The Incremental Multiresolution Matrix Factorization Algorithm

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric matrices -- an important aspect in the success of many vision problems. Our new algorithm, the incremental multiresolution matrix factorization, uncovers such structure one feature at a time, and hence scales well to large matrices. We describe how this multiscale analysis goes much farther than what a direct global factorization of the data can identify. We evaluate the efficacy of the resulting factorizations for relative leveraging within regression tasks using medical imaging data. We also use the factorization on representations learned by popular deep networks, providing evidence of their ability to infer semantic relationships even when they are not explicitly trained to do so. We show that this algorithm can be used as an exploratory tool to improve the network architecture, and within numerous other settings in vision.Comment: Computer Vision and Pattern Recognition (CVPR) 2017, 10 page

The Unbearable Lightness of the Economics-Made-Fun Genre

Several commentators have argued that the Economics-Made-Fun (“EMF”) genre contains very little actual economics. As such, it would seem that criticisms of EMF do not apply economics more broadly. In this paper I take a contrary view, arguing that, in fact, at a deep conceptual level, the engine of EMF analyses is precisely the engine of mainstream economics. Specifically, I argue that both EMF and mainstream economics rest on a conceptual foundation known as the Principal of the Substitution of Similars (“PSS”). Understanding how PSS leads EMF practitioners to make claims well beyond what is warranted by their analysis also offers insight into how PSS leaves mainstream economists in danger of overestimating the power and scope of their analyses. I explore the consequences of such problems through an example of economic analysis of the U.S. housing market in the lead-up to the recent financial crisis.Methodology, Popular Economics, William Stanley Jevons, Ontology, Anthropology of Finance