On the Effectiveness of Hybrid Mutual Information Estimation

• URL: http://arxiv.org/abs/2306.00608v2
• Date: Fri, 2 Jun 2023 08:53:39 GMT
• Title: On the Effectiveness of Hybrid Mutual Information Estimation
• Authors: Marco Federici, David Ruhe, Patrick Forr\'e
• Abstract summary: Estimating the mutual information from samples from a joint distribution is a challenging problem in science and engineering. In this work, we realize a variational bound that generalizes both discriminative and generative approaches. We propose Predictive Quantization (PQ): a simple generative method that can be easily combined with discriminative estimators for minimal computational overhead.
• Score: 1.0312968200748118
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Estimating the mutual information from samples from a joint distribution is a challenging problem in both science and engineering. In this work, we realize a variational bound that generalizes both discriminative and generative approaches. Using this bound, we propose a hybrid method to mitigate their respective shortcomings. Further, we propose Predictive Quantization (PQ): a simple generative method that can be easily combined with discriminative estimators for minimal computational overhead. Our propositions yield a tighter bound on the information thanks to the reduced variance of the estimator. We test our methods on a challenging task of correlated high-dimensional Gaussian distributions and a stochastic process involving a system of free particles subjected to a fixed energy landscape. Empirical results show that hybrid methods consistently improved mutual information estimates when compared to the corresponding discriminative counterpart.

Related papers

• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• Mutual Information Multinomial Estimation [53.58005108981247]
  Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. Our main discovery is that a preliminary estimate of the data distribution can dramatically help estimate. Experiments on diverse tasks including non-Gaussian synthetic problems with known ground-truth and real-world applications demonstrate the advantages of our method.
  arXiv  Detail & Related papers  (2024-08-18T06:27:30Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Estimating Unknown Population Sizes Using the Hypergeometric Distribution [1.03590082373586]
  We tackle the challenge of estimating discrete distributions when both the total population size and the sizes of its constituent categories are unknown. We develop our approach to account for a data generating process where the ground-truth is a mixture of distributions conditional on a continuous latent variable. Empirical data simulation demonstrates that our method outperforms other likelihood functions used to model count data.
  arXiv  Detail & Related papers  (2024-02-22T01:53:56Z)
• Mutual Information Estimation via $f$-Divergence and Data Derangements [6.43826005042477]
  We propose a novel class of discrimi mutual information estimators based on the variational representation of the $f$-divergence. The proposed estimator is flexible since it exhibits an excellent bias/ variance trade-off.
  arXiv  Detail & Related papers  (2023-05-31T16:54:25Z)
• DEMI: Discriminative Estimator of Mutual Information [5.248805627195347]
  Estimating mutual information between continuous random variables is often intractable and challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual information. Our approach is based on training a classifier that provides the probability that a data sample pair is drawn from the joint distribution.
  arXiv  Detail & Related papers  (2020-10-05T04:19:27Z)
• A One-step Approach to Covariate Shift Adaptation [82.01909503235385]
  A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. We propose a novel one-step approach that jointly learns the predictive model and the associated weights in one optimization.
  arXiv  Detail & Related papers  (2020-07-08T11:35:47Z)
• Almost-Matching-Exactly for Treatment Effect Estimation under Network Interference [73.23326654892963]
  We propose a matching method that recovers direct treatment effects from randomized experiments where units are connected in an observed network. Our method matches units almost exactly on counts of unique subgraphs within their neighborhood graphs.
  arXiv  Detail & Related papers  (2020-03-02T15:21:20Z)
• Distributed Sketching Methods for Privacy Preserving Regression [54.51566432934556]
  We leverage randomized sketches for reducing the problem dimensions as well as preserving privacy and improving straggler resilience in asynchronous distributed systems. We derive novel approximation guarantees for classical sketching methods and analyze the accuracy of parameter averaging for distributed sketches. We illustrate the performance of distributed sketches in a serverless computing platform with large scale experiments.
  arXiv  Detail & Related papers  (2020-02-16T08:35:48Z)

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.