C. K. I. Williams's scientific contributions

Publications (4)

Article
Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The trea...

Citations

... This exposition follows (Rasmussen 2003), to which the reader is referred for further detail. The crux of Gaussian process emulation is that, under the assumption that model outputs follow a multivariate Gaussian distribution, a vector of 'test' model outputs f * for model inputs X * can be predicted from 'training' model outputs f computed for model inputs X. ...
... Here, we use the Matern 5/2 kernel that is smooth enough to avoid a rough GP, but not extremely smooth thus being suitable for modelling the physics. The piecewise polynomial, rational quadratic, exponential, and squared exponential functions are other candidates [56]. The parameters (or length scales) in the kernels and other hyperparameters are found via non-linear optimization (L-BFGS-B) using maximum likelihood estimation (MLE). ...
... However, note that GP models scale poorly with data size, and are often cumbersome to use for this reason. Some modeling strategies have been suggested to address this issue: these include coupling GPs with dimension reduction techniques, or using sparse covariance, sparse Cholesky Factorization, sparse precision and low rank approximations of different kinds [155,173,174]. Of particular interest are approaches that leverage the inverse covariance (precision) matrix, since these models retain the physical interpretability and simplicity of GPs, they automatically obtain a partial correlation-based network structure that in many situations may be interpreted to be a causal graphical model, and they are computationally fast. ...
... Although the nature of DM is still unknown, Weakly Interacting Massive Particles (WIMPs) are popular and well-motivated DM candidates, among others. They are predicted to annihilate or decay into Standard Model (SM) particles, whose decay and hadronization processes would produce secondary particles, such as cosmic rays, neutrinos and gamma rays (Buckley & Hooper 2010;Zechlin et al. 2011;Zechlin & Horns 2012;Belikov et al. 2012;Berlin & Hooper 2013;Bertoni et al. 2015Bertoni et al. , 2016Schoonenberg et al. 2016;Calore et al. 2016;Hooper & Witte 2017). The flux of secondary particles may be observed in ground-based or satellite observatories, laying the groundwork for the indirect searches for DM. ...