The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available

Diffeomorphic Metric Mapping and Probabilistic Atlas Generation of Hybrid Diffusion Imaging based on BFOR Signal Basis

We propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI), denoted as LDDMM-HYDI. We then propose a Bayesian model for estimating the white matter atlas from HYDIs. We adopt the work given in Hosseinbor et al. (2012) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and thus reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L2 norm that quantifies the differences in the q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the $q$-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Additionally, we extend the previous Bayesian atlas estimation framework for scalar-valued images to HYDIs and derive the expectation-maximization algorithm for solving the HYDI atlas estimation problem. Using real HYDI datasets, we show the Bayesian model generates the white matter atlas with anatomical details. Moreover, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization and to incorporate the full information of HYDI for aligning mDWI

C-Flow: Conditional Generative Flow Models for Images and 3D Point Clouds

Flow-based generative models have highly desirable properties like exact log-likelihood evaluation and exact latent-variable inference, however they are still in their infancy and have not received as much attention as alternative generative models. In this paper, we introduce C-Flow, a novel conditioning scheme that brings normalizing flows to an entirely new scenario with great possibilities for multi-modal data modeling. C-Flow is based on a parallel sequence of invertible mappings in which a source flow guides the target flow at every step, enabling fine-grained control over the generation process. We also devise a new strategy to model unordered 3D point clouds that, in combination with the conditioning scheme, makes it possible to address 3D reconstruction from a single image and its inverse problem of rendering an image given a point cloud. We demonstrate our conditioning method to be very adaptable, being also applicable to image manipulation, style transfer and multi-modal image-to-image mapping in a diversity of domains, including RGB images, segmentation maps, and edge masks

Privacy-Preserving Shortest Path Computation

Navigation is one of the most popular cloud computing services. But in virtually all cloud-based navigation systems, the client must reveal her location and destination to the cloud service provider in order to learn the fastest route. In this work, we present a cryptographic protocol for navigation on city streets that provides privacy for both the client's location and the service provider's routing data. Our key ingredient is a novel method for compressing the next-hop routing matrices in networks such as city street maps. Applying our compression method to the map of Los Angeles, for example, we achieve over tenfold reduction in the representation size. In conjunction with other cryptographic techniques, this compressed representation results in an efficient protocol suitable for fully-private real-time navigation on city streets. We demonstrate the practicality of our protocol by benchmarking it on real street map data for major cities such as San Francisco and Washington, D.C.Comment: Extended version of NDSS 2016 pape