Bounded-Distortion Metric Learning

Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents {\it bounded-distortion metric learning} (BDML), a new metric learning framework which amounts to finding an optimal Mahalanobis metric space with a bounded-distortion constraint. An efficient solver based on the multiplicative weights update method is proposed. Moreover, we generalize BDML to pseudo-metric learning and devise the semidefinite relaxation and a randomized algorithm to approximately solve it. We further provide theoretical analysis to show that distortion is a key ingredient for stability and generalization ability of our BDML algorithm. Extensive experiments on several benchmark datasets yield promising results

Temporal and spatial dynamics of scaling-specific features of a gene regulatory network in Drosophila

A widely appreciated aspect of developmental robustness is pattern formation in proportion to size. But how such scaling features emerge dynamically remains poorly understood. Here we generate a data set of the expression profiles of six gap genes in Drosophila melanogasterembryos that differ significantly in size. Expression patterns exhibit size-dependent dynamics both spatially and temporally. We uncover a dynamic emergence of under-scaling in the posterior, accompanied by reduced expression levels of gap genes near the middle of large embryos. Simulation results show that a size-dependent Bicoid gradient input can lead to reduced Krüppel expression that can have long-range and dynamic effects on gap gene expression in the posterior. Thus, for emergence of scaled patterns, the entire embryo may be viewed as a single unified dynamic system where maternally derived size-dependent information interpreted locally can be propagated in space and time as governed by the dynamics of a gene regulatory network