Related papers: Distribution Compression in Near-linear Time
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…
We consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…
Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…
Optimal control synthesis in stochastic systems with respect to quantitative temporal logic constraints can be formulated as linear programming problems. However, centralized synthesis algorithms do not scale to many practical systems. To…
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…
A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…
Grammar compression is a general compression framework in which a string $T$ of length $N$ is represented as a context-free grammar of size $n$ whose language contains only $T$. In this paper, we focus on studying the limitations of…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
In systems of programmable matter, we are given a collection of simple computation elements (or particles) with limited (constant-size) memory. We are interested in when they can self-organize to solve system-wide problems of movement,…
A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…
The mean squared error and regularized versions of it are standard loss functions in supervised machine learning. However, calculating these losses for large data sets can be computationally demanding. Modifying an approach of J. Dick and…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
Consider the problem of predicting the next symbol given a sample path of length n, whose joint distribution belongs to a distribution class that may have long-term memory. The goal is to compete with the conditional predictor that knows…
Quantization is a widely used technique to compress and accelerate deep neural networks. However, conventional quantization methods use the same bit-width for all (or most of) the layers, which often suffer significant accuracy degradation…
We propose a communication and computation efficient second-order method for distributed optimization. For each iteration, our method only requires $\mathcal{O}(d)$ communication complexity, where $d$ is the problem dimension. We also…
Time series data from a variety of sensors and IoT devices need effective compression to reduce storage and I/O bandwidth requirements. While most time series databases and systems rely on lossless compression, lossy techniques offer even…
Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…
We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…