Sequential Bayesian updating for Big Data

The velocity, volume, and variety of big data present both challenges and opportunities for cognitive science. We introduce sequential Bayesian updat-ing as a tool to mine these three core properties. In the Bayesian approach, we summarize the current state of knowledge regarding parameters in terms of their posterior distributions, and use these as prior distributions when new data become available. Crucially, we construct posterior distributions in such a way that we avoid having to repeat computing the likelihood of old data as new data become available, allowing the propagation of information without great computational demand. As a result, these Bayesian methods allow continuous inference on voluminous information streams in a timely manner. We illustrate the advantages of sequential Bayesian updating with data from the MindCrowd project, in which crowd-sourced data are used to study Alzheimer’s Dementia. We fit an extended LATER (Linear Ap-proach to Threshold with Ergodic Rate) model to reaction time data from the project in order to separate two distinct aspects of cognitive functioning: speed of information accumulation and caution

Probability models for information retrieval based on divergence from randomness

This thesis devises a novel methodology based on probability theory, suitable for the construction of term-weighting models of Information Retrieval. Our term-weighting functions are created within a general framework made up of three components. Each of the three components is built independently from the others. We obtain the term-weighting functions from the general model in a purely theoretic way instantiating each component with different probability distribution forms. The thesis begins with investigating the nature of the statistical inference involved in Information Retrieval. We explore the estimation problem underlying the process of sampling. De Finetti’s theorem is used to show how to convert the frequentist approach into Bayesian inference and we display and employ the derived estimation techniques in the context of Information Retrieval. We initially pay a great attention to the construction of the basic sample spaces of Information Retrieval. The notion of single or multiple sampling from different populations in the context of Information Retrieval is extensively discussed and used through-out the thesis. The language modelling approach and the standard probabilistic model are studied under the same foundational view and are experimentally compared to the divergence-from-randomness approach. In revisiting the main information retrieval models in the literature, we show that even language modelling approach can be exploited to assign term-frequency normalization to the models of divergence from randomness. We finally introduce a novel framework for the query expansion. This framework is based on the models of divergence-from-randomness and it can be applied to arbitrary models of IR, divergence-based, language modelling and probabilistic models included. We have done a very large number of experiment and results show that the framework generates highly effective Information Retrieval models

Bayesian performance comparison of text classifiers

How can we know whether one classifier is really better than the other? In the area of text classification, since the publication of Yang and Liu's seminal SIGIR-1999 paper, it has become a standard practice for researchers to apply null-hypothesis significance testing (NHST) on their experimental results in order to establish the superiority of a classifier. However, such a frequentist approach has a number of inherent deficiencies and limitations, e.g., the inability to accept the null hypothesis (that the two classifiers perform equally well), the difficulty to compare commonly-used multivariate performance measures like F1 scores instead of accuracy, and so on. In this paper, we propose a novel Bayesian approach to the performance comparison of text classifiers, and argue its advantages over the traditional frequentist approach based on t-test etc. In contrast to the existing probabilistic model for F1 scores which is unpaired, our proposed model takes the correlation between classifiers into account and thus achieves greater statistical power. Using several typical text classification algorithms and a benchmark dataset, we demonstrate that the our approach provides rich information about the difference between two classifiers' performances

A pilot inference study for a beta-Bernoulli spatial scan statistic

The Bernoulli spatial scan statistic is used to detect localised clusters in binary labelled point data, such as that used in spatial or spatio-temporal case/control studies. We test the inferential capability of a recently developed beta-Bernoulli spatial scan statistic, which adds a beta prior to the original statistic. This pilot study, which includes two test scenarios with 6,000 data sets each, suggests a marked increase in power for a given false alert rate. We suggest a more extensive study would be worthwhile to corroborate the findings. We also speculate on an explanation for the observed improvement