Hybrid Random Features

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the defined regions of interest. Special instantiations of HRFs lead to well-known methods such as trigonometric (Rahimi and Recht, 2007) or (recently introduced in the context of linear-attention Transformers) positive random features (Choromanski et al., 2021). By generalizing Bochner's Theorem for softmax/Gaussian kernels and leveraging random features for compositional kernels, the HRF-mechanism provides strong theoretical guarantees - unbiased approximation and strictly smaller worst-case relative errors than its counterparts. We conduct exhaustive empirical evaluation of HRF ranging from pointwise kernel estimation experiments, through tests on data admitting clustering structure to benchmarking implicit-attention Transformers (also for downstream Robotics applications), demonstrating its quality in a wide spectrum of machine learning problems.

Joint Person Segmentation and Identification in Synchronized First- and Third-person Videos

In a world of pervasive cameras, public spaces are often captured from multiple perspectives by cameras of different types, both fixed and mobile. An important problem is to organize these heterogeneous collections of videos by finding connections between them, such as identifying correspondences between the people appearing in the videos and the people holding or wearing the cameras. In this paper, we wish to solve two specific problems: (1) given two or more synchronized third-person videos of a scene, produce a pixel-level segmentation of each visible person and identify corresponding people across different views (i.e., determine who in camera A corresponds with whom in camera B), and (2) given one or more synchronized third-person videos as well as a first-person video taken by a mobile or wearable camera, segment and identify the camera wearer in the third-person videos. Unlike previous work which requires ground truth bounding boxes to estimate the correspondences, we perform person segmentation and identification jointly. We find that solving these two problems simultaneously is mutually beneficial, because better fine-grained segmentation allows us to better perform matching across views, and information from multiple views helps us perform more accurate segmentation. We evaluate our approach on two challenging datasets of interacting people captured from multiple wearable cameras, and show that our proposed method performs significantly better than the state-of-the-art on both person segmentation and identification.