This position paper argues that, in debiased machine learning, balancing functions should be derived from the Neyman orthogonal score, not chosen only as functions of covariates. Covariate balancing is effective when the regression error entering the score can be represented by functions of covariates alone, and it is the natural finite-dimensional approximation for targets such as ATT counterfactual means. For ATE estimation under treatment effect heterogeneity, however, the score error generally contains treatment-specific components because the outcome regression is a function of the full regressor $X=(D,Z)$. In that case, balancing common functions of $Z$ can leave the treatment-specific component unbalanced. We therefore advocate regressor balancing, implemented by Riesz regression with basis functions of $X$, as the general balancing principle for DML. The position is not that covariate balancing is invalid, but that covariate balancing should be understood as the special case that is appropriate when the score-relevant regression error is a function of covariates alone.

Neural networks have shown great predictive power when applied to unstructured data such as images and natural languages.

Neural Information Processing Systems http://nips.cc/

Fine-tuning is a widely used strategy for adapting pre-trained models to new tasks, yet its methodology and theoretical properties in high-dimensional nonparametric settings with variable selection have not yet been developed. This paper introduces the fine-tuning factor augmented neural Lasso (FAN-Lasso), a transfer learning framework for high-dimensional nonparametric regression with variable selection that simultaneously handles covariate and posterior shifts. We use a low-rank factor structure to manage high-dimensional dependent covariates and propose a novel residual fine-tuning decomposition in which the target function is expressed as a transformation of a frozen source function and other variables to achieve transfer learning and nonparametric variable selection. This augmented feature from the source predictor allows for the transfer of knowledge to the target domain and reduces model complexity there. We derive minimax-optimal excess risk bounds for the fine-tuning FAN-Lasso, characterizing the precise conditions, in terms of relative sample sizes and function complexities, under which fine-tuning yields statistical acceleration over single-task learning. The proposed framework also provides a theoretical perspective on parameter-efficient fine-tuning methods. Extensive numerical experiments across diverse covariate- and posterior-shift scenarios demonstrate that the fine-tuning FAN-Lasso consistently outperforms standard baselines and achieves near-oracle performance even under severe target sample size constraints, empirically validating the derived rates.

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Many machine learning tools for regression are based on recursive partitioning of the covariate space into smaller regions, where the regression function can be estimated locally. Among these, regression trees and their ensembles have demonstrated impressive empirical performance. In this work, we shed light on the machinery behind Bayesian variants of these methods. In particular, we study Bayesian regression histograms, such as Bayesian dyadic trees, in the simple regression case with just one predictor. We focus on the reconstruction of regression surfaces that are piecewise constant, where the number of jumps is unknown.

We study algorithms for online nonparametric regression that learn the directions along which the regression function is smoother. Our algorithm learns the Mahalanobis metric based on the gradient outer product matrix $\boldsymbol{G}$ of the regression function (automatically adapting to the effective rank of this matrix), while simultaneously bounding the regret ---on the same data sequence--- in terms of the spectrum of $\boldsymbol{G}$. As a preliminary step in our analysis, we extend a nonparametric online learning algorithm by Hazan and Megiddo enabling it to compete against functions whose Lipschitzness is measured with respect to an arbitrary Mahalanobis metric.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/