Related papers: Negative Dependence in Knockout Tournaments
Pokrovskiy conjectured that there is a function $f: \mathbb{N} \rightarrow \mathbb{N}$ such that any $2k$-strongly-connected tournament with minimum out and in-degree at least $f(k)$ is $k$-linked. In this paper, we show that any…
A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our…
In order to develop complex relationships between their inputs and outputs, deep neural networks train and adjust large number of parameters. To make these networks work at high accuracy, vast amounts of data are needed. Sometimes, however,…
We study the robust Nash equilibrium (RNE) for a class of games in communications systems and networks where the impact of users on each other is an additive function of their strategies. Each user measures this impact, which may be…
Model-free knockoffs is a recently proposed technique for identifying covariates that is likely to have an effect on a response variable. The method is an efficient method to control the false discovery rate in hypothesis tests for separate…
Tournaments are orientations of the complete graph, and the directed Ramsey number $R(k)$ is the minimum number of vertices a tournament must have to be guaranteed to contain a transitive subtournament of size $k$, which we denote by…
This paper analyzes the behavior of selfish transmitters under imperfect location information. The scenario considered is that of a wireless network consisting of selfish nodes that are randomly distributed over the network domain according…
We show that if $D$ is a tournament of arbitrary size then $D$ has finite strong components after reversing a locally finite sequence of cycles. In turn, we prove that any tournament can be covered by two acyclic sets after reversing a…
A tournament is a directed graph resulting from an orientation of the complete graph; so, if $M$ is a tournament's adjacency matrix, then $M + M^T$ is a matrix with $0$s on its diagonal and all other entries equal to $1$. An outstanding…
Knockoffs is a new framework for controlling the false discovery rate (FDR) in multiple hypothesis testing problems involving complex statistical models. While there has been great emphasis on Type-I error control, Type-II errors have been…
Recurrent neural networks (RNNs) with Long Short-Term memory cells currently hold the best known results in unconstrained handwriting recognition. We show that their performance can be greatly improved using dropout - a recently proposed…
We present a family of pairwise tournaments reducing $k$-class classification to binary classification. These reductions are provably robust against a constant fraction of binary errors. The results improve on the PECOC construction…
In her recent paper [Negative dependence, scrambled nets, and variance bounds. Math. Oper. Res. 43 (2018), 228-251] Christiane Lemieux studied a framework to analyze the dependence structure of sampling schemes. The main goal of the…
Model-X knockoff has garnered significant attention among various feature selection methods due to its guarantees for controlling the false discovery rate (FDR). Since its introduction in parametric design, knockoff techniques have evolved…
We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an…
A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erd\H{o}s and J. W. Moon. By probabilistic methods, the existence of "unrankable" tournaments was proved. On the other hand, they…
A digraph $D$ is $k$-linked if it satisfies that for every choice of disjoint sets $\{x_1,\ldots{},x_k\}$ and $\{y_1,\ldots{},y_k\}$ of vertices of $D$ there are vertex disjoint paths $P_1,\ldots{},P_k$ such that $P_i$ is an…
Barber and Candes recently introduced a feature selection method called knockoff+ that controls the false discovery rate (FDR) among the selected features in the classical linear regression problem. Knockoff+ uses the competition between…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
The paper reviews some axioms of additivity concerning ranking methods used for generalized tournaments with possible missing values and multiple comparisons. It is shown that one of the most natural properties, called consistency, has…