Towards a Unified Information-Theoretic Framework for Generalization
Authors: Mahdi Haghifam, Gintare Karolina Dziugaite, Shay Moran, Dan Roy
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we investigate the expressiveness of the conditional mutual information (CMI) framework of Steinke and Zakynthinou [1] and the prospect of using it to provide a unified framework for proving generalization bounds in the realizable setting. We first demonstrate that one can use this framework to express non-trivial (but sub-optimal) bounds for any learning algorithm that outputs hypotheses from a class of bounded VC dimension. We then explore two directions of strengthening this bound: (i) Can the CMI framework express optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal optimal bounds for VC classes? (ii) Can the CMI framework be used to analyze algorithms whose output hypothesis space is unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted unrestricted (i.e. has an unbounded VC dimension)? With respect to Item (i) we prove that the CMI framework yields the optimal bound on the expected risk of Support Vector Machines (SVMs) for learning halfspaces. This result is an application of our general result showing that stable compression schemes [2] of size k have uniformly bounded CMI of order O(k). |
| Researcher Affiliation | Collaboration | Mahdi Haghifam University of Toronto, Vector Institute Gintare Karolina Dziugaite Mila Shay Moran Technion, Google Research Daniel M. Roy University of Toronto, Vector Institute Part of the work was done the author was an intern at Element AI, a Service Now company. This work was carried out while the author was at Service Now. It was finalized at Google Brain. |
| Pseudocode | No | The paper does not include any structured pseudocode or algorithm blocks. It focuses on theoretical derivations and proofs. |
| Open Source Code | No | The paper does not contain any statement about releasing source code or provide links to a code repository. |
| Open Datasets | No | The paper is theoretical and does not involve empirical training on specific datasets. It discusses 'training samples' in a conceptual, mathematical context, but does not provide access information for any dataset. |
| Dataset Splits | No | The paper is theoretical and does not perform empirical validation on data splits. 'Validation' in this context refers to theoretical soundness, not a data split. |
| Hardware Specification | No | The paper does not provide any details about specific hardware (e.g., CPU, GPU models, memory, cloud instances) used for any computations. |
| Software Dependencies | No | The paper does not list any specific software dependencies with version numbers. |
| Experiment Setup | No | This is a theoretical paper, and thus does not include details on an experimental setup such as hyperparameters, training configurations, or system-level settings for empirical runs. |