Related papers: Exact Inference with Approximate Computation for D…
This paper concerns differentially private Bayesian estimation of the parameters of a population distribution, when a statistic of a sample from that population is shared in noise to provide differential privacy. This work mainly addresses…
Large language models (LLMs), especially those based on the Transformer architecture, have had a profound impact on various aspects of daily life, such as natural language processing, content generation, research methodologies, and more.…
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…
Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…
Reliable uncertainty estimation is crucial for machine learning models, especially in safety-critical domains. While exact Bayesian inference offers a principled approach, it is often computationally infeasible for deep neural networks.…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
Approximate Bayesian Computation (ABC) methods are commonly used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Classical ABC methods are based on nearest neighbor type algorithms…
Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional…
A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…
Many differentially private (DP) data release systems either output DP synthetic data and leave analysts to perform inference as usual, which can lead to severe miscalibration, or output a DP point estimate without a principled way to do…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
Many practical problems involve estimating low dimensional statistical quantities with high-dimensional models and datasets. Several approaches address these estimation tasks based on the theory of influence functions, such as…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
The likelihood-free sequential Approximate Bayesian Computation (ABC) algorithms, are increasingly popular inference tools for complex biological models. Such algorithms proceed by constructing a succession of probability distributions over…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…