A machine learning oracle for parameter estimation

Abstract

Competing procedures, involving data smoothing, weighting, imputation, outlier removal, etc., may be available to prepare data for parametric model estimation. Often, however, little is known about the best choice of preparatory procedure for the planned estimation and the observed data. A machine learning-based decision rule, an “oracle,” can be constructed in such cases to decide the best procedure from a set $\mathcal{C}$ of available preparatory procedures. The oracle learns the decision regions associated with $\mathcal{C}$ based on training data synthesized solely from the given data using model parameters with high posterior probability. An estimator in combination with an oracle to guide data preparation is called an oracle estimator. Oracle estimator performance is studied in two estimation problems: slope estimation in simple linear regression (SLR) and changepoint estimation in continuous two-linear-segments regression (CTLSR). In both examples, the regression response is given to be increasing, and the oracle must decide whether to isotonically smooth the response data preparatory to fitting the regression model. A measure of performance called headroom is proposed to assess the oracle's potential for reducing estimation error. Experiments with SLR and CTLSR find for important ranges of problem configurations that the headroom is high, the oracle's empirical performance is near the headroom, and the oracle estimator offers clear benefit.