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Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…
Advances in techniques for thermal sampling in classical and quantum systems would deepen understanding of the underlying physics. Unfortunately, one often has to rely solely on inexact numerical simulation, due to the intractability of…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
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…
The Kingman coalescent is a fundamental process in population genetics modelling the ancestry of a sample of individuals backwards in time. In this paper, in a large-sample-size regime, we study asymptotic properties of the coalescent under…
Various problems of any credit card fraud detection based on machine learning come from the imbalanced aspect of transaction datasets. Indeed, the number of frauds compared to the number of regular transactions is tiny and has been shown to…
This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies…
We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Sampling strategies have been widely applied in many recommendation systems to accelerate model learning from implicit feedback data. A typical strategy is to draw negative instances with uniform distribution, which however will severely…
Quantum re-uploading models have been extensively investigated as a form of machine learning within the context of variational quantum algorithms. Their trainability and expressivity are not yet fully understood and are critical to their…
When gene copies are sampled from various species, the resulting gene tree might disagree with the containing species tree. The primary causes of gene tree and species tree discord include lineage sorting, horizontal gene transfer, and gene…
High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates…
It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This…
Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Discovering valuable insights from data through meaningful associations is a crucial task. However, it becomes challenging when trying to identify representative patterns in quantitative databases, especially with large datasets, as…
Iterated sampling importance resampling (i-SIR) is a Markov chain Monte Carlo (MCMC) algorithm which is based on $N$ independent proposals. As $N$ grows, its samples become nearly independent, but with an increased computational cost. We…
The cost of deriving actionable knowledge from large datasets has been decreasing thanks to a convergence of positive factors: low cost data generation, inexpensively scalable storage and processing infrastructure (cloud), software…