ITR: Representation Learning: Transformations and Kernels for Collections of Tuples

统计机器学习工具允许科学家和工程师直接从现实世界的数据中自动估计计算模型，以进行预测、分类和推断。然而，在学习之前，从业者需要知道如何以一致的、不变的、行为良好的数字形式正确地表示数据，以便通过各种技术进行处理。该提案减少了这一负担，并通过新颖的算法促进了机器学习的应用，这些算法不仅可以建模数据，还可以自动处理不变性并发现数据的适当表示。该建议形式化了各种潜在的转换，并将它们嵌入到一个有原则的学习框架中。这使得处理数据非线性转换、转换和变化的真实场景成为可能，并有效地为传统工具创造了许多困难。该建议考虑的有趣转换集合还包括排列。处理排列允许算法在数据集中的每个数据点是任意排序的元组的集合时学习。例如，数字彩色图像可以表示为一袋任意排序的像素。然后，该项目开发必要的算法，以实现排列、重新排序、转换和许多其他影响数据的转换的不变性。该提案利用并扩展了机器学习领域的最新技术，包括贝叶斯网络、核方法和凸规划。主要应用包括人脸识别和监控。为了从视频中识别人脸身份，所提出的算法补偿了真实图像中人脸平移、变形和旋转时可能发生的变换。使用标准化和具有挑战性的人脸识别数据集进行评估。一般来说，表示学习方法也促进了机器学习，在数据经历转换的其他应用领域，包括计算视觉、语音、时间序列分析和生物信息学，有可能产生潜在影响。

Statistical machine learning tools permit scientists and engineers to automatically estimate computational models directly from real-world data for making predictions, classifications and inferences. However, before learning can take place, the practitioner needs to know how to properly represent data in a consistent, invariant and well-behavednumerical form for processing by the various techniques. This proposal reduces this burden and facilitates applications of machine learning via novel algorithms that not only model data but also automatically handle invariances and discover appropriaterepresentations of the data.This proposal formalizes a variety of potential transformations and embeds them within a principled learning framework. This makes it possible to handle real scenarios where data transforms, translates, changes nonlinearly and effectively creates many difficulties fortraditional tools. The set of interesting transformations the proposal considers also includes permutations. Handling permutation allows algorithms to learn when each data-point in the dataset is a collection of tuples whose ordering is arbitrary. For example, adigital color image can be represented as a bag of pixels whose ordering is arbitrary. This project then develops the necessary algorithms for invariance to permutations, re-orderings, translations, and many other transformations affecting data in practice.The proposal makes use of and extends state-of-the-art techniques in the machine learning field including Bayesian networks, kernel methods and convex programming. Primary applications include face recognition and surveillance. To recognize human face identity from video, the proposed algorithms compensate for possible transformations as faces translate, deform and rotate in real images. Standardized and challenging face recognition datasets are used for evaluation. The representation learning methods also facilitate machine learning in general, promising potential impact in other applied fields where data undergoes transformations including computational vision, speech, timeseries analysis and bio-informatics.