Related papers: On consistent estimation of the missing mass
Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we…
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…
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…
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…
The brilliant method due to Good and Turing allows for estimating objects not occurring in a sample. The problem, known under names "sample coverage" or "missing mass" goes back to their cryptographic work during WWII, but over years has…
The Good-Turing (GT) estimator for the missing mass (i.e., total probability of missing symbols) in $n$ samples is the number of symbols that appeared exactly once divided by $n$. For i.i.d. samples, the bias and squared-error risk of the…
Large sample size equivalence between the celebrated {\it approximated} Good-Turing estimator of the probability to discover a species already observed a certain number of times (Good, 1953) and the modern Bayesian nonparametric counterpart…
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.…
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 estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics,…
When faced with a small sample from a large universe of possible outcomes, scientists often turn to the venerable Good--Turing estimator. Despite its pedigree, however, this estimator comes with considerable drawbacks, such as the need to…
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.…
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 consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no…
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…
A random variable is sampled from a discrete distribution. The missing mass is the probability of the set of points not observed in the sample. We sharpen and simplify McAllester and Ortiz's results (JMLR, 2003) bounding the probability of…
We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and the…
Given $n$ i.i.d. samples from an unknown discrete distribution over an unknown set, the unseen species problem is to predict how many new outcomes would be observed in $m$ additional samples. For small $m$ we show that the Good-Toulmin…
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 consider the problem of estimating the probability of an observed string drawn i.i.d. from an unknown distribution. The key feature of our study is that the length of the observed string is assumed to be of the same order as the size of…