相关论文: Card Guessing with Partial Feedback

Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…

Machine language acquisition is often presented as a problem of imitation learning: there exists a community of language users from which a learner observes speech acts and attempts to decode the mappings between utterances and situations.…

We consider the game of Cops and Robber played on the Cartesian product of two trees. Assuming the players play perfectly, it is shown that if there are two cops in the game, then the length of the game (known as the 2-capture time of the…

The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…

EvenQuads is a new card game that is a generalization of the SET game, where each card is characterized by three attributes, each taking four possible values. Four cards form a quad when, for each attribute, the values are the same, all…

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of…

Recently Wilson [Ann. Appl. Probab. 14 (2004) 274--325] introduced an important new technique for lower bounding the mixing time of a Markov chain. In this paper we extend Wilson's technique to find lower bounds of the correct order for…

We investigate the mathematics behind unshuffles, a type of card shuffle closely related to classical perfect shuffles. To perform an unshuffle, deal all the cards alternately into two piles and then stack the one pile on top of the other.…

In trick-taking card games, a two-step process of state sampling and evaluation is widely used to approximate move values. While the evaluation component is vital, the accuracy of move value estimates is also fundamentally linked to how…

We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop…

Learning under one-sided feedback (i.e., where we only observe the labels for examples we predicted positively on) is a fundamental problem in machine learning -- applications include lending and recommendation systems. Despite this, there…

Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss…

We introduce a new model of interactive learning in which an expert examines the predictions of a learner and partially fixes them if they are wrong. Although this kind of feedback is not i.i.d., we show statistical generalization bounds on…

One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be…

We show how to test whether a graph with n vertices and m edges is a partial cube, and if so how to find a distance-preserving embedding of the graph into a hypercube, in the near-optimal time bound O(n^2), improving previous O(nm)-time…

Despite their performance and widespread use, little is known about the theory of Random Forests. A major unanswered question is whether, or when, the Random Forest algorithm is consistent. The literature explores various variants of the…

Conformal prediction has emerged as an effective strategy for uncertainty quantification by modifying a model to output sets of labels instead of a single label. These prediction sets come with the guarantee that they contain the true label…

The 21 card trick is well known. It was recently shown in an episode of the popular YouTube channel Numberphile. In that trick, the audience is asked to remember a card, and through a series of steps, the magician is able to find the card.…

We consider a repeated game where a player self-reports her usage of a service and is charged a payment accordingly by a center. The center observes a partial signal, representing part of the player's true consumption, which is generated…

Experiments suggest that people fail to take into account interdependencies between their choices -- they do not broadly bracket. Researchers often instead assume that people narrowly bracket, but existing designs do not test it. We design…