Related papers: An approximation algorithm for random generation o…
We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
Previous work identifying depth-optimal $n$-channel sorting networks for $9\leq n \leq 16$ is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper…
Synthetic likelihood is an attractive approach to likelihood-free inference when an approximately Gaussian summary statistic for the data, informative for inference about the parameters, is available. The synthetic likelihood method derives…
In this paper, we develop approximate dynamic programming methods for stochastic systems modeled as Markov Decision Processes, given both soft performance criteria and hard constraints in a class of probabilistic temporal logic called…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art…
We propose a randomized algorithm for enumerating the vertices of a zonotope, which is a low-dimensional linear projection of a hypercube. The algorithm produces a pair of the zonotope's vertices by sampling a random linear combination of…
Given a n points in two dimensional space, a Manhattan Network G is a network that connects all n points with either horizontal or vertical edges, with the property that for any two point in G should be connected by a Manhattan path and…
We define a notion of isotropy for discrete set distributions. If $\mu$ is a distribution over subsets $S$ of a ground set $[n]$, we say that $\mu$ is in isotropic position if $P[e \in S]$ is the same for all $e\in [n]$. We design a new…
We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an…
We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…
We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
This paper investigates the approximation power of three types of random neural networks: (a) infinite width networks, with weights following an arbitrary distribution; (b) finite width networks obtained by subsampling the preceding…
We present a new approach to the bootstrap for chains of infinite order taking values on a finite alphabet. It is based on a sequential Bootstrap Central Limit Theorem for the sequence of canonical Markov approximations of the chain of…
We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…
The problem of implementing a class of functions with particular conditions by using monotonic multilayer functions is considered. A genetic algorithm is used to create monotonic functions of a certain class, and these are implemented with…
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the…