Related papers: A characterization of product-form exchangeable fe…
A group of $n$ agents with numerical preferences for each other are to be assigned to the $n$ seats of a dining table. We study two natural topologies:~circular (cycle) tables and panel (path) tables. For a given seating arrangement, an…
A collaborative filtering recommender system predicts user preferences by discovering common features among users and items. We implement such inference using a Bayesian double feature allocation model, that is, a model for random pairs of…
For a fixed permutation $\sigma \in S_k$, let $N_{\sigma}$ denote the function which counts occurrences of $\sigma$ as a pattern in permutations from $S_n$. We study the expected value (and $d$-th moments) of $N_{\sigma}$ on conjugacy…
The problem of characterizing a multivariate distribution of a random vector using examination of univariate combinations of vector components is an essential issue of multivariate analysis. The likelihood principle plays a prominent role…
In this work we suggest a new model for generating random satisfiable k-CNF formulas. To generate such formulas -- randomly permute all 2^k\binom{n}{k} possible clauses over the variables x_1, ..., x_n, and starting from the empty formula,…
We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…
We define spreadability systems as a generalization of exchangeability systems in order to unify various notions of independence and cumulants known in noncommutative probability. In particular, our theory covers monotone independence and…
Feature attribution methods have become essential for explaining machine learning models. Many popular approaches, such as SHAP and Banzhaf values, are grounded in power indices from cooperative game theory, which measure the contribution…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
With nonignorable missing data, likelihood-based inference should be based on the joint distribution of the study variables and their missingness indicators. These joint models cannot be estimated from the data alone, thus requiring the…
Paper 1 of this research programme develops a resolution-aware risk-design framework for the simplest event-linked perpetual: a contract whose underlying tracks a single binary prediction-market probability through resolution. The…
We propose a framework to study models of computation of indeterministic data, represented by abstract "distributions". In these distributions, probabilities are replaced by "amplitudes" drawn from a fixed semi-ring $S$, of which the…
We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that…
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
De Finetti's theorem, also called the de Finetti-Hewitt-Savage theorem, is a foundational result in probability and statistics. Roughly, it says that an infinite sequence of exchangeable random variables can always be written as a mixture…
We propose an easy-to-use methodology to allocate one of the groups which have been previously built from a complete learning data base, to new individuals. The learning data base contains continuous and categorical variables for each…
Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty…
Multi-item revenue-optimal mechanisms are known to be extremely complex, often offering buyers randomized lotteries of goods. In the standard buy-one model, it is known that optimal mechanisms can yield revenue infinitely higher than that…