Convergence of Chao Unseen Species Estimator

重新审视未见物种问题

The Unseen Species Problem Revisited

本文重新审视未见物种问题，提出新估计器改进MSE，并在大m情况下展示简单估计器的优越性能，同时扩展了率保证至事件数据。

Estimating the number of unseen species: A bird in the hand is worth $\log n $ in the bush

Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher, uses $n$ samples to predict the number $U$ of hitherto unseen species that would be observed if $t\cdot n$ new samples were collected. Of considerable interest is the largest ratio $t$ between the number of new and existing samples for which $U$ can be accurately predicted. In seminal works, Good and Toulmin constructed an intriguing estimator that predicts $U$ for all $t\le 1$, thereby showing that the number of species can be estimated for a popula…

Near-optimal estimation of the unseen under regularly varying tail populations

Given $n$ samples from a population of individuals belonging to different species, what is the number $U$ of hitherto unseen species that would be observed if $λn$ new samples were collected? This is an important problem in many scientific endeavors, and it has been the subject of recent works introducing non-parametric estimators of $U$ that are minimax near-optimal and consistent all the way up to $λ\asymp\log n$. These works do not rely on any assumption on the underlying unknown distribution $p$ of the population, and therefore, while providing a theory in its greatest generality, worst-ca…

Chaos Is a LADDER: 超越不变性的领域泛化——通过重加权实现

Chaos Is a LADDER: Domain Generalization Beyond Invariance via Reweighting

该研究针对领域泛化中域调节因果-响应映射的问题，提出LADDER方法，通过固定模型的源域分类器重加权实现目标域泛化，在模拟、FMoW等数据集上提升了整体与组平均准确率。

A New Estimator for the Number of Species in a Population

We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We look first at the Chao-Lee estimator: we initially show that such estimator can be obtained by reconciling two estimators of the unobserved probability, and then develop a sequence of improvements culminating in a Dirichlet prior Bayesian reinterpretation of the estimation problem. By means of this, we obtain simultaneous estimates of T, of the normalized interspecies variance $γ^2$ and of the parameter $λ$ of the prior. Several simulations show that …

A Good-Turing estimator for feature allocation models

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 study the problem of estimating the missing mass $M_{n}$, namely the expected number hitherto unseen features that would be observed if one additional individual was sampled. This is motivated by numerous applied problems where the sampling procedure is expensive, in terms of time and/or financial resources allocated, and further samples can be only motivated by…