First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint

• URL: http://arxiv.org/abs/2605.02827v1
• Date: Mon, 04 May 2026 17:02:17 GMT
• Title: First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint
• Abstract summary: We propose an efficiency-Aware Surrogate-adjusted Estimator (EASE) that directly chooses the sampling law and surrogate to minimize the first-order MSE.<n>We demonstrate that EASE consistently outperforms state-of-the-art estimators for various probabilistic values.
• Score: 18.696678371045216
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Probabilistic values, including Shapley values and semivalues, provide a model-agnostic framework to attribute the behavior of a black-box model to data points or features, with a wide range of applications including explainable artificial intelligence and data valuation. However, their exact computation requires utility evaluations over exponentially many coalitions, making Monte Carlo approximation essential in modern machine learning applications. Existing estimators are often developed through different identification strategies, including weighted averages, self-normalized weighting, regression adjustment, and weighted least squares. Our key observation is that these seemingly distinct constructions share a common first-order error structure, in which the leading term is an augmented inverse-probability weighted influence term determined by the sampling law and a working surrogate function. This first-order representation yields an explicit expression for the leading mean squared error (MSE), which characterizes how the sampling law and the surrogate jointly determine statistical efficiency. Guided by this criterion, we propose an Efficiency-Aware Surrogate-adjusted Estimator (EASE) that directly chooses the sampling law and surrogate to minimize the first-order MSE. We demonstrate that EASE consistently outperforms state-of-the-art estimators for various probabilistic values.

Related papers

• STAR : Bridging Statistical and Agentic Reasoning for Large Model Performance Prediction [78.0692157478247]
  We propose STAR, a framework that bridges data-driven STatistical expectations with knowledge-driven Agentic Reasoning.<n>We show that STAR consistently outperforms all baselines on both score-based and rank-based metrics.
  arXiv  Detail & Related papers  (2026-02-12T16:30:07Z)
• Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals [18.612081365101464]
  We develop a framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains.<n>Across simulations, our one-step estimator substantially improves ranking accuracy with gains increasing as model output noise grows.<n>Experiments on GPQA Diamond, AIME 2025 and GSM8K further demonstrate more precise performance estimation and more reliable model rankings.
  arXiv  Detail & Related papers  (2026-02-03T03:40:01Z)
• AICO: Feature Significance Tests for Supervised Learning [0.9474649136535703]
  AICO asks, for any trained regression or classification model, whether each feature genuinely improves model performance.<n>It does so by masking the feature's information and measuring the resulting change in performance.<n>AICO consistently pinpoints the variables that drive model behavior.
  arXiv  Detail & Related papers  (2025-06-29T21:15:40Z)
• Model-free Methods for Event History Analysis and Efficient Adjustment (PhD Thesis) [55.2480439325792]
  This thesis is a series of independent contributions to statistics unified by a model-free perspective.<n>The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction techniques from machine learning.<n>The second chapter studies the concept of local independence, which describes whether the evolution of one process is directly influenced by another.
  arXiv  Detail & Related papers  (2025-02-11T19:24:09Z)
• Bayesian Estimation and Tuning-Free Rank Detection for Probability Mass Function Tensors [17.640500920466984]
  This paper presents a novel framework for estimating the joint PMF and automatically inferring its rank from observed data. We derive a deterministic solution based on variational inference (VI) to approximate the posterior distributions of various model parameters. Additionally, we develop a scalable version of the VI-based approach by leveraging variational inference (SVI) Experiments involving both synthetic data and real movie recommendation data illustrate the advantages of our VI and SVI-based methods in terms of estimation accuracy, automatic rank detection, and computational efficiency.
  arXiv  Detail & Related papers  (2024-10-08T20:07:49Z)
• Stratified Prediction-Powered Inference for Hybrid Language Model Evaluation [62.2436697657307]
  Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data.<n>We propose a method called Stratified Prediction-Powered Inference (StratPPI)<n>We show that the basic PPI estimates can be considerably improved by employing simple data stratification strategies.
  arXiv  Detail & Related papers  (2024-06-06T17:37:39Z)
• Consensus-Adaptive RANSAC [104.87576373187426]
  We propose a new RANSAC framework that learns to explore the parameter space by considering the residuals seen so far via a novel attention layer. The attention mechanism operates on a batch of point-to-model residuals, and updates a per-point estimation state to take into account the consensus found through a lightweight one-step transformer.
  arXiv  Detail & Related papers  (2023-07-26T08:25:46Z)
• Leveraging Variational Autoencoders for Parameterized MMSE Estimation [10.141454378473972]
  We propose a variational autoencoder-based framework for parameterizing a conditional linear minimum mean squared error estimator. The derived estimator is shown to approximate the minimum mean squared error estimator by utilizing the variational autoencoder as a generative prior for the estimation problem. We conduct a rigorous analysis by bounding the difference between the proposed and the minimum mean squared error estimator.
  arXiv  Detail & Related papers  (2023-07-11T15:41:34Z)
• Semi-Supervised Quantile Estimation: Robust and Efficient Inference in High Dimensional Settings [0.5735035463793009]
  We consider quantile estimation in a semi-supervised setting, characterized by two available data sets. We propose a family of semi-supervised estimators for the response quantile(s) based on the two data sets.
  arXiv  Detail & Related papers  (2022-01-25T10:02:23Z)
• Conceptually Diverse Base Model Selection for Meta-Learners in Concept Drifting Data Streams [3.0938904602244355]
  We present a novel approach for estimating the conceptual similarity of base models, which is calculated using the Principal Angles (PAs) between their underlying subspaces. We evaluate these methods against thresholding using common ensemble pruning metrics, namely predictive performance and Mutual Information (MI) in the context of online Transfer Learning (TL) Our results show that conceptual similarity thresholding has a reduced computational overhead, and yet yields comparable predictive performance to thresholding using predictive performance and MI.
  arXiv  Detail & Related papers  (2021-11-29T13:18:53Z)
• Deconfounding Scores: Feature Representations for Causal Effect Estimation with Weak Overlap [140.98628848491146]
  We introduce deconfounding scores, which induce better overlap without biasing the target of estimation. We show that deconfounding scores satisfy a zero-covariance condition that is identifiable in observed data. In particular, we show that this technique could be an attractive alternative to standard regularizations.
  arXiv  Detail & Related papers  (2021-04-12T18:50:11Z)
• 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)

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.