Learning the Structure of Deep Sparse Graphical Models

Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single infinitely wide hidden layer. In this paper, we introduce the cascading Indian buffet process (CIBP), which provides a nonparametric prior on the structure of a layered, directed belief network that is unbounded in both depth and width, yet allows tractable inference. We use the CIBP prior with the nonlinear Gaussian belief network so each unit can additionally vary its behavior between discrete and continuous representations. We provide Markov chain Monte Carlo algorithms for inference in these belief networks and explore the structures learned on several image data sets.

Tree-Structured Stick Breaking Processes for Hierarchical Data

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

Low power all-optical switch in a passive InGaAsP multiple quantum well waveguide

We demonstrate the use of resonant bandfilling nonlinearity in an InGaAsP/InGaAsP Multiple Quantum Well (MQW) waveguide due to photogenerated carriers to obtain switching at pulse powers, which can readily be obtained from an erbium amplified diode laser source. In order to produce gating a polarisation rotation gate was used, which relies on an asymmetry in the nonlinear refraction on the principle axes of the waveguide.

The Gaussian process density sampler

We present the Gaussian Process Density Sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a fixed density function that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We can also infer the hyperparameters of the Gaussian process. We compare this density modeling technique to several existing techniques on a toy problem and a skullreconstruction task.

Avoiding pathologies in very deep networks

Choosing appropriate architectures and regularization strategies of deep networks is crucial to good predictive performance. To shed light on this problem, we analyze the analogous problem of constructing useful priors on compositions of functions. Specifically, we study the deep Gaussian process, a type of infinitely-wide, deep neural network. We show that in standard architectures, the representational capacity of the network tends to capture fewer degrees of freedom as the number of layers increases, retaining only a single degree of freedom in the limit. We propose an alternate network architecture which does not suffer from this pathology. We also examine deep covariance functions, obtained by composing infinitely many feature transforms. Lastly, we characterize the class of models obtained by performing dropout on Gaussian processes.

Contractile and mechanical properties of epithelia with perturbed actomyosin dynamics.

Mechanics has an important role during morphogenesis, both in the generation of forces driving cell shape changes and in determining the effective material properties of cells and tissues. Drosophila dorsal closure has emerged as a reference model system for investigating the interplay between tissue mechanics and cellular activity. During dorsal closure, the amnioserosa generates one of the major forces that drive closure through the apical contraction of its constituent cells. We combined quantitation of live data, genetic and mechanical perturbation and cell biology, to investigate how mechanical properties and contraction rate emerge from cytoskeletal activity. We found that a decrease in Myosin phosphorylation induces a fluidization of amnioserosa cells which become more compliant. Conversely, an increase in Myosin phosphorylation and an increase in actin linear polymerization induce a solidification of cells. Contrary to expectation, these two perturbations have an opposite effect on the strain rate of cells during DC. While an increase in actin polymerization increases the contraction rate of amnioserosa cells, an increase in Myosin phosphorylation gives rise to cells that contract very slowly. The quantification of how the perturbation induced by laser ablation decays throughout the tissue revealed that the tissue in these two mutant backgrounds reacts very differently. We suggest that the differences in the strain rate of cells in situations where Myosin activity or actin polymerization is increased arise from changes in how the contractile forces are transmitted and coordinated across the tissue through ECadherin-mediated adhesion. Altogether, our results show that there is an optimal level of Myosin activity to generate efficient contraction and suggest that the architecture of the actin cytoskeleton and the dynamics of adhesion complexes are important parameters for the emergence of coordinated activity throughout the tissue.