Active Mini-Batch Sampling using Repulsive Point Processes

The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient estimator. This generalizes recent work on using Determinantal Point Processes (DPPs) for mini-batch diversification (Zhang et al., 2017) to the broader class of repulsive point processes. We first show that the phenomenon of variance reduction by diversified sampling generalizes in particular to non-stationary point processes. We then show that other point processes may be computationally much more efficient than DPPs. In particular, we propose and investigate Poisson Disk sampling---frequently encountered in the computer graphics community---for this task. We show empirically that our approach improves over standard SGD both in terms of convergence speed as well as final model performance

TOWARDS A COMPUTATIONAL MODEL OF RETINAL STRUCTURE AND BEHAVIOR

Human vision is our most important sensory system, allowing us to perceive our surroundings. It is an extremely complex process that starts with light entering the eye and ends inside of the brain, with most of its mechanisms still to be explained. When we observe a scene, the optics of the eye focus an image on the retina, where light signals are processed and sent all the way to the visual cortex of the brain, enabling our visual sensation. The progress of retinal research, especially on the topography of photoreceptors, is often tied to the progress of retinal imaging systems. The latest adaptive optics techniques have been essential for the study of the photoreceptors and their spatial characteristics, leading to discoveries that challenge the existing theories on color sensation. The organization of the retina is associated with various perceptive phenomena, some of them are straightforward and strictly related to visual performance like visual acuity or contrast sensitivity, but some of them are more difficult to analyze and test and can be related to the submosaics of the three classes of cone photoreceptors, like how the huge interpersonal differences between the ratio of different cone classes result in negligible differences in color sensation, suggesting the presence of compensation mechanisms in some stage of the visual system. In this dissertation will be discussed and addressed issues regarding the spatial organization of the photoreceptors in the human retina. A computational model has been developed, organized into a modular pipeline of extensible methods each simulating a different stage of visual processing. It does so by creating a model of spatial distribution of cones inside of a retina, then applying descriptive statistics for each photoreceptor to contribute to the creation of a graphical representation, based on a behavioral model that determines the absorption of photoreceptors. These apparent color stimuli are reconstructed in a representation of the observed scene. The model allows the testing of different parameters regulating the photoreceptor's topography, in order to formulate hypothesis on the perceptual differences arising from variations in spatial organization

General Point Sampling with Adaptive Density and Correlations

ISSN:1467-8659ISSN:0167-705