Local Prediction-Powered Inference

• URL: http://arxiv.org/abs/2409.18321v1
• Date: Thu, 26 Sep 2024 22:15:53 GMT
• Title: Local Prediction-Powered Inference
• Authors: Yanwu Gu, Dong Xia,
• Abstract summary: This paper introduces a specific algorithm for local multivariable regression using PPI. The confidence intervals, bias correction, and coverage probabilities are analyzed and proved the correctness and superiority of our algorithm.
• Score: 7.174572371800217
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To infer a function value on a specific point $x$, it is essential to assign higher weights to the points closer to $x$, which is called local polynomial / multivariable regression. In many practical cases, a limited sample size may ruin this method, but such conditions can be improved by the Prediction-Powered Inference (PPI) technique. This paper introduced a specific algorithm for local multivariable regression using PPI, which can significantly reduce the variance of estimations without enlarge the error. The confidence intervals, bias correction, and coverage probabilities are analyzed and proved the correctness and superiority of our algorithm. Numerical simulation and real-data experiments are applied and show these conclusions. Another contribution compared to PPI is the theoretical computation efficiency and explainability by taking into account the dependency of the dependent variable.

Related papers

• Fundamental Computational Limits in Pursuing Invariant Causal Prediction and Invariance-Guided Regularization [11.940138507727577]
  Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way. Existing methods that can attain sample-efficient estimation are based on exponential time algorithms. This paper proposes a method capable of attaining both computationally and statistically efficient estimation under additional conditions.
  arXiv  Detail & Related papers  (2025-01-29T00:29:36Z)
• Automatic Double Reinforcement Learning in Semiparametric Markov Decision Processes with Applications to Long-Term Causal Inference [33.14076284663493]
  We study efficient inference on linear functionals of the $Q$-function in time-invariant Markov Decision Process (MDPs) These restrictions can reduce the overlap requirement and lower the efficiency bound, yielding more precise estimates. As a special case, we propose a novel adaptive debiased plug-in estimator that uses isotonic-adaptive fitted $Q$-iteration - a new calibration algorithm for MDPs.
  arXiv  Detail & Related papers  (2025-01-12T20:35:28Z)
• Statistical Inference for Temporal Difference Learning with Linear Function Approximation [62.69448336714418]
  We study the consistency properties of TD learning with Polyak-Ruppert averaging and linear function approximation. First, we derive a novel high-dimensional probability convergence guarantee that depends explicitly on the variance and holds under weak conditions. We further establish refined high-dimensional Berry-Esseen bounds over the class of convex sets that guarantee faster rates than those in the literature.
  arXiv  Detail & Related papers  (2024-10-21T15:34:44Z)
• Policy Gradient with Active Importance Sampling [55.112959067035916]
  Policy gradient (PG) methods significantly benefit from IS, enabling the effective reuse of previously collected samples. However, IS is employed in RL as a passive tool for re-weighting historical samples. We look for the best behavioral policy from which to collect samples to reduce the policy gradient variance.
  arXiv  Detail & Related papers  (2024-05-09T09:08:09Z)
• Online non-parametric likelihood-ratio estimation by Pearson-divergence functional minimization [55.98760097296213]
  We introduce a new framework for online non-parametric LRE (OLRE) for the setting where pairs of iid observations $(x_t sim p, x'_t sim q)$ are observed over time. We provide theoretical guarantees for the performance of the OLRE method along with empirical validation in synthetic experiments.
  arXiv  Detail & Related papers  (2023-11-03T13:20:11Z)
• U-Statistics for Importance-Weighted Variational Inference [29.750633016889655]
  We propose the use of U-statistics to reduce variance for estimation in importance-weighted variational inference. We find empirically that U-statistic variance reduction can lead to modest to significant improvements in inference performance on a range of models.
  arXiv  Detail & Related papers  (2023-02-27T16:08:43Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Variance Minimization in the Wasserstein Space for Invariant Causal Prediction [72.13445677280792]
  In this work, we show that the approach taken in ICP may be reformulated as a series of nonparametric tests that scales linearly in the number of predictors. Each of these tests relies on the minimization of a novel loss function that is derived from tools in optimal transport theory. We prove under mild assumptions that our method is able to recover the set of identifiable direct causes, and we demonstrate in our experiments that it is competitive with other benchmark causal discovery algorithms.
  arXiv  Detail & Related papers  (2021-10-13T22:30:47Z)
• Input Dependent Sparse Gaussian Processes [1.1470070927586014]
  We use a neural network that receives the observed data as an input and outputs the inducing points locations and the parameters of $q$. We evaluate our method in several experiments, showing that it performs similar or better than other state-of-the-art sparse variational GP approaches.
  arXiv  Detail & Related papers  (2021-07-15T12:19:10Z)
• SLOE: A Faster Method for Statistical Inference in High-Dimensional Logistic Regression [68.66245730450915]
  We develop an improved method for debiasing predictions and estimating frequentist uncertainty for practical datasets. Our main contribution is SLOE, an estimator of the signal strength with convergence guarantees that reduces the computation time of estimation and inference by orders of magnitude.
  arXiv  Detail & Related papers  (2021-03-23T17:48:56Z)

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.