Related papers: An effective Procedure for Speeding up Algorithms
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
Kolmogorov complexity is the length of the ultimately compressed version of a file (that is, anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query…
The growing amount of high dimensional data in different machine learning applications requires more efficient and scalable optimization algorithms. In this work, we consider combining two techniques, parallelism and Nesterov's…
A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…
We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…
Most exact algorithms for general partially observable Markov decision processes (POMDPs) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
We study the problem of scheduling $n$ independent moldable tasks on $m$ processors that arises in large-scale parallel computations. When tasks are monotonic, the best known result is a $(\frac{3}{2}+\epsilon)$-approximation algorithm for…
Decoding for many NLP tasks requires an effective heuristic algorithm for approximating exact search since the problem of searching the full output space is often intractable, or impractical in many settings. The default algorithm for this…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
Computing a minimum $s$-$t$ cut in a graph is a solution to a wide range of computer vision problems, and is often done using the Boykov-Kolmogorov (BK) algorithm. In this paper, we revisit the BK algorithm from both a theoretical and…
For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every…
We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…
We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel…
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover…