REVIEW 6 cited by
Fast rates for empirical risk minimization over c\`adl\`ag functions with bounded sectional variation norm
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Fast rates for empirical risk minimization over c\`adl\`ag functions with bounded sectional variation norm
read the original abstract
Empirical risk minimization over classes functions that are bounded for some version of the variation norm has a long history, starting with Total Variation Denoising (Rudin et al., 1992), and has been considered by several recent articles, in particular Fang et al., 2019 and van der Laan, 2015. In this article, we consider empirical risk minimization over the class $\mathcal{F}_d$ of c\`adl\`ag functions over $[0,1]^d$ with bounded sectional variation norm (also called Hardy-Krause variation). We show how a certain representation of functions in $\mathcal{F}_d$ allows to bound the bracketing entropy of sieves of $\mathcal{F}_d$, and therefore derive rates of convergence in nonparametric function estimation. Specifically, for sieves whose growth is controlled by some rate $a_n$, we show that the empirical risk minimizer has rate of convergence $O_P(n^{-1/3} (\log n)^{2(d-1)/3} a_n)$. Remarkably, the dimension only affects the rate in $n$ through the logarithmic factor, making this method especially appropriate for high dimensional problems. In particular, we show that in the case of nonparametric regression over sieves of c\`adl\`ag functions with bounded sectional variation norm, this upper bound on the rate of convergence holds for least-squares estimators, under the random design, sub-exponential errors setting.
Forward citations
Cited by 6 Pith papers
-
Evaluating causal indirect effects when mediators are left-censored by assay limit of quantification
A semi-parametric framework using fractional imputation and EM algorithm for estimating causal direct and indirect effects with left-censored mediators due to assay limits.
-
Calibeating Prediction-Powered Inference
Post-hoc calibration of miscalibrated black-box predictions on a labeled sample improves efficiency of prediction-powered inference for semisupervised mean estimation.
-
Fitted $Q$ Evaluation Without Bellman Completeness via Stationary Weighting
Stationary-weighted FQE achieves finite-sample linear convergence to the projected Bellman fixed point without Bellman completeness by reweighting regressions to the target stationary norm.
-
An Online Meta-Level Adaptive Design Framework with Targeted Learning Inference: Applications to Evaluating and Utilizing Surrogate Outcomes in Adaptive Designs
A framework defining new causal estimands for adaptive designs and using TMLE to enable online selection among designs, including surrogate-guided ones, while handling data dependence.
-
Evaluating causal indirect effects when mediators are left-censored by assay limit of quantification
Proposes a fractional imputation plus semi-parametric EM framework for estimating natural direct and indirect effects under deterministic left-censoring of the mediator by assay limit of quantification.
-
Stationary Reweighting Yields Local Convergence of Soft Fitted Q-Iteration
Stationary reweighting of soft fitted Q-iteration yields finite-sample local linear convergence to the projected fixed point under approximate realizability and controlled weighting error, even without Bellman completeness.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.