Bayesian Sets is a new framework for information retrieval based on how humans learn new concepts and generalize. In this framework a query consists of a set of items which are examples of some concept. Bayesian Sets automatically infers which other items belong to that concept and retrieves them. As an example, for the query with the two animated movies, “Lilo & Stitch” and “Up”, Bayesian Sets would return other similar animated movies, like “Toy Story“.
How does this work? Human generalization has been intensely studied in cognitive science and various models have been proposed based on some measure of similarity and feature relevance. Recently, Bayesian methods have emerged as models of both human cognition and as the basis of machine learning systems.
Bayesian Sets – a novel framework for information retrieval
Consider a universe of items, where the items could be web pages, documents, images, ads, social and professional profiles, publications, audio, articles, video, investments, patents, resumes, medical records, or any other class of items we may want to query.
An individual item is represented by a vector of features of that item. For example, for text documents, the features could be counts of word occurrences, while for images the features could be the amounts of different color and texture elements.
Given a query consisting of a small set of items (e.g. a few images of buildings) the task is to retrieve other items (e.g. other images) that belong to the concept exemplified by the query. To achieve the task, we need a measure, or score, of how well an available item fits in with the query items.
A concept can be characterized by using a statistical model, which defines the generative process for the features of items belonging to the concept. Parameters control specific statistical properties of the features of items. For example, a Gaussian distribution has parameters which control the mean and variance of each feature. Generally these parameters are not known, but a prior distribution can represent our beliefs about plausible parameter values.
The score used for ranking the relevance of each item x given the set of query items Q compares the probabilities of two hypotheses. The first hypothesis is that the item x came from the same concept as the query items Q. For this hypothesis, compute the probability that the feature vectors representing all the items in Q and the item x were generated from the same model with the same, though unknown, model parameters. The alternative hypothesis is that the item x does not belong to the same concept as the query examples Q. Under this alternative hypothesis, compute the probability that the features in item x were generated from different model parameters than those that generated the query examples Q. The ratio of the probabilities of these two hypotheses is the Bayesian score at the heart of Bayesian Sets, and can be computed efficiently for any item x to see how well it “fits into” the set Q.
This approach to scoring items can be used with any probabilistic generative model for the data, making it applicable to any problem domain for which a probabilistic model of data can be defined. In many instances, items can be represented by a vector of features, where each feature can either be present or absent in the item. For example, in the case of documents the features may be words in some vocabulary, and a document can be represented by a binary vector x where element j of this vector represents the presence or absence of vocabulary word j in the document. For such binary data, a multivariate Bernoulli distribution can be used to model the feature vectors of items, where the jth parameter in the distribution represents the frequency of feature j. Using the beta distribution as the natural prior the score can be computed extremely efficiently.