Related papers: Generalized Interacting Urn Models
This paper considers a model with general regressors and unobservable factors. An estimator based on iterated principal components is proposed, which is shown to be not only asymptotically normal and oracle efficient, but under certain…
We consider triangular P\'olya urns and show under very weak conditions a general strong limit theorem of the form $X_{ni}/a_{ni}\to \mathcal{X}_i$ a.s., where $X_{ni}$ is the number of balls of colour $i$ after $n$ draws; the constants…
We introduce and study a new interacting particles model with a wall and two kinds of interactions - blocking and pushing - which maintain particles in a certain order. We show that it involves a random matrix model.
We consider a generalized version of the sign uncertainty principle for the Fourier transform, first proposed by Bourgain, Clozel and Kahane in 2010 and revisited by Cohn and Gon\c{c}alves in 2019. In our setup, the signs of a function and…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer''…
Generating realistic artificial preference distributions is an important part of any simulation analysis of electoral systems. While this has been discussed in some detail in the context of a single electoral district, many electoral…
Recent work has demonstrated that problems-- particularly imitation learning and structured prediction-- where a learner's predictions influence the input-distribution it is tested on can be naturally addressed by an interactive approach…
Most model-free reinforcement learning methods leverage state representations (embeddings) for generalization, but either ignore structure in the space of actions or assume the structure is provided a priori. We show how a policy can be…
An urn containing specified numbers of balls of distinct ordered colors is considered. A multiple q-Polya urn model is introduced by assuming that the probability of q-drawing a ball of a specific color from the urn varies geometrically,…
Consider an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is $p>1/2$. Condorcet's Jury Theorem which he derived from the weak law of large…
This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the…
Bona [2007+] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley [1978]. Recently, Janson [2008+] showed the connection between Stirling permutations and plane…
We present a new strategic voting model where we use uncertainty representation to model preferences. Specifically, we use probability sets as uncertainty representations, together with lower and upper expected utility gains to take…
We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…
We study a generalized P\'{o}lya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black…
While recent progress has spawned very powerful machine learning systems, those agents remain extremely specialized and fail to transfer the knowledge they gain to similar yet unseen tasks. In this paper, we study a simple reinforcement…
We consider a generalization of the Bernoulli-Laplace model in which there are two urns and $n$ total balls, of which $r$ are red and $n - r$ white, and where the left urn holds $m$ balls. At each time increment, $k$ balls are chosen…
We consider multicolor urn models with multiple drawings. An urn model is called linear if the conditional expected value of the urn composition at time $n$ is a linear function of the composition at time $n-1$. For four different sampling…
We consider a version of the classical Ehrenfest urn model with two urns and two types of balls: regular and heavy. Each ball is selected independently according to a Poisson process having rate $1$ for regular balls and rate…