exists ...

Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, ...

We show that for n points in d-dimensional Euclidean space, a data oblivious random projection of the columns onto m∈ O((logk+loglogn)ε⁻⁶log1/ε) dimensions is sufficient to approximate the cost of all k-means clusterings up to a multiplicative (1±ε) ...

Let ε∈(0,1) and X⊂^d be arbitrary with |X| having size n>1. The Johnson-Lindenstrauss lemma states there exists f:X→^m with m = O(ε⁻²logn) such that <table><tr><td> ∀ x∈ X ∀ y∈ X, ||x−y||₂ ≤ ||f(x)−f(y)||₂ ≤ (1+ε)||x−y||₂ . </td></tr></table> We show that ...

We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of AND, OR, and NOT gates. Our hierarchy theorem says that for every d ≥ 2, there is an explicit n-variable Boolean function f, computed by a linear-size depth-...

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In this paper, we ...

We show that any polynomial-size Frege refutation of a certain linear-size unsatisfiable 3-CNF formula over n variables must have depth Ω(√logn). This is an exponential improvement over the previous best results (Pitassi et al. 1993, Krajíček et al. ...

We show that any depth-d circuit for determining whether an n-node graph has an s-to-t path of length at most k must have size n^Ω(k1/d/d) when k(n) ≤ n^1/5, and n^Ω(k1/5d/d) when k(n)≤ n. The previous best circuit size lower bounds were n^{kexp(−O(d))} (by ...

Estimations of distribution algorithms EDAs are a major branch of evolutionary algorithms EA with some unique advantages in principle. They are able to take advantage of correlation structure to drive the search more efficiently, and they are able to ...

Content identification based on digital content fingerprinting attracts significant attention in different emerging applications. In this paper, we consider content identification based on the sign-magnitude decomposition of fingerprint codewords and ...

In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: what is the probability that a needle thrown randomly on a ground made of equispaced parallel strips lies on two ...

There is an alarming increase in the amount of malware that is generated today. However, several studies have shown that most of these new malware are just variants of existing ones. Fast detection of these variants plays an effective role in thwarting ...

The proliferation of the web presents an unsolved problem of automatically analyzing billions of pages of natural language. We introduce a scalable algorithm that clusters hundreds of millions of web pages into hundreds of thousands of clusters. It does ...

We present a new methodology for solving linear Support Vector Machines (SVMs) that capitalizes on multiple 1D projections. We show that the approach approximates the optimal solution with high accuracy and comes with analytical guarantees. Our solution ...

This paper considers the problem of distributed compressive detection under a perfect secrecy constraint. More specifically, we consider the problem where the distributed inference network operates in the presence of an eavesdropper who wants to ...

Kurtosis of 1D projections provides important statistical characteristics of natural images. In this work, we first provide a theoretical underpinning to a recently observed phenomenon known as projection kurtosis concentration that the kurtosis of ...

Predictive state representations (PSRs) offer an expressive framework for modelling partially observable systems. By compactly representing systems as functions of observable quantities, the PSR learning approach avoids using local-minima prone ...