A Framework for Sample Efficient Interval Estimation with Control Variates

• URL: http://arxiv.org/abs/2006.10287v1
• Date: Thu, 18 Jun 2020 05:42:30 GMT
• Title: A Framework for Sample Efficient Interval Estimation with Control Variates
• Authors: Shengjia Zhao, Christopher Yeh, Stefano Ermon
• Abstract summary: We consider the problem of estimating confidence intervals for the mean of a random variable. Under certain conditions, we show improved efficiency compared to existing estimation algorithms.
• Score: 94.32811054797148
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this problem in the general case, improved performance is possible under additional assumptions. In particular, we design an estimation algorithm to take advantage of side information in the form of a control variate, leveraging order statistics. Under certain conditions on the quality of the control variates, we show improved asymptotic efficiency compared to existing estimation algorithms. Empirically, we demonstrate superior performance on several real world surveying and estimation tasks where we use the output of regression models as the control variates.

Related papers

• Gradient Descent Efficiency Index [0.0]
  This study introduces a new efficiency metric, Ek, designed to quantify the effectiveness of each iteration. The proposed metric accounts for both the relative change in error and the stability of the loss function across iterations. Ek has the potential to guide more informed decisions in the selection and tuning of optimization algorithms in machine learning applications.
  arXiv  Detail & Related papers  (2024-10-25T10:22:22Z)
• RHiOTS: A Framework for Evaluating Hierarchical Time Series Forecasting Algorithms [0.393259574660092]
  RHiOTS is designed to assess the robustness of hierarchical time series forecasting models and algorithms on real-world datasets. RHiOTS incorporates an innovative visualization component, turning complex, multidimensional robustness evaluation results into intuitive, easily interpretable visuals. Our findings show that traditional statistical methods are more robust than state-of-the-art deep learning algorithms, except when the transformation effect is highly disruptive.
  arXiv  Detail & Related papers  (2024-08-06T18:52:15Z)
• Best-Effort Adaptation [62.00856290846247]
  We present a new theoretical analysis of sample reweighting methods, including bounds holding uniformly over the weights. We show how these bounds can guide the design of learning algorithms that we discuss in detail. We report the results of a series of experiments demonstrating the effectiveness of our best-effort adaptation and domain adaptation algorithms.
  arXiv  Detail & Related papers  (2023-05-10T00:09:07Z)
• Adaptive Sampling Quasi-Newton Methods for Zeroth-Order Stochastic Optimization [1.7513645771137178]
  We consider unconstrained optimization problems with no available gradient information. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a simulation function using finite differences within a common random number framework. We develop modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the approximations and provide global convergence results to the neighborhood of the optimal solution.
  arXiv  Detail & Related papers  (2021-09-24T21:49:25Z)
• Optimal Off-Policy Evaluation from Multiple Logging Policies [77.62012545592233]
  We study off-policy evaluation from multiple logging policies, each generating a dataset of fixed size, i.e., stratified sampling. We find the OPE estimator for multiple loggers with minimum variance for any instance, i.e., the efficient one.
  arXiv  Detail & Related papers  (2020-10-21T13:43:48Z)
• Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization [62.47170258504037]
  This paper presents a framework that encompasses and generalizes existing approaches that use controls, kernels and neural networks. Novel theoretical results are presented to provide insight into the variance reduction that can be achieved, and an empirical assessment, including applications to Bayesian inference, is provided in support.
  arXiv  Detail & Related papers  (2020-06-12T22:03:25Z)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)
• Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis [102.29671176698373]
  We address the problem of policy evaluation in discounted decision processes, and provide Markov-dependent guarantees on the $ell_infty$error under a generative model. We establish both and non-asymptotic versions of local minimax lower bounds for policy evaluation, thereby providing an instance-dependent baseline by which to compare algorithms.
  arXiv  Detail & Related papers  (2020-03-16T17:15:28Z)

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.