INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915175091666944 |
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| author | Foresti, Alberto Franzese, Giulio Michiardi, Pietro |
| author_facet | Foresti, Alberto Franzese, Giulio Michiardi, Pietro |
| contents | Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem, particularly in the case of high-dimensional discrete distributions. Current approaches typically rely on embedding discrete data into a continuous space and applying neural estimators originally designed for continuous distributions, a process that may not fully capture the discrete nature of the underlying data. We consider Continuous-Time Markov Chains (CTMCs), stochastic processes on discrete state-spaces which have gained popularity due to their generative modeling applications. In this work, we introduce INFO-SEDD, a novel method for estimating information-theoretic quantities of discrete data, including mutual information and entropy. Our approach requires the training of a single parametric model, offering significant computational and memory advantages. Additionally, it seamlessly integrates with pretrained networks, allowing for efficient reuse of pretrained generative models. To evaluate our approach, we construct a challenging synthetic benchmark. Our experiments demonstrate that INFO-SEDD is robust and outperforms neural competitors that rely on embedding techniques. Moreover, we validate our method on a real-world task: estimating the entropy of an Ising model. Overall, INFO-SEDD outperforms competing methods and shows scalability to high-dimensional scenarios, paving the way for new applications where estimating MI between discrete distribution is the focus. The promising results in this complex, high-dimensional scenario highlight INFO-SEDD as a powerful new estimator in the toolkit for information-theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators Foresti, Alberto Franzese, Giulio Michiardi, Pietro Machine Learning Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem, particularly in the case of high-dimensional discrete distributions. Current approaches typically rely on embedding discrete data into a continuous space and applying neural estimators originally designed for continuous distributions, a process that may not fully capture the discrete nature of the underlying data. We consider Continuous-Time Markov Chains (CTMCs), stochastic processes on discrete state-spaces which have gained popularity due to their generative modeling applications. In this work, we introduce INFO-SEDD, a novel method for estimating information-theoretic quantities of discrete data, including mutual information and entropy. Our approach requires the training of a single parametric model, offering significant computational and memory advantages. Additionally, it seamlessly integrates with pretrained networks, allowing for efficient reuse of pretrained generative models. To evaluate our approach, we construct a challenging synthetic benchmark. Our experiments demonstrate that INFO-SEDD is robust and outperforms neural competitors that rely on embedding techniques. Moreover, we validate our method on a real-world task: estimating the entropy of an Ising model. Overall, INFO-SEDD outperforms competing methods and shows scalability to high-dimensional scenarios, paving the way for new applications where estimating MI between discrete distribution is the focus. The promising results in this complex, high-dimensional scenario highlight INFO-SEDD as a powerful new estimator in the toolkit for information-theoretical analysis. |
| title | INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.19183 |