Related papers: Redundancy of Exchangeable Estimators
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks…
This work applies modern AI tools (transformers) to solving one of the oldest statistical problems: Poisson means under empirical Bayes (Poisson-EB) setting. In Poisson-EB a high-dimensional mean vector $\theta$ (with iid coordinates…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…
Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…
We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
We consider the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population…
We show that when the proportions of a countable set of species are organized as an exchangeable partition of the unit interval and we take a sample on it, then the Bayesian posterior entropy converges a.s. and in L^1 to the entropy of the…
Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a…
We consider the problem of estimating the mean of a random variable Y subject to non-ignorable missingness, i.e., where the missingness mechanism depends on Y . We connect the auxiliary proxy variable framework for non-ignorable missingness…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…
This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size $m$. In particular, the size of the sample is allowed to be…
Our object of study is the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian non-parametric priors in an unexplored direction. We give conditions to assure the respective…
When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…