相关论文: Kelly Criterion: From a Simple Random Walk to L\'{…

Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…

Sports analytics -- broadly defined as the pursuit of improvement in athletic performance through the analysis of data -- has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this…

Fixed-budget theory is concerned with computing or bounding the fitness value achievable by randomized search heuristics within a given budget of fitness function evaluations. Despite recent progress in fixed-budget theory, there is a lack…

Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose…

In Major League Baseball, strategy and planning are major factors in determining the outcome of a game. Previous studies have aided this by building machine learning models for predicting the winning team of any given game. We extend this…

Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter $\theta$…

We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely…

We prove game-theoretic versions of several classical results on nonrepetitive sequences, showing the existence of winning strategies using an extension of the Lov\'asz Local Lemma which can dramatically reduce the number of edges needed in…

Humanity has been fascinated by the pursuit of fortune since time immemorial, and many successful outcomes benefit from strokes of luck. But success is subject to complexity, uncertainty, and change - and at times becoming increasingly…

Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also…

Stochastic clocks represent a class of time change methods for incorporating trading activity into continuous-time financial models, with the ability to deal with typical asymmetrical and tail risks in financial returns. In this paper we…

We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit…

Tournaments can be used to model a variety of practical scenarios including sports competitions and elections. A natural notion of strength of alternatives in a tournament is a generalized king: an alternative is said to be a $k$-king if it…

I unravel the basic long run dynamics of the broker call money market, which is the pile of cash that funds margin loans to retail clients (read: continuous time Kelly gamblers). Call money is assumed to supply itself perfectly…

Fairness-aware learning studies the development of algorithms that avoid discriminatory decision outcomes despite biased training data. While most studies have concentrated on immediate bias in static contexts, this paper highlights the…

This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger (2002) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…