The Surprising Benefits of Base Rate Neglect in Robust Aggregation

• URL: http://arxiv.org/abs/2406.13490v1
• Date: Wed, 19 Jun 2024 12:20:29 GMT
• Title: The Surprising Benefits of Base Rate Neglect in Robust Aggregation
• Authors: Yuqing Kong, Shu Wang, Ying Wang,
• Abstract summary: Our work considers experts who tend to ignore the base rate. We find that a certain degree of base rate neglect helps with robust forecast aggregation.
• Score: 14.286448842405678
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Robust aggregation integrates predictions from multiple experts without knowledge of the experts' information structures. Prior work assumes experts are Bayesian, providing predictions as perfect posteriors based on their signals. However, real-world experts often deviate systematically from Bayesian reasoning. Our work considers experts who tend to ignore the base rate. We find that a certain degree of base rate neglect helps with robust forecast aggregation. Specifically, we consider a forecast aggregation problem with two experts who each predict a binary world state after observing private signals. Unlike previous work, we model experts exhibiting base rate neglect, where they incorporate the base rate information to degree $\lambda\in[0,1]$, with $\lambda=0$ indicating complete ignorance and $\lambda=1$ perfect Bayesian updating. To evaluate aggregators' performance, we adopt Arieli et al. (2018)'s worst-case regret model, which measures the maximum regret across the set of considered information structures compared to an omniscient benchmark. Our results reveal the surprising V-shape of regret as a function of $\lambda$. That is, predictions with an intermediate incorporating degree of base rate $\lambda<1$ can counter-intuitively lead to lower regret than perfect Bayesian posteriors with $\lambda=1$. We additionally propose a new aggregator with low regret robust to unknown $\lambda$. Finally, we conduct an empirical study to test the base rate neglect model and evaluate the performance of various aggregators.

Related papers

• Rejection via Learning Density Ratios [50.91522897152437]
  Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. We propose a different distributional perspective, where we seek to find an idealized data distribution which maximizes a pretrained model's performance. Our framework is tested empirically over clean and noisy datasets.
  arXiv  Detail & Related papers  (2024-05-29T01:32:17Z)
• Robust Decision Aggregation with Adversarial Experts [4.021926055330022]
  We consider a robust aggregation problem in the presence of both truthful and adversarial experts. We aim to find the optimal aggregator that outputs a forecast minimizing regret under the worst information structure and adversarial strategies.
  arXiv  Detail & Related papers  (2024-03-13T03:47:08Z)
• Optimal score estimation via empirical Bayes smoothing [13.685846094715364]
  We study the problem of estimating the score function of an unknown probability distribution $rho*$ from $n$ independent and identically distributed observations in $d$ dimensions. We show that a regularized score estimator based on a Gaussian kernel attains this rate, shown optimal by a matching minimax lower bound.
  arXiv  Detail & Related papers  (2024-02-12T16:17:40Z)
• Functional Ensemble Distillation [18.34081591772928]
  We investigate how to best distill an ensemble's predictions using an efficient model. We find that learning the distilled model via a simple augmentation scheme in the form of mixup augmentation significantly boosts the performance.
  arXiv  Detail & Related papers  (2022-06-05T14:07:17Z)
• Sharp regret bounds for empirical Bayes and compound decision problems [42.397889421982555]
  In a Bayes setting the optimal estimator is given by the prior-dependent conditional mean. We show that for the Poisson model with compactly supported and subexponential priors, the optimal regret scales as $Theta(fraclog nloglog n)2)$ and $Theta(log3 n)$.
  arXiv  Detail & Related papers  (2021-09-08T21:34:47Z)
• Towards an Understanding of Benign Overfitting in Neural Networks [104.2956323934544]
  Modern machine learning models often employ a huge number of parameters and are typically optimized to have zero training loss. We examine how these benign overfitting phenomena occur in a two-layer neural network setting. We show that it is possible for the two-layer ReLU network interpolator to achieve a near minimax-optimal learning rate.
  arXiv  Detail & Related papers  (2021-06-06T19:08:53Z)
• Fast Rates for the Regret of Offline Reinforcement Learning [69.23654172273085]
  We study the regret of reinforcement learning from offline data generated by a fixed behavior policy in an infinitehorizon discounted decision process (MDP) We show that given any estimate for the optimal quality function $Q*$, the regret of the policy it defines converges at a rate given by the exponentiation of the $Q*$-estimate's pointwise convergence rate.
  arXiv  Detail & Related papers  (2021-01-31T16:17:56Z)
• Optimal Algorithms for Stochastic Multi-Armed Bandits with Heavy Tailed Rewards [24.983866845065926]
  We consider multi-armed bandits with heavy-tailed rewards, whose $p$-th moment is bounded by a constant $nu_p$ for $1pleq2$. We propose a novel robust estimator which does not require $nu_p$ as prior information. We show that an error probability of the proposed estimator decays exponentially fast.
  arXiv  Detail & Related papers  (2020-10-24T10:44:02Z)
• Nonparametric Estimation of the Fisher Information and Its Applications [82.00720226775964]
  This paper considers the problem of estimation of the Fisher information for location from a random sample of size $n$. An estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. A new estimator, termed a clipped estimator, is proposed.
  arXiv  Detail & Related papers  (2020-05-07T17:21:56Z)
• Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks [65.24701908364383]
  We show that a sufficient condition for a uncertainty on a ReLU network is "to be a bit Bayesian calibrated" We further validate these findings empirically via various standard experiments using common deep ReLU networks and Laplace approximations.
  arXiv  Detail & Related papers  (2020-02-24T08:52:06Z)
• Bayesian Deep Learning and a Probabilistic Perspective of Generalization [56.69671152009899]
  We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization. We also propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction.
  arXiv  Detail & Related papers  (2020-02-20T15:13:27Z)

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.