相关论文: Pass the Buck on a Complete Binary Tree
When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average…
In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns…
In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…
Strong Branching (SB) is a cornerstone of all modern branching rules used in the Branch-and-Bound (BnB) algorithm, which is at the center of Mixed-Integer Programming solvers. In its full form, SB evaluates all variables to branch on and…
American football is an increasingly popular sport, with a growing audience in many countries in the world. The most watched American football league in the world is the United States' National Football League (NFL), where every offensive…
Stochastic branching processes are a classical model for describing random trees, which have applications in numerous fields including biology, physics, and natural language processing. In particular, they have recently been proposed to…
In the broadcasting problem on trees, a $\{-1,1\}$-message originating in an unknown node is passed along the tree with a certain error probability $q$. The goal is to estimate the original message without knowing the order in which the…
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…
A popular challenge on the social media app TikTok is to place the output of a random number generator in ascending order without arriving at a contradiction. Most players rely on intuition to construct their sequences and debate has…
We consider two varieties of labeled rooted trees, and the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree…
We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…
Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and…
Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants…
Consider a binary tree, to the vertices of which are assigned independent Bernoulli random variables with mean $p\leq1/2$. How many of these Bernoullis one must look at in order to find a path of length $n$ from the root which maximizes, up…
Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the…
Many network applications are based on binary-state networks, where each component has one of two states: success or failure. Efficient algorithms to evaluate binary-state network reliability are continually being developed. Reliability…
Zero-sum mean payoff games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair $(u,\lambda)$ solution of $T(u)=\lambda \mathbf{1} + u$ where $T:\mathbb{R}^n…
We consider multi-agent systems where agents actions and beliefs are determined aleatorically, or "by the throw of dice". This system consists of possible worlds that assign distributions to independent random variables, and agents who…
We develop here the Stochastic Perron Method in the framework of two-player zero-sum differential games. We consider the formulation of the game where both players play, symmetrically, feed-back strategies (as in [CR09] or [PZ12]) as…