相关论文: Statistical Curse of the Second Half Rank
The role of skill (fitness) and luck (randomness) as driving forces on the dynamics of resource accumulation in a myriad of systems have long puzzled scientists. Fueled by undisputed inequalities that emerge from actual competitions, there…
Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over-subscribed schools using randomly assigned lottery numbers, non-lottery tie-breakers like test scores, or…
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
The leaderboard in machine learning competitions is a tool to show the performance of various participants and to compare them. However, the leaderboard quickly becomes no longer accurate, due to hack or overfitting. This article gives two…
In this paper, we penalised the standard random walk by several functions of its maximum. The aim is to show that in spite of very close penalisation functions, under the new probabilities, the canonical process behaves very differently.
Scoring models support decision-making in financial institutions. Their estimation and evaluation are based on the data of previously accepted applicants with known repayment behavior. This creates sampling bias: the available labeled data…
A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…
We consider the problem of estimating a structured multivariate density, subject to Markov conditions implied by an undirected graph. In the worst case, without Markovian assumptions, this problem suffers from the curse of dimensionality.…
A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…
In the double rank analysis of research publications, the local rank position of a country or institution publication is expressed as a function of the world rank position. Excluding some highly or lowly cited publications, the double rank…
The Josephus problem is a well--studied elimination problem consisting in determining the position of the survivor after repeated applications of a deterministic rule removing one person at a time from a given group. A natural probabilistic…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
When solving large scale semidefinite programs that admit a low-rank solution, an efficient heuristic is the Burer-Monteiro factorization: instead of optimizing over the full matrix, one optimizes over its low-rank factors. This reduces the…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
In a binary classification problem where the goal is to fit an accurate predictor, the presence of corrupted labels in the training data set may create an additional challenge. However, in settings where likelihood maximization is poorly…
While rankings are at the heart of social science research, little is known about how to analyze ranking data in experimental studies. This paper introduces a potential-outcomes framework to perform causal inference when outcome data are…
Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal…
Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we…
The quality of consequences in a decision making problem under (severe) uncertainty must often be compared among different targets (goals, objectives) simultaneously. In addition, the evaluations of a consequence's performance under the…
Statistical algorithms are usually helping in making decisions in many aspects of our lives. But, how do we know if these algorithms are biased and commit unfair discrimination of a particular group of people, typically a minority?…