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We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction…
Determinantal points processes are a promising but relatively under-developed tool in machine learning and statistical modelling, being the canonical statistical example of distributions with repulsion. While their mathematical formulation…
Importance sampling (IS) is an important technique to reduce the estimation variance in Monte Carlo simulations. In many practical problems, however, the use of IS method may result in unbounded variance, and thus fail to provide reliable…
Recent advances in Markov chain Monte Carlo (MCMC) extend the scope of Bayesian inference to models for which the likelihood function is intractable. Although these developments allow us to estimate model parameters, other basic problems…
The inefficiency of using an unbiased estimator in a Monte Carlo procedure can be quantified using an inefficiency constant, equal to the product of the variance of the estimator and its mean computational cost. We develop methods for…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
Auxiliary variable is extensively used in survey sampling to improve the precision of estimates. Whenever there is availability of auxiliary information, we want to utilize it in the method of estimation to obtain the most efficient…
Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology…
When the target parameter for inference is a real-valued, continuous function of probabilities in the $k$-sample multinomial problem, variance estimation may be challenging. In small samples or when the function is nondifferentiable at the…
Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies…
In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the…
We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
In the field of structural reliability, the Monte-Carlo estimator is considered as the reference probability estimator. However, it is still untractable for real engineering cases since it requires a high number of runs of the model. In…