Related papers: On computing and the complexity of computing highe…
A \emph{tensor-relational} computation is a relational computation where individual tuples carry vectors, matrices, or higher-dimensional arrays. An advantage of tensor-relational computation is that the overall computation can be executed…
Besides tensor contractions, one of the most pronounced computational bottlenecks in the non-orthogonally spin-adapted forms of the quantum chemistry methods CCSDT and CCSDTQ, and their approximate forms---including CCSD(T) and…
Probabilistic programming methods have revolutionised Bayesian inference, making it easier than ever for practitioners to perform Markov-chain-Monte-Carlo sampling from non-conjugate posterior distributions. Here we focus on Stan, arguably…
Informatics and technological advancements have triggered generation of huge volume of data with varied complexity in its management and analysis. Big Data analytics is the practice of revealing hidden aspects of such data and making…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
Union-Find (or Disjoint-Set Union) is one of the fundamental problems in computer science; it has been well-studied from both theoretical and practical perspectives in the sequential case. Recently, there has been mounting interest in…
This paper presents a new method, which we call SUSTain, that extends real-valued matrix and tensor factorizations to data where values are integers. Such data are common when the values correspond to event counts or ordinal measures. The…
A recently discovered universal rank-based matrix method to extract trends from noisy time series is described in [1] but the formula for the output matrix elements, implemented there as an open-access supplement MATLAB computer code, is…
Applications integrating analysis components require a programmable interface which defines statistical operations independently of any programming language. By separating concerns of scientific computing from application and implementation…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
Data-based classification is fundamental to most branches of science. While recent years have brought enormous progress in various areas of statistical computing and clustering, some general challenges in clustering remain: model selection,…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…