Related papers: Randomness-efficient Curve Samplers
Reconstructing a finite set of curves from an unordered set of sample points is a well studied topic. There has been less effort that considers how much better the reconstruction can be if tangential information is given as well. We show…
A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to…
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving…
The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…
Slice sampling is an efficient Markov Chain Monte Carlo algorithm to sample from an unnormalized density with acceptance ratio always $1$. However, when the variable to sample is unbounded, its "stepping-out" heuristic works only locally,…
Uncertainty sampling, a popular active learning algorithm, is used to reduce the amount of data required to learn a classifier, but it has been observed in practice to converge to different parameters depending on the initialization and…
Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…
Consistent sampling is a technique for specifying, in small space, a subset $S$ of a potentially large universe $U$ such that the elements in $S$ satisfy a suitably chosen sampling condition. Given a subset $\mathcal{I}\subseteq U$ it…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…