Related papers: Divide and Conquer in Non-standard Problems and th…
We provide a comprehensive characterisation of the theoretical properties of the divide-and-conquer sequential Monte Carlo (DaC-SMC) algorithm. We firmly establish it as a well-founded method by showing that it possesses the same basic…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n…
Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard assessment tools for such outcomes (e.g. deviance residuals) often show a large discrepancy from the…
Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…
Doubly robust estimators of causal effects are a popular means of estimating causal effects. Such estimators combine an estimate of the conditional mean of the outcome given treatment and confounders (the so-called outcome regression) with…
A fundamental functional in nonparametric statistics is the Mann-Whitney functional ${\theta} = P (X < Y )$ , which constitutes the basis for the most popular nonparametric procedures. The functional ${\theta}$ measures a location or…
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…
Consider a quite arbitrary (semi)parametric model with a Euclidean parameter of interest and assume that an asymptotically (semi)parametrically efficient estimator of it is given. If the parameter of interest is known to lie on a general…
This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the…
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…
A fundamental challenge in semi-supervised learning lies in the observed data's disproportional size when compared with the size of the data collected with missing outcomes. An implicit understanding is that the dataset with missing…
Universal probabilistic programming systems (PPSs) provide a powerful framework for specifying rich probabilistic models. They further attempt to automate the process of drawing inferences from these models, but doing this successfully is…
Bayesian computational algorithms tend to scale poorly as data size increases. This has motivated divide-and-conquer-based approaches for scalable inference. These divide the data into subsets, perform inference for each subset in parallel,…
Divide and Conquer (DC) is conceptually well suited to high-dimensional optimization by decomposing a problem into multiple small-scale sub-problems. However, appealing performance can be seldom observed when the sub-problems are…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…