Related papers: Outperforming Good-Turing: Preliminary Report
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution p(k) of the elements k of a population can be approximated by the…
Animals perform near-optimal probabilistic inference in a wide range of psychophysical tasks. Probabilistic inference requires trial-to-trial representation of the uncertainties associated with task variables and subsequent use of this…
Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
Typical causal effects are defined based on the marginal distribution of potential outcomes. However, many real-world applications require causal estimands involving the joint distribution of potential outcomes to enable more nuanced…
Recent prompt optimisation approaches use the generative nature of language models to produce prompts -- even rivaling the performance of human-curated prompts. In this paper, we demonstrate that randomly sampling tokens from the model…
The statistical problem of using an initial sample to estimate the number of species in a larger sample has found important applications in fields far removed from ecology. Here we address the general problem of estimating the number of…
In this work, we propose two methods that utilize data symbols in addition to pilot symbols for improved channel estimation quality in a multi-user system, so-called semi-blind channel estimation. To this end, a subspace is estimated based…
This paper presents a clustering approach that allows for rigorous statistical error control similar to a statistical test. We develop estimators for both the unknown number of clusters and the clusters themselves. The estimators depend on…
This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
When primed with only a handful of training samples, very large, pretrained language models such as GPT-3 have shown competitive results when compared to fully-supervised, fine-tuned, large, pretrained language models. We demonstrate that…
We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…
Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme…
Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…