Extrapolation-Aware Nonparametric Statistical Inference

• URL: http://arxiv.org/abs/2402.09758v2
• Date: Wed, 12 Jun 2024 12:45:53 GMT
• Title: Extrapolation-Aware Nonparametric Statistical Inference
• Authors: Niklas Pfister, Peter Bühlmann,
• Abstract summary: Extrapolating occurs in many data analysis applications and can invalidate the resulting conclusions if not taken into account. We extend the nonparametric statistical model to explicitly allow for extrapolation and introduce a class of extrapolation assumptions.
• Score: 8.090257544386482
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation occurs in many data analysis applications and can invalidate the resulting conclusions if not taken into account. While extrapolating is straightforward in parametric models, it becomes challenging in nonparametric models. In this work, we extend the nonparametric statistical model to explicitly allow for extrapolation and introduce a class of extrapolation assumptions that can be combined with existing inference techniques to draw extrapolation-aware conclusions. The proposed class of extrapolation assumptions stipulate that the conditional function attains its minimal and maximal directional derivative, in each direction, within the observed support. We illustrate how the framework applies to several statistical applications including prediction and uncertainty quantification. We furthermore propose a consistent estimation procedure that can be used to adjust existing nonparametric estimates to account for extrapolation by providing lower and upper extrapolation bounds. The procedure is empirically evaluated on both simulated and real-world data.

Related papers

• Progression: an extrapolation principle for regression [0.0]
  We propose a novel statistical extrapolation principle. It assumes a simple relationship between predictors and the response at the boundary of the training predictor samples. Our semi-parametric method, progression, leverages this extrapolation principle and offers guarantees on the approximation error beyond the training data range.
  arXiv  Detail & Related papers  (2024-10-30T17:29:51Z)
• Probabilistic Conformal Prediction with Approximate Conditional Validity [81.30551968980143]
  We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution. Our method consistently outperforms existing approaches in terms of conditional coverage.
  arXiv  Detail & Related papers  (2024-07-01T20:44:48Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach [3.085995273374333]
  Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous process conditioned on the realization of a random intensity function. Existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions.
  arXiv  Detail & Related papers  (2023-06-11T19:48:39Z)
• Doubly Robust Counterfactual Classification [1.8907108368038217]
  We study counterfactual classification as a new tool for decision-making under hypothetical (contrary to fact) scenarios. We propose a doubly-robust nonparametric estimator for a general counterfactual classifier.
  arXiv  Detail & Related papers  (2023-01-15T22:04:46Z)
• Divergence Frontiers for Generative Models: Sample Complexity, Quantization Level, and Frontier Integral [58.434753643798224]
  Divergence frontiers have been proposed as an evaluation framework for generative models. We establish non-asymptotic bounds on the sample complexity of the plug-in estimator of divergence frontiers. We also augment the divergence frontier framework by investigating the statistical performance of smoothed distribution estimators.
  arXiv  Detail & Related papers  (2021-06-15T06:26:25Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Performance metrics for intervention-triggering prediction models do not reflect an expected reduction in outcomes from using the model [71.9860741092209]
  Clinical researchers often select among and evaluate risk prediction models. Standard metrics calculated from retrospective data are only related to model utility under certain assumptions. When predictions are delivered repeatedly throughout time, the relationship between standard metrics and utility is further complicated.
  arXiv  Detail & Related papers  (2020-06-02T16:26:49Z)
• Nonparametric inverse probability weighted estimators based on the highly adaptive lasso [0.966840768820136]
  Inparametric inverse probability weighted estimators are known to be inefficient and suffer from the curse of dimensionality. We propose a class of nonparametric inverse probability weighted estimators in which the weighting mechanism is estimated via undersmoothing of the highly adaptive lasso. Our developments have broad implications for the construction of efficient inverse probability weighted estimators in large statistical models and a variety of problem settings.
  arXiv  Detail & Related papers  (2020-05-22T17:49:46Z)
• Machine learning for causal inference: on the use of cross-fit estimators [77.34726150561087]
  Doubly-robust cross-fit estimators have been proposed to yield better statistical properties. We conducted a simulation study to assess the performance of several estimators for the average causal effect (ACE) When used with machine learning, the doubly-robust cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage.
  arXiv  Detail & Related papers  (2020-04-21T23:09:55Z)

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.