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The performance of a machine learning system is usually evaluated by using i.i.d.\ observations with true labels. However, acquiring ground truth labels is expensive, while obtaining unlabeled samples may be cheaper. Stratified sampling can…
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
We study the problem of estimating the probability density function of a circular random variable subject to censoring. To this end, we propose a fully computable quotient estimator that combines a projection estimator on linear sieves with…
Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
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 a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an…
Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory,…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques…