Variational Inference with Coverage Guarantees in Simulation-Based Inference

• URL: http://arxiv.org/abs/2305.14275v3
• Date: Thu, 25 Jul 2024 05:53:46 GMT
• Title: Variational Inference with Coverage Guarantees in Simulation-Based Inference
• Authors: Yash Patel, Declan McNamara, Jackson Loper, Jeffrey Regier, Ambuj Tewari,
• Abstract summary: We propose Conformalized Amortized Neural Variational Inference (CANVI) CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation.
• Score: 18.818573945984873
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Amortized variational inference is an often employed framework in simulation-based inference that produces a posterior approximation that can be rapidly computed given any new observation. Unfortunately, there are few guarantees about the quality of these approximate posteriors. We propose Conformalized Amortized Neural Variational Inference (CANVI), a procedure that is scalable, easily implemented, and provides guaranteed marginal coverage. Given a collection of candidate amortized posterior approximators, CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. CANVI ensures that the resulting predictor constructs regions that contain the truth with a user-specified level of probability. CANVI is agnostic to design decisions in formulating the candidate approximators and only requires access to samples from the forward model, permitting its use in likelihood-free settings. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation. Finally, we demonstrate the accurate calibration and high predictive efficiency of CANVI on a suite of simulation-based inference benchmark tasks and an important scientific task: analyzing galaxy emission spectra.

Related papers

• Statistical Inference for Temporal Difference Learning with Linear Function Approximation [62.69448336714418]
  Temporal Difference (TD) learning, arguably the most widely used for policy evaluation, serves as a natural framework for this purpose. In this paper, we study the consistency properties of TD learning with Polyak-Ruppert averaging and linear function approximation, and obtain three significant improvements over existing results.
  arXiv  Detail & Related papers  (2024-10-21T15:34:44Z)
• Optimizing Probabilistic Conformal Prediction with Vectorized Non-Conformity Scores [6.059745771017814]
  We propose a novel framework that enhances efficiency by first vectorizing the non-conformity scores with ranked samples and then optimizing the shape of the prediction set by varying the quantiles for samples at the same rank. Our method delivers valid coverage while producing discontinuous and more efficient prediction sets, making it particularly suited for high-stakes applications.
  arXiv  Detail & Related papers  (2024-10-17T16:37:03Z)
• 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)
• Calibrated Probabilistic Forecasts for Arbitrary Sequences [58.54729945445505]
  Real-world data streams can change unpredictably due to distribution shifts, feedback loops and adversarial actors. We present a forecasting framework ensuring valid uncertainty estimates regardless of how data evolves.
  arXiv  Detail & Related papers  (2024-09-27T21:46:42Z)
• Probabilistic Scores of Classifiers, Calibration is not Enough [0.32985979395737786]
  In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications. In this study, we highlight approaches that prioritize the alignment between predicted scores and true probability distributions. Our findings reveal limitations in traditional calibration metrics, which could undermine the reliability of predictive models for critical decision-making.
  arXiv  Detail & Related papers  (2024-08-06T19:53:00Z)
• 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)
• Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability [50.44439018155837]
  We propose to include a calibration term directly into the training objective of the neural model. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference.
  arXiv  Detail & Related papers  (2023-10-20T10:20:45Z)
• Efficient and Differentiable Conformal Prediction with General Function Classes [96.74055810115456]
  We propose a generalization of conformal prediction to multiple learnable parameters. We show that it achieves approximate valid population coverage and near-optimal efficiency within class. Experiments show that our algorithm is able to learn valid prediction sets and improve the efficiency significantly.
  arXiv  Detail & Related papers  (2022-02-22T18:37:23Z)
• Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression [51.770998056563094]
  Probabilistic Gradient Boosting Machines (PGBM) is a method to create probabilistic predictions with a single ensemble of decision trees. We empirically demonstrate the advantages of PGBM compared to existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-03T08:32:13Z)
• Robust Validation: Confident Predictions Even When Distributions Shift [19.327409270934474]
  We describe procedures for robust predictive inference, where a model provides uncertainty estimates on its predictions rather than point predictions. We present a method that produces prediction sets (almost exactly) giving the right coverage level for any test distribution in an $f$-divergence ball around the training population. An essential component of our methodology is to estimate the amount of expected future data shift and build robustness to it.
  arXiv  Detail & Related papers  (2020-08-10T17:09:16Z)

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.