相关论文: On the Concentration of the Missing Mass
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…
The missing mass refers to the probability of elements not observed in a sample, and since the work of Good and Turing during WWII, has been studied extensively in many areas including ecology, linguistic, networks and information theory.…
We study the estimation and concentration on its expectation of the probability to observe data further than a specified distance from a given iid sample in a metric space. The problem extends the classical problem of estimation of the…
We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like…
Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for…
The missing mass refers to the proportion of data points in an unknown population of classifier inputs that belong to classes not present in the classifier's training data, which is assumed to be a random sample from that unknown…
This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete…
We consider the problem of estimating the missing mass, partition function or evidence and its probability distribution in the case that for each sample point in the discrete sample space its (unnormalized) probability mass is revealed.…
Distribution estimation under error-prone or non-ideal sampling modelled as "sticky" channels have been studied recently motivated by applications such as DNA computing. Missing mass, the sum of probabilities of missing letters, is an…
Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics,…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Consider a random sample $(X_{1},\ldots,X_{n})$ from an unknown discrete distribution $P=\sum_{j\geq1}p_{j}\delta_{s_{j}}$ on a countable alphabet $\mathbb{S}$, and let $(Y_{n,j})_{j\geq1}$ be the empirical frequencies of distinct symbols…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
Estimating the underlying distribution from \textit{iid} samples is a classical and important problem in statistics. When the alphabet size is large compared to number of samples, a portion of the distribution is highly likely to be…
The problem of missing mass in statistical inference (posed by McAllester and Ortiz, NIPS'02; most recently revisited by Changa and Thangaraj, ISIT'2019) seeks to estimate the weight of symbols that have not been sampled yet from a source.…
The problem of estimating the missing mass or total probability of unseen elements in a sequence of $n$ random samples is considered under the squared error loss function. The worst-case risk of the popular Good-Turing estimator is shown to…
An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this probability distribution where $N$ may be…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
Existing approaches to model uncertainty typically either compare models using a quantitative model selection criterion or evaluate posterior model probabilities having set a prior. In this paper, we propose an alternative strategy which…
Feature models are popular in machine learning and they have been recently used to solve many unsupervised learning problems. In these models every observation is endowed with a finite set of features, usually selected from an infinite…