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We study an urn process containing red and blue balls and two different strategies to reinforce the urn. Namely, a generalized P\'olya-type strategy versus an i.i.d. one. At each step, one of the two reinforcement strategies is chosen by…
We establish a simple recurrence formula for the number $Q_g^n$ of rooted orientable maps counted by edges and genus. We also give a weighted variant for the generating polynomial $Q_g^n(x)$ where $x$ is a parameter taking the number of…
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet…
Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
We study a missing-value imputation method, termed kNNSampler, that imputes a given unit's missing response by randomly sampling from the observed responses of the $k$ most similar units to the given unit in terms of the observed…
In participatory budgeting we are given a set of projects---each with a cost, an available budget, and a set of voters who in some form express their preferences over the projects. The goal is to select---based on voter preferences---a…
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…
Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability…
The evaluation of the probability of union of a large number of independent events requires several combinations involving the factorial and the use of high performance computers with several hours of processing. Bounds and simplifications…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
Correspondence analysis (CA) is a popular technique to visualize the relationship between two categorical variables. CA uses the data from a two-way contingency table and is affected by the presence of outliers. The supplementary points…
In this work we generalize Polya urn schemes with possibly infinitely many colors and extend the earlier models described in [4, 5, 7]. We provide a novel and unique approach of representing the observed sequence of colors in terms a…
In this paper, using the structural approach is derived a mathematical model of the discrete coupon bond with the provision that allow the holder to demand early redemption at any coupon dates prior to the maturity and based on this model…
Recursive formulas are derived for the number of solutions of linear and quadratic Diophantine equations with positive coefficients. This result is further extended to general non-linear additive Diophantine equations. It is shown that all…
Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap…
The wisdom of the crowd has long become the de facto approach for eliciting information from individuals or experts in order to predict the ground truth. However, classical democratic approaches for aggregating individual \emph{votes} only…
The generating function of the cumulants in random matrix models, as well as the cumulants themselves, can be expanded as asymptotic (divergent) series indexed by maps. While at fixed genus the sums over maps converge, the sums over genera…
The aim of this paper is to study the asymptotic behavior of strongly reinforced interacting urns with partial memory sharing. The reinforcement mechanism considered is as follows: draw at each step and for each urn a white or black ball…
In the Possible Winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear…