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Modern statistical analysis often encounters datasets with large sizes. For these datasets, conventional estimation methods can hardly be used immediately because practitioners often suffer from limited computational resources. In most…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. However, most of current batch approaches do not scale well with the batch size. That is, their performances…
Automatic prompt optimization reduces manual prompt engineering, but relies on task performance measured on a small, often randomly sampled evaluation subset as its main source of feedback signal. Despite this, how to select that evaluation…
The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter…
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…
Importance Sampling methods are broadly used to approximate posterior distributions or some of their moments. In its standard approach, samples are drawn from a single proposal distribution and weighted properly. However, since the…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
We consider the problem of subset selection for $\ell_{p}$ subspace approximation, i.e., given $n$ points in $d$ dimensions, we need to pick a small, representative subset of the given points such that its span gives $(1+\epsilon)$…
This article introduces subbagging (subsample aggregating) estimation approaches for big data analysis with memory constraints of computers. Specifically, for the whole dataset with size $N$, $m_N$ subsamples are randomly drawn, and each…
Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this…
Image segmentation methods are usually trained with pixel-level annotations, which require significant human effort to collect. The most common solution to address this constraint is to implement weakly-supervised pipelines trained with…
Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become…
A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
Data reduction is a fundamental challenge of modern technology, where classical statistical methods are not applicable because of computational limitations. We consider multiple linear regression for an extraordinarily large number of…
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…
Machine learning systems have been extensively used as auxiliary tools in domains that require critical decision-making, such as healthcare and criminal justice. The explainability of decisions is crucial for users to develop trust on these…
A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies…
With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter to have likelihood functions that elude analytical formulations. Even…