Sensing Structured Signals with Active and Ensemble Methods
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Modern problems in signal processing and machine learning involve the analysis of data that is either high-volume or high-dimensional. In one example, scientists studying the environment must choose their set of measurements from an infinite set of possible sample locations. In another, performing inference on high-resolution images involves operating on vectors whose dimensionality is on the order of tens of thousands. To combat the challenges presented by these and other applications, researchers rely on two key features intrinsic to many large datasets. First, large volumes of data can often be accurately represented by a few key points, allowing for efficient processing, summary, and collection of data. Second, high-dimensional data often has low-dimensional intrinsic structure that can be leveraged for processing and storage. In this talk, we will describe ways to leverage these facts to develop and analyze algorithms capable of handling the challenges presented by modern data. We will focus on the union-of-subspaces model, a generalization of PCA in which data vectors are drawn from one of several low-dimensional linear subspaces, and demonstrate how ideas from active learning and ensemble methods can be used in combination with the underlying problem geometry to develop efficient and principled methods for subspace clustering.