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Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble. An estimate of a mechanical property, like energy, of an equilibrium system, can be made by averaging over a large number…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
A central task of artificial intelligence is the design of artificial agents that act towards specified goals in partially observed environments. Since such environments frequently include interaction over time with other agents with their…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
Ensemble weather forecasts enable a measure of uncertainty to be attached to each forecast, by computing the ensemble's spread. However, generating an ensemble with a good spread-error relationship is far from trivial, and a wide range of…
We present a method for calibrating the Ensemble of Exemplar SVMs model. Unlike the standard approach, which calibrates each SVM independently, our method optimizes their joint performance as an ensemble. We formulate joint calibration as a…
We provide an efficient unified plug-in approach for estimating symmetric properties of distributions given $n$ independent samples. Our estimator is based on profile-maximum-likelihood (PML) and is sample optimal for estimating various…
Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method,…
Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…
This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…
Envelope methodology is succinctly pitched as a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives \citep[first sentence of page 1]{cook2018introduction}. This description is true…
Since Rendle and Krichene argued that commonly used sampling-based evaluation metrics are "inconsistent" with respect to the global metrics (even in expectation), there have been a few studies on the sampling-based recommender system…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…
For systems that self assemble into finite-sized objects, it is sometimes convenient to compute the thermodynamics for a small system where a single assembly can form. However, we show that in the canonical ensemble the use of small systems…
The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…
The free energetics of water density fluctuations in bulk water, at interfaces, and in hydrophobic confinement inform the hydration of hydrophobic solutes as well as their interactions and assembly. The characterization of such free…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
This paper develops a variance estimation framework for matching estimators that enables valid population inference for treatment effects. We provide theoretical analysis of a variance estimator that addresses key limitations in the…