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arXiv 2004.14941cs.LGstat.ML
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信息瓶颈问题及其在机器学习中的应用

The Information Bottleneck Problem and Its Applications in Machine Learning

Cornell University(康奈尔大学);Massachusetts Institute of Technology(麻省理工学院)

Ziv Goldfeld, Yury Polyanskiy

摘要:

近年来,机器学习(ML)系统的推理能力飞速发展,在社会的各个方面发挥着举足轻重的作用。统计学习的目标是使用数据来获得简单的算法,用于从相关的观察$X$预测随机变量$Y$。由于$X$的维数通常很大,因此计算上可行的解决方案应该将其概括为低维特征向量$T$,从中预测$Y$。如果$T$是$Y$的良好代理,则该算法将成功地进行预测,尽管进行了所述降维。现在有无数的ML算法(主要采用深度学习(DL))用于基于真实世界数据找到这种表示$T$。虽然这些方法在实践中往往是有效的,他们的成功是阻碍了缺乏一个全面的理论来解释it.The信息瓶颈(IB)理论最近出现作为一个大胆的信息理论范式分析DL系统。采用互信息作为品质因数,提出最佳的$T$表示应该是最大程度地提供关于$Y$的信息,同时最小化与$X$的互信息.在本教程中,我们调查这个抽象原则的信息理论起源,以及它对DL的最新影响。对于后者,我们涵盖了IB问题对DL理论的影响,以及受其启发的实际算法。我们的目标是提供一个统一的和内聚的描述。当前知识的清晰视图对于进一步利用IB和其他信息理论思想来研究DL模型特别重要。

英文摘要:

Inference capabilities of machine learning (ML) systems skyrocketed in recent years, now playing a pivotal role in various aspect of society. The goal in statistical learning is to use data to obtain simple algorithms for predicting a random variable $Y$ from a correlated observation $X$. Since the dimension of $X$ is typically huge, computationally feasible solutions should summarize it into a lower-dimensional feature vector $T$, from which $Y$ is predicted. The algorithm will successfully make the prediction if $T$ is a good proxy of $Y$, despite the said dimensionality-reduction. A myriad of ML algorithms (mostly employing deep learning (DL)) for finding such representations $T$ based on real-world data are now available. While these methods are often effective in practice, their success is hindered by the lack of a comprehensive theory to explain it. The information bottleneck (IB) theory recently emerged as a bold information-theoretic paradigm for analyzing DL systems. Adopting mutual information as the figure of merit, it suggests that the best representation $T$ should be maximally informative about $Y$ while minimizing the mutual information with $X$. In this tutorial we survey the information-theoretic origins of this abstract principle, and its recent impact on DL. For the latter, we cover implications of the IB problem on DL theory, as well as practical algorithms inspired by it. Our goal is to provide a unified and cohesive description. A clear view of current knowledge is particularly important for further leveraging IB and other information-theoretic ideas to study DL models.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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