Multiple Kernel Learning: A Unifying Probabilistic Viewpoint

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the marginal likelihood and contains many regularised risk approaches as special cases. Furthermore, we derive an efficient and provably convergent optimisation algorithm

Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling.Comment: 19 pages, 4 figure

Learning an Interactive Segmentation System

Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluated by computing the accuracy of their solutions under some fixed set of user interactions. This paper proposes a new evaluation and learning method which brings the user in the loop. It is based on the use of an active robot user - a simulated model of a human user. We show how this approach can be used to evaluate and learn parameters of state-of-the-art interactive segmentation systems. We also show how simulated user models can be integrated into the popular max-margin method for parameter learning and propose an algorithm to solve the resulting optimisation problem.Comment: 11 pages, 7 figures, 4 table

Fast Convergent Algorithms for Expectation Propagation Approximate Bayesian Inference

We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is provably convergent. By marrying convergent EP ideas from (Opper&Winther 05) with covariance decoupling techniques (Wipf&Nagarajan 08, Nickisch&Seeger 09), it runs at least an order of magnitude faster than the most commonly used EP solver.Comment: 16 pages, 3 figures, submitted for conference publicatio

Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.Comment: 34 pages, 6 figures, technical report (submitted

Multi-Resolution 3D Convolutional Neural Networks for Automatic Coronary Centerline Extraction in Cardiac CT Angiography Scans

We propose a deep learning-based automatic coronary artery tree centerline tracker (AuCoTrack) extending the vessel tracker by Wolterink (arXiv:1810.03143). A dual pathway Convolutional Neural Network (CNN) operating on multi-scale 3D inputs predicts the direction of the coronary arteries as well as the presence of a bifurcation. A similar multi-scale dual pathway 3D CNN is trained to identify coronary artery endpoints for terminating the tracking process. Two or more continuation directions are derived based on the bifurcation detection. The iterative tracker detects the entire left and right coronary artery trees based on only two ostium landmarks derived from a model-based segmentation of the heart. The 3D CNNs were trained on a proprietary dataset consisting of 43 CCTA scans. An average sensitivity of 87.1% and clinically relevant overlap of 89.1% was obtained relative to a refined manual segmentation. In addition, the MICCAI 2008 Coronary Artery Tracking Challenge (CAT08) training and test datasets were used to benchmark the algorithm and to assess its generalization. An average overlap of 93.6% and a clinically relevant overlap of 96.4% were obtained. The proposed method achieved better overlap scores than the current state-of-the-art automatic centerline extraction techniques on the CAT08 dataset with a vessel detection rate of 95%