47 research outputs found
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