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By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Boson sampling is a problem intractable for classical computers, but can be naturally solved on a specialized photonic quantum simulator which requires less resources than building a universal quantum computer. The biggest challenge to…

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…

In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental goals. The first, and the most…

Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…

Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms.Here, we introduce…

Increased access to computing resources has led to the development of algorithms that can run efficiently on multi-core processing units or in distributed computing environments. In the context of Bayesian inference, many parallel computing…

Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there is evidence that noiseless Gaussian boson sampling is hard to efficiently simulate using a classical computer, the current Gaussian…

Estimating the number of components is a fundamental challenge in unsupervised learning, particularly when dealing with high-dimensional data with many components or severely imbalanced component sizes. This paper addresses this challenge…

We study the classical complexity of the exact Boson Sampling problem where the objective is to produce provably correct random samples from a particular quantum mechanical distribution. The computational framework was proposed by Aaronson…

Although the Schr{\"o}dinger and Heisenberg pictures are equivalent formulations of quantum mechanics, simulations performed choosing one over the other can greatly impact the computational resources required to solve a problem. Here we…

We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed…

Gaussian boson sampling (GBS) has emerged as a promising quantum computing paradigm, demonstrating its potential in various applications. However, most existing works focus on theoretical aspects or simple tasks, with limited exploration of…

We discuss an efficient implementation of the iterative proportional scaling procedure in the multivariate Gaussian graphical models. We show that the computational cost can be reduced by localization of the update procedure in each…

We present a novel extension of Thompson Sampling for stochastic sequential decision problems with graph feedback, even when the graph structure itself is unknown and/or changing. We provide theoretical guarantees on the Bayesian regret of…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

Boson sampling devices are a prime candidate for exhibiting quantum supremacy, yet their application for solving problems of practical interest is less well understood. Here we show that Gaussian boson sampling (GBS) can be used for dense…

Boson sampling has been theoretically proposed and experimentally demonstrated to show quantum computational advantages. However, it still lacks the deep understanding of the practical applications of boson sampling. Here we propose that…