A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees

• URL: http://arxiv.org/abs/2105.15197v1
• Date: Mon, 31 May 2021 17:57:02 GMT
• Title: A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees
• Authors: Victor Chernozhukov, Whitney K. Newey, Rahul Singh
• Abstract summary: We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference.
• Score: 4.55274575362193
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals (i.e. scalar summaries) of machine learning algorithms. For example, an analyst may desire the confidence interval for a treatment effect estimated with a neural network. We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. The rate of convergence is root-n for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a new double robustness property for ill posed inverse problems.

Related papers

• Efficient Model-Free Exploration in Low-Rank MDPs [76.87340323826945]
  Low-Rank Markov Decision Processes offer a simple, yet expressive framework for RL with function approximation. Existing algorithms are either (1) computationally intractable, or (2) reliant upon restrictive statistical assumptions. We propose the first provably sample-efficient algorithm for exploration in Low-Rank MDPs.
  arXiv  Detail & Related papers  (2023-07-08T15:41:48Z)
• A new approach to generalisation error of machine learning algorithms: Estimates and convergence [0.0]
  We introduce a new approach to the estimation of the (generalisation) error and to convergence. Our results include estimates of the error without any structural assumption on the neural networks.
  arXiv  Detail & Related papers  (2023-06-23T20:57:31Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Less is More: Rethinking Few-Shot Learning and Recurrent Neural Nets [2.824895388993495]
  We provide theoretical guarantees for reliable learning under the information-theoretic AEP. We then focus on a highly efficient recurrent neural net (RNN) framework and propose a reduced-entropy algorithm for few-shot learning. Our experimental results demonstrate significant potential for improving learning models' sample efficiency, generalization, and time complexity.
  arXiv  Detail & Related papers  (2022-09-28T17:33:11Z)
• A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics [41.99023989695363]
  We explore the potential for semiparametric theory to be used to improve neural networks and machine learning algorithms. We propose a new neural network method MultiNet, which seeks the flexibility and diversity of an ensemble using a single architecture.
  arXiv  Detail & Related papers  (2022-02-18T09:35:51Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• Statistically Meaningful Approximation: a Case Study on Approximating Turing Machines with Transformers [50.85524803885483]
  This work proposes a formal definition of statistically meaningful (SM) approximation which requires the approximating network to exhibit good statistical learnability. We study SM approximation for two function classes: circuits and Turing machines.
  arXiv  Detail & Related papers  (2021-07-28T04:28:55Z)
• Predicting Unreliable Predictions by Shattering a Neural Network [145.3823991041987]
  Piecewise linear neural networks can be split into subfunctions. Subfunctions have their own activation pattern, domain, and empirical error. Empirical error for the full network can be written as an expectation over subfunctions.
  arXiv  Detail & Related papers  (2021-06-15T18:34:41Z)
• Function Approximation via Sparse Random Features [23.325877475827337]
  This paper introduces the sparse random feature method that learns parsimonious random feature models utilizing techniques from compressive sensing. We show that the sparse random feature method outperforms shallow networks for well-structured functions and applications to scientific machine learning tasks.
  arXiv  Detail & Related papers  (2021-03-04T17:53:54Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.