Related papers: Lessons from the German Tank Problem
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
We consider the minimax setup for Gaussian one-armed bandit problem, i.e. the two-armed bandit problem with Gaussian distributions of incomes and known distribution corresponding to the first arm. This setup naturally arises when the…
Epidemiologists have a growing interest in employing computational approaches to solve analytic problems, with simulation being arguably the most accessible among all approaches. While previous literature discussed the utility of simulation…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
Machine teaching addresses the problem of finding the best training data that can guide a learning algorithm to a target model with minimal effort. In conventional settings, a teacher provides data that are consistent with the true data…
In sports, individuals and teams are typically interested in final rankings. Final results, such as times or distances, dictate these rankings, also known as places. Places can be further associated with ordered random variables, commonly…
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…
The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with $n$ anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity.…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
We consider the problem of retrieving the most relevant labels for a given input when the size of the output space is very large. Retrieval methods are modeled as set-valued classifiers which output a small set of classes for each input,…
Hierarchically-organized data arise naturally in many psychology and neuroscience studies. As the standard assumption of independent and identically distributed samples does not hold for such data, two important problems are to accurately…
We focus on the problem of best-arm identification in a stochastic multi-arm bandit with temporally decreasing variances for the arms' rewards. We model arm rewards as Gaussian random variables with fixed means and variances that decrease…
After more than 80 years from the seminal work of Weizs\"acker and the liquid drop model of the atomic nucleus, deviations from experiments of mass models ($\sim$ MeV) are orders of magnitude larger than experimental errors ($\lesssim$…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
Maximum subarray is a classical problem in computer science that given an array of numbers aims to find a contiguous subarray with the largest sum. We focus on its use for a noisy statistical problem of localizing an interval with a mean…
We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and…
Over the past few years, the multi-armed bandit model has become increasingly popular in the machine learning community, partly because of applications including online content optimization. This paper reviews two different sequential…
A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…
Let a stick be broken at random at n-1 points to form n pieces. We consider three problems on forming k-gons with k out of these n pieces, and show how a statistical approach, through a linear transformation of variables, yields simple…