Related papers: A rapid algorithm to calculate joint probability m…
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
In the last few years, much effort has been devoted to developing join algorithms in order to achieve worst-case optimality for join queries over relational databases. Towards this end, the database community has had considerable success in…
We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…
A probabilistic query may not be estimable from observed data corrupted by missing values if the data are not missing at random (MAR). It is therefore of theoretical interest and practical importance to determine in principle whether a…
The key issue in importance sampling is the choice of the alternative sampling distribution, which is often chosen from the exponential tilt family of the underlying distribution. However, when the problem exhibits certain kind of…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
Discovering "good" algorithms for an operation is often considered an art best left to experts. What if there is a simple methodology, an algorithm, for systematically deriving a family of algorithms as well as their cost analyses, so that…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
In maximum-likelihood quantum state tomography, both the sample size and dimension grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic first-order method, just like stochastic gradient descent for…
Generalized mutual entropy is defined for networks and applied for analysis of complex network structures. The method is tested for the case of computer simulated scale free networks, random networks, and their mixtures. The possible…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…
We give the first sorting algorithm with bounds in terms of higher-order entropies: let $S$ be a sequence of length $m$ containing $n$ distinct elements and let (H_\ell (S)) be the $\ell$th-order empirical entropy of $S$, with (n^{\ell + 1}…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe…