相关论文: Exploring mazes at random
Consider Bernoulli(1/2) percolation on $\Z^d$, and define a perfect matching between open and closed vertices in a way that is a deterministic equivariant function of the configuration. We want to find such matching rules that make the…
Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a…
How to best exploit patchy resources? This long-standing question belongs to the extensively studied class of explore/exploit problems that arise in a wide range of situations, from animal foraging, to robotic exploration, and to human…
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.
The exploration-exploitation dilemma has been an intriguing and unsolved problem within the framework of reinforcement learning. "Optimism in the face of uncertainty" and model building play central roles in advanced exploration methods.…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
We study the problem of learning a good search policy for combinatorial search spaces. We propose retrospective imitation learning, which, after initial training by an expert, improves itself by learning from \textit{retrospective…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
Consider two random walks on $\mathbb{Z}$. The transition probabilities of each walk is dependent on trajectory of the other walker i.e. a drift $p>1/2$ is obtained in a position the other walker visited twice or more. This simple model has…
We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and…
We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…
The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…
We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of…
We discuss a class of problems which we call lattice exit models. At one level, these problems provide undergraduate level exercises in labeling the vertices of graphs (e.g., depth first search). At another level (theorems about large scale…