Related papers: Asymptotically optimum estimation of a probability…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size…
We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…
Stochastic linear bandits are a natural and simple generalisation of finite-armed bandits with numerous practical applications. Current approaches focus on generalising existing techniques for finite-armed bandits, notably the optimism…
Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection…
In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…
We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum…
We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator that estimates vectors from with a controlled associated…
The probability of benefit is a valuable and important measure of treatment effect, which has advantages over the average treatment effect. Particularly for an ordinal outcome, it has a better interpretation and can make apparent different…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
This paper presents a model-agnostic ensemble approach for supervised learning. The proposed approach is based on a parametric version of Random Subspace, in which each base model is learned from a feature subset sampled according to a…
We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…
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…
Sequential detection of independent anomalous processes among K processes is considered. At each time, only M processes can be observed, and the observations from each chosen process follow two different distributions, depending on whether…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be…