Oliver J. Hines

Oliver J. Hines, Christian L. Hines

Gradient boosted decision trees require a stopping rule to avoid overfitting. The standard rule monitors a validation loss and stops if the loss fails to improve for a fixed patience period. However, the patience parameter has no interpretable scale and validation losses can be noisy or implicitly defined by a user-specified gradient. We propose ScoreStop, a gradient-based early-stopping rule that casts the stopping decision at each iteration as a test of the null hypothesis that the current predictor is the population risk minimizer. We use a functional score test, computed on validation data, with a statistic that is scale-invariant in the update direction, with a known asymptotic distribution under the null. Because our test uses gradients rather than loss values, the same construction applies to implicit losses such as LambdaRank, and data-dependent losses such as Cox regression via influence functions. In synthetic experiments and real-data benchmarks, we show that ScoreStop is competitive with loss-based methods.

Christian L. Hines, Oliver J. Hines

Causal and nonparametric estimands in economics and biostatistics can often be viewed as the mean of a linear functional applied to an unknown outcome regression function. Naively learning the regression function and taking a sample mean of the target functional results in biased estimators, and a rich debiasing literature has developed where one additionally learns the so-called Riesz representer (RR) of the target estimand (targeted learning, double ML, automatic debiasing etc.). Learning the RR via its derived functional form can be challenging, e.g. due to extreme inverse probability weights or the need to learn conditional density functions. Such challenges have motivated recent advances in automatic debiasing (AD), where the RR is learned directly via minimization of a bespoke loss. We propose moment-constrained learning as a new RR learning approach that addresses some shortcomings in AD, constraining the predicted moments and improving the robustness of RR estimates to optimization hyperparamters. Though our approach is not tied to a particular class of learner, we illustrate it using neural networks, and evaluate on the problems of average treatment/derivative effect estimation using semi-synthetic data. Our numerical experiments show improved performance versus state of the art benchmarks.

Oliver J. Hines, Caleb H. Miles

The ratio of two probability density functions is a fundamental quantity that appears in many areas of statistics and machine learning, including causal inference, reinforcement learning, covariate shift, outlier detection, independence testing, importance sampling, and diffusion modeling. Naively estimating the numerator and denominator densities separately using, e.g., kernel density estimators, can lead to unstable performance and suffers from the curse of dimensionality as the number of covariates increases. For this reason, several methods have been developed for estimating the density ratio directly based on (a) Bregman divergences or (b) recasting the density ratio as the odds in a probabilistic classification model that predicts whether an observation is sampled from the numerator or denominator distribution. Additionally, the density ratio can be viewed as the Riesz representer of a continuous linear map, making it amenable to estimation via (c) minimization of the so-called Riesz loss, which was developed to learn the Riesz representer in the Riesz regression procedure in causal inference. In this paper we show that all three of these methods can be unified in a common framework, which we call Bregman-Riesz regression. We further show how data augmentation techniques can be used to apply density ratio learning methods to causal problems, where the numerator distribution typically represents an unobserved intervention. We show through simulations how the choice of Bregman divergence and data augmentation strategy can affect the performance of the resulting density ratio learner. A Python package is provided for researchers to apply Bregman-Riesz regression in practice using gradient boosting, neural networks, and kernel methods.