Related papers: Hamming distance completeness and sparse matrix mu…
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the persistence diagrams associated with the convex combinations…
We design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in…
We introduce a class of paired binary matrices called admixed arrays, which arise in analyses of large-scale genetic data and can be viewed as weighted edge colorings of complete bipartite graphs. This combinatorial structure gives rise to…
Feature hashing, also known as {\em the hashing trick}, introduced by Weinberger et al. (2009), is one of the key techniques used in scaling-up machine learning algorithms. Loosely speaking, feature hashing uses a random sparse projection…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in $O(\log^2{n} / \epsilon)$ rounds on unweighted…
Most research into similarity search in metric spaces relies upon the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations $\pi$ and $\tau$, represented as sequences of integers, and the task is to determine whether $\tau$ contains a subsequence order-isomorphic to…
Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$ f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1, $$ where…
We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as…
We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for…
Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…
To multiply astronomic matrices using parallel workers subject to straggling, we recommend interleaving checksums with some fast matrix multiplication algorithms. Nesting the parity-checked algorithms, we weave a product code flavor…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
The number-theoretic codes are a class of codes defined by single or multiple congruences and are mainly used for correcting insertion and deletion errors. Since the number-theoretic codes are generally non-linear, the analysis method for…
We present a new similarity measure based on information theoretic measures which is superior than Normalized Compression Distance for clustering problems and inherits the useful properties of conditional Kolmogorov complexity. We show that…
Recent work has highlighted the centrality of smooth calibration [Kakade and Foster, 2008] as a robust measure of calibration error. We generalize, unify, and extend previous results on smooth calibration, both as a robust calibration…