Related papers: Characterization of exchangeable measure-valued P\…
We characterize the class of exchangeable feature allocations assigning probability $V_{n,k}\prod_{l=1}^{k}W_{m_{l}}U_{n-m_{l}}$ to a feature allocation of $n$ individuals, displaying $k$ features with counts $(m_{1},\ldots,m_{k})$ for…
In this paper, we prove functional limit theorems for P\'olya urn processes whose number of draws and initial number of balls tend to infinity together. This is motivated by recent work of Borovkov [5], where they prove a functional limit…
This paper introduces a novel method for quantifying vowel overlap. There is a tension in previous work between using multivariate measures, such as those derived from empirical distributions, and the ability to control for unbalanced data…
We establish two versions of Vizing's theorem for Borel multi-graphs whose vertex degrees and edge multiplicities are uniformly bounded by respectively $\Delta$ and $\pi$. The ``approximate'' version states that, for any Borel probability…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
Random permutation set (RPS) is a recently proposed framework designed to represent order-structured uncertain information. Measuring the distance between permutation mass functions is a key research topic in RPS theory (RPST). This paper…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question if a given data vector can be expressed as a finite sum of others, only assuming that 1) the domain is…
The real Production Possibility Set (PPS) is completely generated by observations in the real approach, but generating the integer PPS may not be possible by only using observations in the integer approach. In other words, this phenomenon…
A new class of dependent random measures which we call {\it compound random measures} are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
Examining residuals such as Pearson and deviance residuals, is a standard tool for assessing normal regression. However, for discrete response, these residuals cluster on lines corresponding to distinct response values. Their distributions…
A fundamental task in kernel methods is to pick nodes and weights, so as to approximate a given function from an RKHS by the weighted sum of kernel translates located at the nodes. This is the crux of kernel density estimation, kernel…
Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize…
In the present paper we prove that the probabilities of the P\'olya urn distribution (with negative replacement) satisfy a monotonicity property similar to that of the binomial distribution (P\'olya urn distribution with no replacement). As…
This paper develops a multiply robust (MR) dose-response estimator for causal inference problems involving multivalued treatments. We combine a family of generalised propensity score (GPS) models and a family of outcome regression (OR)…
We propose a new, nonparametric approach to estimating the value function in reinforcement learning. This approach makes use of a recently developed representation of conditional distributions as functions in a reproducing kernel Hilbert…
The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…