On Uncertainty Quantification for Near-Bayes Optimal Algorithms

• URL: http://arxiv.org/abs/2403.19381v2
• Date: Mon, 21 Oct 2024 08:26:52 GMT
• Title: On Uncertainty Quantification for Near-Bayes Optimal Algorithms
• Authors: Ziyu Wang, Chris Holmes,
• Abstract summary: We show that it is possible to recover the Bayesian posterior defined by the task distribution, which is unknown but optimal in this setting, by building a martingale posterior using the algorithm. Experiments based on a variety of non-NN and NN algorithms demonstrate the efficacy of our method.
• Score: 2.622066970118316
• License:
• Abstract: Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian counterpart. In this work we present a promising approach to address this challenge, based on the hypothesis that commonly used ML algorithms are efficient across a wide variety of tasks and may thus be near Bayes-optimal w.r.t. an unknown task distribution. We prove that it is possible to recover the Bayesian posterior defined by the task distribution, which is unknown but optimal in this setting, by building a martingale posterior using the algorithm. We further propose a practical uncertainty quantification method that apply to general ML algorithms. Experiments based on a variety of non-NN and NN algorithms demonstrate the efficacy of our method.

Related papers

• Stochastic Ratios Tracking Algorithm for Large Scale Machine Learning Problems [0.7614628596146599]
  We propose a novel algorithm for adaptive step length selection in the classical SGD framework. Under reasonable conditions, the algorithm produces step lengths in line with well-established theoretical requirements. We show that the algorithm can generate step lengths comparable to the best step length obtained from manual tuning.
  arXiv  Detail & Related papers  (2023-05-17T06:22:11Z)
• Representation Learning with Multi-Step Inverse Kinematics: An Efficient and Optimal Approach to Rich-Observation RL [106.82295532402335]
  Existing reinforcement learning algorithms suffer from computational intractability, strong statistical assumptions, and suboptimal sample complexity. We provide the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics.
  arXiv  Detail & Related papers  (2023-04-12T14:51:47Z)
• An adaptive Bayesian quantum algorithm for phase estimation [0.0]
  We present a coherence-based phase-estimation algorithm which can achieve the optimal quadratic scaling in the mean absolute error and the mean squared error. In the presence of noise, our algorithm produces errors that approach the theoretical lower bound.
  arXiv  Detail & Related papers  (2023-03-02T19:00:01Z)
• A Learning-Based Optimal Uncertainty Quantification Method and Its Application to Ballistic Impact Problems [1.713291434132985]
  This paper concerns the optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) measure is only partially/imperfectly known. We demonstrate the learning based framework on the uncertainty optimization problem. We show that the approach can be used to construct maps for the performance certificate and safety in engineering practice.
  arXiv  Detail & Related papers  (2022-12-28T14:30:53Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Benchmarking Simulation-Based Inference [5.3898004059026325]
  Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency.
  arXiv  Detail & Related papers  (2021-01-12T18:31:22Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• A Dynamical Systems Approach for Convergence of the Bayesian EM Algorithm [59.99439951055238]
  We show how (discrete-time) Lyapunov stability theory can serve as a powerful tool to aid, or even lead, in the analysis (and potential design) of optimization algorithms that are not necessarily gradient-based. The particular ML problem that this paper focuses on is that of parameter estimation in an incomplete-data Bayesian framework via the popular optimization algorithm known as maximum a posteriori expectation-maximization (MAP-EM) We show that fast convergence (linear or quadratic) is achieved, which could have been difficult to unveil without our adopted S&C approach.
  arXiv  Detail & Related papers  (2020-06-23T01:34:18Z)
• Active Model Estimation in Markov Decision Processes [108.46146218973189]
  We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP) We show that our Markov-based algorithm outperforms both our original algorithm and the maximum entropy algorithm in the small sample regime.
  arXiv  Detail & Related papers  (2020-03-06T16:17:24Z)
• To quantum or not to quantum: towards algorithm selection in near-term quantum optimization [0.0]
  We study the problem of detecting problem instances of where QAOA is most likely to yield an advantage over a conventional algorithm. We achieve cross-validated accuracy well over 96%, which would yield a substantial practical advantage.
  arXiv  Detail & Related papers  (2020-01-22T20:42:02Z)

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.