Partial Sample Regression

Article Hudson & Thames

Summary

This document explains history-weighted, or partial sample, regression as a way to make predictions from observations judged relevant to a new input. It defines similarity using negative Mahalanobis distance and informativeness by how far an observation lies from the training data mean. Their combination ranks historical observations; a selected top-quantile subsample is then used in a relevance-weighted prediction.

The article connects the method to ordinary least squares: when the full sample is retained, the prediction reduces to the OLS result. It also distinguishes the approach from weighted least squares and from fitting a separate regression on the selected subset, since relevance is calculated using the full-sample covariance. An example forecasts quarterly US GDP from economic indicators and notes that full-sample regression matches OLS. The method depends on a suitable covariance estimate and relevance selection; the article gives no broad performance comparison or evidence that selecting a subsample improves forecasts. Feature rescaling can help numerical conditioning without changing the prediction.

Key ideas

Mahalanobis distance measures how similar two observations are relative to feature covariance.
Informativeness increases as an observation lies farther from the training data mean.
Partial sample regression ranks observations by relevance and predicts from a selected subset.
Using the entire training sample makes the prediction equivalent to ordinary least squares.
The full-sample covariance is retained even when only a subset of observations is selected.

Partial Sample Regression Using Historical Relevance

Summary

Key ideas

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