Collaborative Research: CIF: Small: Theory for Learning Lossless and Lossy Coding

据估计，每天产生的各种形式的数据有33万亿个字节：视频、图像和音乐，还有科学、经济和工业内容。大量的数据已经以透明的方式（社交媒体）和不直接可见的方式（通过更好的建模、预测和使用数据来推进科学、商业和经济目标）改变了现代生活。数据通常以无线方式以多种格式进行大规模通信：视频、图像和音乐，以及实时应用程序，如游戏、流媒体内容、视频通话和远程医疗。为了处理如此大量的数据，需要通过算法对数据进行压缩，这些算法检查数据以了解底层结构并删除冗余描述，从而寻求使用更少的位来表示相同的内容。传统的压缩方法包括众所周知的JPEG（联合摄影专家组）对智能手机图像的压缩。这是一种有损压缩方法，因为会丢失一些图像质量。无损压缩，没有质量损失，通常用于压缩计算机文件（例如，Zip）和无损音乐流。近年来，机器学习已经变得非常强大，并被用于解决许多问题，如自动驾驶、语音识别和实现聊天机器人。最近的一个焦点是使用机器学习进行数据压缩。这个项目的目的是了解机器学习数据压缩的基本理论，例如什么类型的机器学习算法可以很好地压缩数据，需要多少样本才能很好地学习压缩。通过对使用机器学习的数据压缩的基本理解，我们的目标是开发更强大的压缩方法，从而更有效地利用无线频谱，减少移动设备的能耗。最近，研究人员和高科技公司都在努力开发用于源代码的机器学习方法。这些方法在一定程度上战胜了传统的源编码方法。该项目旨在为无损和有损源编码的学习性能开发基本界限。问题是在一个可能近似正确（PAC）的学习框架中构建的，包括统一的和非统一的。研究的第一部分考虑无损源编码，这既是对其本身的兴趣，也是对有损源编码的基础，旨在开发学习的界限。该项目调查了影响学习收敛性的因素。这是一个主动学习框架的扩展，在这个框架中，算法可以调整他们需要检查的数据量，为更精细的模型使用更多的数据，为更简单的模型使用更少的数据，并通过所谓的“停止规则”来确定底层模型何时可能是简单的。第二部分研究了有损源编码，特别是几乎无损源编码和实值源的无损编码。目的是了解在什么意义上可以学习源编码（例如，统一与非统一PAC），并在此基础上开发性能界限。估计、压缩和学习一直被认为是微妙的不同，这些细微差别转化为利用它们的问题的可量化的重大影响；这项研究将解决其中的一些问题，特别是对于具有记忆的来源。通过这个项目对编码学习的基本理解将反过来导致更好的编码方法的开发。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

An estimated 330,000 billion bytes of data is generated daily in various forms: video, images, and music, but also scientific, economic, and industrial content. This enormous amount of data has already transformed modern life in ways that are transparent (social media) and in ways that are not immediately visible (furthering scientific, business, and economic goals through better modeling, forecast and use of data). Data is communicated, often wirelessly, on massive scales in many formats: videos, images, and music, and in real time applications such as gaming, streaming content, video calls and telemedicine. In order to handle this amount of data, it needs to be compressed by algorithms that examine the data to understand the underlying structure and remove redundant descriptions, seeking thus to use fewer bits to represent the same. Traditional compression method includes the well-known JPEG (joint photographic experts group) compression for images from smartphones, for example. This is a lossy compression method, as some image quality is lost. Lossless compression, with no quality loss, is typically used for compressing computer files (e.g., with Zip) and for lossless music streaming. In recent years, machine learning has become very powerful and used to solve many problems like autonomous driving, speech recognition, and implementing chatbots. A recent focus is to use machine learning for data compression. The aim of this project is to understand the fundamental theory of machine learning for data compression, for example what type of machine learning algorithms can compress data well and how many samples are needed to learn compression well. Through this fundamental understanding of data compression using machine learning, the aim is to develop more powerful compression methods, leading to more efficient use of wireless spectrum and less energy consumption by mobile devices.Recently, there has been much effort in developing machine learning methods for source coding by both researchers and high tech companies. These methods have had some success in beating traditional source coding methods. The project aims to develop fundamental bounds for performance of learning for both lossless and lossy source coding. The problem is framed in a probably approximately correct (PAC) learning framework, both uniform and non-uniform. The first part of the research considers lossless source coding, both of interest in itself and as a basis of lossy source coding, and aims to develop bounds for learning. The project investigates what factors influence the convergence of learning. This is extended with an active learning framework, where the algorithms can adapt how much data they need to examine, using more data for more subtle models and less data for simpler models, and figuring out when the underlying model may be simple with what is known as a "stopping rule." The second part of the research considers lossy source coding, in particular almost lossless source coding and lossless coding of real-valued sources. The aim is to understand in what sense source coding can be learned (e.g., uniform vs non-uniform PAC), and based on this to develop performance bounds. Estimation, compression, and learning have always been known to be subtly different, and these nuances translate into quantifiably large implications for problems harnessing them; this research will resolve some of these tangles, particularly for sources with memory. The fundamental understanding of learning for coding developed through this project will in turn result in the development of better coding methods.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.