Non-Asymptotic Uniform Rates of Consistency for k-NN Regression

We derive high-probability finite-sample uniform rates of consistency for $k$-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that $k$-NN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the $k$-NN regression rates to establish new results about estimating the level sets and global maxima of a function from noisy observations.Comment: In Proceedings of 33rd AAAI Conference on Artificial Intelligence (AAAI 2019

Nonparametric Stochastic Contextual Bandits

We analyze the $K$-armed bandit problem where the reward for each arm is a noisy realization based on an observed context under mild nonparametric assumptions. We attain tight results for top-arm identification and a sublinear regret of $\widetilde{O}\Big(T^{\frac{1+D}{2+D}}\Big)$, where $D$ is the context dimension, for a modified UCB algorithm that is simple to implement ($k$NN-UCB). We then give global intrinsic dimension dependent and ambient dimension independent regret bounds. We also discuss recovering topological structures within the context space based on expected bandit performance and provide an extension to infinite-armed contextual bandits. Finally, we experimentally show the improvement of our algorithm over existing multi-armed bandit approaches for both simulated tasks and MNIST image classification.Comment: AAAI 201

Quickshift++: Provably Good Initializations for Sample-Based Mean Shift

We provide initial seedings to the Quick Shift clustering algorithm, which approximate the locally high-density regions of the data. Such seedings act as more stable and expressive cluster-cores than the singleton modes found by Quick Shift. We establish statistical consistency guarantees for this modification. We then show strong clustering performance on real datasets as well as promising applications to image segmentation.Comment: ICML 2018. Code release: https://github.com/google/quickshif

Programmed cell death in type II neuroblast lineages is required for central complex development in the Drosophila brain

Background: The number of neurons generated by neural stem cells is dependent upon the regulation of cell proliferation and by programmed cell death. Recently, novel neural stem cells that amplify neural proliferation through intermediate neural progenitors, called type II neuroblasts, have been discovered, which are active during brain development in Drosophila. We investigated programmed cell death in the dorsomedial (DM) amplifying type II lineages that contribute neurons to the development of the central complex in Drosophila, using clonal mosaic analysis with a repressible cell marker (MARCM) and lineage-tracing techniques. Results: A significant number of the adult-specific neurons generated in these DM lineages were eliminated by programmed cell death. Programmed cell death occurred during both larval and pupal stages. During larval development, approximately one-quarter of the neuronal (but not glial) cells in the lineages were eliminated by apoptosis before the formation of synaptic connectivity during pupal stages. Lineage-tracing experiments documented the extensive contribution of intermediate neural progenitor-containing DM lineages to all of the major modular substructures of the adult central complex. Moreover, blockage of apoptotic cell death specifically in these lineages led to prominent innervation defects of DM-derived neural progeny in the major neuropile substructures of the adult central complex. Conclusions: Our findings indicate that significant neural overproliferation occurs normally in type II DM lineage development, and that elimination of excess neurons in these lineages through programmed cell death is required for the formation of correct neuropile innervation in the developing central complex. Thus, amplification of neuronal proliferation through intermediate progenitors and reduction of neuronal number through programmed cell death operate in concert in type II neural stem-cell lineages during brain development