Interactive Prior Elicitation of Feature Similarities for Small Sample Size Prediction

TL;DR

This paper presents an interactive method for eliciting expert knowledge on feature similarities to improve small sample size prediction in Bayesian regression, demonstrating enhanced accuracy over non-interactive approaches.

Contribution

The paper introduces a novel interactive scatterplot-based approach for eliciting feature similarity priors, improving prediction in small sample Bayesian regression tasks.

Findings

Eliciting feature similarities improves prediction accuracy.

Interactive scatterplots outperform list-based elicitation.

Method effective on both simulated and real data.

Abstract

Regression under the "small $n$, large $p$" conditions, of small sample size $n$ and large number of features $p$ in the learning data set, is a recurring setting in which learning from data is difficult. With prior knowledge about relationships of the features, $p$ can effectively be reduced, but explicating such prior knowledge is difficult for experts. In this paper we introduce a new method for eliciting expert prior knowledge about the similarity of the roles of features in the prediction task. The key idea is to use an interactive multidimensional-scaling (MDS) type scatterplot display of the features to elicit the similarity relationships, and then use the elicited relationships in the prior distribution of prediction parameters. Specifically, for learning to predict a target variable with Bayesian linear regression, the feature relationships are used to construct a Gaussian prior with a full covariance matrix for the regression coefficients. Evaluation of our method in experiments with simulated and real users on text data confirm that prior elicitation of feature similarities improves prediction accuracy. Furthermore, elicitation with an interactive scatterplot display outperforms straightforward elicitation where the users choose feature pairs from a feature list.