Related papers: Fast Bayesian Updates via Harmonic Representations

Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…

Fast convolution algorithms, including Winograd and FFT, can efficiently accelerate convolution operations in deep models. However, these algorithms depend on high-precision arithmetic to maintain inference accuracy, which conflicts with…

This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…

Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs…

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

Neural networks are powerful function approximators with tremendous potential in learning complex distributions. However, they are prone to overfitting on spurious patterns. Bayesian inference provides a principled way to regularize neural…

We present a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of…

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…

A Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte Carlo methods are generally used to compute the predictive.…

We first review the convolution fast-Fourier-transform (CFFT) approach for the numerical solution of backward stochastic differential equations (BSDEs) introduced in (Hyndman and Oyono Ngou, 2017). We then propose a method for improving the…

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…

The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…