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We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
We present a generic model of (non-destructive) quantum measurement. Being formulated within reversible quantum mechanics, the model illustrates a mechanism of a measurement process --- a transition of the measured system to an eigenstate…
The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…
Recent advances in coreset methods have shown that a selection of representative datapoints can replace massive volumes of data for Bayesian inference, preserving the relevant statistical information and significantly accelerating…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is…
We construct a measure for the adiabatic contribution to quantum transitions in an arbitrary basis, tackling the generic complex case where dynamics is only partially adiabatic, simultaneously populates several eigenstates and transitions…
The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
Generation and manipulation of randomness is a relevant task for several applications of information technology. It has been shown that quantum mechanics offers some advantages for this type of task. A promising model for randomness…
Predictive constructions are a powerful way of characterizing the probability law of stochastic processes with certain forms of invariance, such as exchangeability or Markov exchangeability. When de Finetti-like representation theorems are…
A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…
Understanding how different classes are distributed in an unlabeled data set is an important challenge for the calibration of probabilistic classifiers and uncertainty quantification. Approaches like adjusted classify and count, black-box…
Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian…
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…
We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…