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We describe a flexible nonparametric approach to latent variable modelling in which the number of latent variables is unbounded. This approach is based on a probability distribution over equivalence classes of binary matrices with a finite number of rows, corresponding to the data points, and an unbounded number of columns, corresponding to the latent… (More)

- Peter Sollich
- 1998

We solve exactly and describe in detail a simplified scalar model for the low frequency shear rheology of ͑1997͔͒. The model attributes similarities in the rheology of such ''soft glassy materials'' to the shared features of structural disorder and metastability. By focusing on the dynamics of mesoscopic elements, it retains a generic character.… (More)

I describe a framework for interpreting Support Vector Machines (SVMs) as maximum a posteriori (MAP) solutions to inference problems with Gaussian Process priors. This probabilistic interpretation can provide intuitive guidelines for choosing a 'good' SVM kernel. Beyond this, it allows Bayesian methods to be used for tackling two of the outstanding… (More)

- Peter Sollich, François Lequeux, Pascal Hébraud, Michael E Cates
- 1997

We attribute similarities in the rheology of many soft materials (foams, emulsions, slurries, etc.) to the shared features of structural disorder and metastability. A generic model for the mesoscopic dynamics of " soft glassy matter " is introduced, with interactions represented by a mean-field noise temperature x. We find power-law fluid behavior either… (More)

We study the dynamics of the East model, comprising a chain of uncoupled spins in a downward-pointing field. Glassy effects arise at low temperatures T from the kinetic constraint that spins can only flip if their left neighbor is up. We give details of our previous solution of the nonequilibrium coarsening dynamics after a quench to low T [Phys. Rev. Lett.… (More)

- Anders Krogh, Peter Sollich
- 1996

Within the context of learning a rule from examples, we study the general characteristics of learning with ensembles. The generalization performance achieved by a simple model ensemble of linear students is calculated exactly in the thermodynamic limit of a large number of input components and shows a surprisingly rich behavior. Our main findings are the… (More)

- Peter Sollich, Anders Krogh
- 1996

We study the general characteristics of learning with ensembles. Solving exactly the simple model scenario of an ensemble of linear students, we nd surprisingly rich behaviour. For learning in large ensembles, it is advantageous to use under-regularized students , which actually overt the training data. Globally optimal generalization performance can be… (More)

I consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. A simple expression for the generalization error in terms of the eigenvalue decomposition of the covariance function is derived, and used as the starting point for several approximation schemes. I identify where these… (More)

The equivalent kernel [1] is a way of understanding how Gaussian process regression works for large sample sizes based on a continuum limit. In this paper we show (1) how to approximate the equivalent kernel of the widely-used squared exponential (or Gaussian) kernel and related kernels , and (2) how analysis using the equivalent kernel helps to understand… (More)