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- 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)

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)

- Peter Sollich
- Machine Learning
- 2002

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
- 1999

Support Vector Machines (SVMs) can be interpreted as maximum a posteriori solutions to inference problems with Gaussian Process (GP) priors and appropriate likelihood functions. Focussing on the case of classiication, I show rst that such an interpretation gives a clear intuitive meaning to SVM kernels, as covariance functions of GP priors; this can be used… (More)

- Peter Sollich, Anders Krogh
- NIPS
- 1995

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

- Peter Sollich
- NIPS
- 1999

I describe a framework for interpreting Support Vector Machines (SVMs) as maximum a posteriori (MAP) solutions to inference problems with Gaussian Process priors. This can provide intuitive guidelines for choosing a 'good' SVM kernel. It can also assign (by evidence maximization) optimal values to parameters such as the noise level C which cannot be… (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)

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, David Barber
- Neural Computation
- 1998

We analyze online gradient descent learning from finite training sets at noninfinitesimal learning rates eta. Exact results are obtained for the time-dependent generalization error of a simple model system: a linear network with a large number of weights N, trained on p = alphaN examples. This allows us to study in detail the effects of finite training set… (More)

- Peter Sollich, Christopher K. I. Williams
- NIPS
- 2004

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)