Neural Estimation and Optimization of Directed Information over Continuous Spaces

Dor Tsur, Ziv Aharoni, Ziv Goldfeld, Haim Permuter

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This work develops a new method for estimating and optimizing the directed information rate between two jointly stationary and ergodic stochastic processes. Building upon recent advances in machine learning, we propose a recurrent neural network (RNN)-based estimator which is optimized via gradient ascent over the RNN parameters. The estimator does not require prior knowledge of the underlying joint/marginal distributions and can be easily optimized over continuous input processes realized by a deep generative model. We prove consistency of the proposed estimation and optimization methods and combine them to obtain end-to-end performance guarantees. Applications for channel capacity estimation of continuous channels with memory are explored, and empirical results demonstrating the scalability and accuracy of our method are provided. When the channel is memoryless, we investigate the mapping learned by the optimized input generator.

Original languageEnglish
Pages (from-to)4777-4798
Number of pages22
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - 5 Apr 2023


  • Channel capacity
  • directed information
  • neural estimation
  • recurrent neural networks

ASJC Scopus subject areas

  • Information Systems
  • Library and Information Sciences
  • Computer Science Applications


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