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Register a new userGaussian Process Deep Belief Networks: A Smooth Generative Model of Shape with Uncertainty Propagation
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The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to model due to complicated likelihood functions leading to intractable posteriors. In this paper we present a generative model of shapes which provides a low dimensional latent encoding which importantly resides on a smooth manifold with respect to the silhouette images. The proposed model propagates uncertainty in a principled manner allowing it to learn from small amounts of data and providing predictions with associated uncertainty. We provide experiments that show how our proposed model provides favorable quantitative results compared with the state-of-the-art while simultaneously providing a representation that resides on a low-dimensional interpretable manifold.
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Deep neural networks (DNNs) have achieved unprecedented performance on a wide range of complex tasks, rapidly outpacing our understanding of the nature of their solutions. This has caused a recent surge of interest in methods for rendering modern neural systems more interpretable. In this work, we propose to address the interpretability problem in modern DNNs using the rich history of problem descriptions, theories and experimental methods developed by cognitive psychologists to study the human mind. To explore the potential value of these tools, we chose a well-established analysis from developmental psychology that explains how children learn word labels for objects, and applied that analysis to DNNs. Using datasets of stimuli inspired by the original cognitive psychology experiments, we find that state-of-the-art one shot learning models trained on ImageNet exhibit a similar bias to that observed in humans: they prefer to categorize objects according to shape rather than color. The magnitude of this shape bias varies greatly among architecturally identical, but differently seeded models, and even fluctuates within seeds throughout training, despite nearly equivalent classification performance. These results demonstrate the capability of tools from cognitive psychology for exposing hidden computational properties of DNNs, while concurrently providing us with a computational model for human word learning.
Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and our approach dispenses with the necessity of estimating a branching structure for the posterior, as we perform inference on an aggregated sum of Gaussian Processes. Efficient approximate Bayesian inference is achieved via data augmentation, and we describe a mean--field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from three different domains and compare it to previously reported results.
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a posterior distribution of compositions of multiple functions giving rise to the observations. However, exact Bayesian inference is intractable for DGPs, motivating the use of various approximations. We show that the application of simplifying mean-field assumptions across the hierarchy leads to the layers of a DGP collapsing to near-deterministic transformations. We argue that such an inference scheme is suboptimal, not taking advantage of the potential of the model to discover the compositional structure in the data. To address this issue, we examine alternative variational inference schemes allowing for dependencies across different layers and discuss their advantages and limitations.
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanaris linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.
Quantification of anatomical shape changes currently relies on scalar global indexes which are largely insensitive to regional or asymmetric modifications. Accurate assessment of pathology-driven anatomical remodeling is a crucial step for the diagnosis and treatment of many conditions. Deep learning approaches have recently achieved wide success in the analysis of medical images, but they lack interpretability in the feature extraction and decision processes. In this work, we propose a new interpretable deep learning model for shape analysis. In particular, we exploit deep generative networks to model a population of anatomical segmentations through a hierarchy of conditional latent variables. At the highest level of this hierarchy, a two-dimensional latent space is simultaneously optimised to discriminate distinct clinical conditions, enabling the direct visualisation of the classification space. Moreover, the anatomical variability encoded by this discriminative latent space can be visualised in the segmentation space thanks to the generative properties of the model, making the classification task transparent. This approach yielded high accuracy in the categorisation of healthy and remodelled left ventricles when tested on unseen segmentations from our own multi-centre dataset as well as in an external validation set, and on hippocampi from healthy controls and patients with Alzheimers disease when tested on ADNI data. More importantly, it enabled the visualisation in three-dimensions of both global and regional anatomical features which better discriminate between the conditions under exam. The proposed approach scales effectively to large populations, facilitating high-throughput analysis of normal anatomy and pathology in large-scale studies of volumetric imaging.
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