Hannes Nickisch

JMLR Journal 2019 Journal Article

Change Surfaces for Expressive Multidimensional Changepoints and Counterfactual Prediction

• William Herlands
• Daniel B. Neill
• Hannes Nickisch
• Andrew Gordon Wilson

Identifying changes in model parameters is fundamental in machine learning and statistics. However, standard changepoint models are limited in expressiveness, often addressing unidimensional problems and assuming instantaneous changes. We introduce change surfaces as a multidimensional and highly expressive generalization of changepoints. We provide a model-agnostic formalization of change surfaces, illustrating how they can provide variable, heterogeneous, and non-monotonic rates of change across multiple dimensions. Additionally, we show how change surfaces can be used for counterfactual prediction. As a concrete instantiation of the change surface framework, we develop Gaussian Process Change Surfaces (GPCS). We demonstrate counterfactual prediction with Bayesian posterior mean and credible sets, as well as massive scalability by introducing novel methods for additive non-separable kernels. Using two large spatio-temporal datasets we employ GPCS to discover and characterize complex changes that can provide scientific and policy relevant insights. Specifically, we analyze twentieth century measles incidence across the United States and discover previously unknown heterogeneous changes after the introduction of the measles vaccine. Additionally, we apply the model to requests for lead testing kits in New York City, discovering distinct spatial and demographic patterns. [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

ICML Conference 2018 Conference Paper

State Space Gaussian Processes with Non-Gaussian Likelihood

• Hannes Nickisch
• Arno Solin
• Alexander Grigorevskiy

We provide a comprehensive overview and tooling for GP modelling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensonal GP models in O(n) time and memory complexity. While existing literature has focused on the connection between GP regression and state space methods, the computational primitives allowing for inference using general likelihoods in combination with the Laplace approximation (LA), variational Bayes (VB), and assumed density filtering (ADF) / expectation propagation (EP) schemes has been largely overlooked. We present means of combining the efficient O(n) state space methodology with existing inference methods. We also furher extend existing methods, and provide unifying code implementing all approaches.

NeurIPS Conference 2017 Conference Paper

Scalable Log Determinants for Gaussian Process Kernel Learning

• Kun Dong
• David Eriksson
• Hannes Nickisch
• David Bindel
• Andrew Wilson

For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an n by n positive definite matrix, and its derivatives---leading to prohibitive O(n^3) computations. We propose novel O(n) approaches to estimating these quantities from only fast matrix vector multiplications (MVMs). These stochastic approximations are based on Chebyshev, Lanczos, and surrogate models, and converge quickly even for kernel matrices that have challenging spectra. We leverage these approximations to develop a scalable Gaussian process approach to kernel learning. We find that Lanczos is generally superior to Chebyshev for kernel learning, and that a surrogate approach can be highly efficient and accurate with popular kernels.

ICML Conference 2015 Conference Paper

Fast Kronecker Inference in Gaussian Processes with non-Gaussian Likelihoods

• Seth R. Flaxman
• Andrew Gordon Wilson
• Daniel B. Neill
• Hannes Nickisch
• Alexander J. Smola

Gaussian processes (GPs) are a flexible class of methods with state of the art performance on spatial statistics applications. However, GPs require O(n^3) computations and O(n^2) storage, and popular GP kernels are typically limited to smoothing and interpolation. To address these difficulties, Kronecker methods have been used to exploit structure in the GP covariance matrix for scalability, while allowing for expressive kernel learning (Wilson et al. , 2014). However, fast Kronecker methods have been confined to Gaussian likelihoods. We propose new scalable Kronecker methods for Gaussian processes with non-Gaussian likelihoods, using a Laplace approximation which involves linear conjugate gradients for inference, and a lower bound on the GP marginal likelihood for kernel learning. Our approach has near linear scaling, requiring O(D n^(D+1)/D) operations and O(D n^2/D) storage, for n training data-points on a dense D > 1 dimensional grid. Moreover, we introduce a log Gaussian Cox process, with highly expressive kernels, for modelling spatiotemporal count processes, and apply it to a point pattern (n = 233, 088) of a decade of crime events in Chicago. Using our model, we discover spatially varying multiscale seasonal trends and produce highly accurate long-range local area forecasts.

ICML Conference 2015 Conference Paper

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

• Andrew Gordon Wilson
• Hannes Nickisch

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.

JMLR Journal 2012 Journal Article

glm-ie: Generalised Linear Models Inference & Estimation Toolbox

• Hannes Nickisch

The glm-ie toolbox contains functionality for estimation and inference in generalised linear models over continuous-valued variables. Besides a variety of penalised least squares solvers for estimation, it offers inference based on (convex) variational bounds, on expectation propagation and on factorial mean field. Scalable and efficient inference in fully-connected undirected graphical models or Markov random fields with Gaussian and non-Gaussian potentials is achieved by casting all the computations as matrix vector multiplications. We provide a wide choice of penalty functions for estimation, potential functions for inference and matrix classes with lazy evaluation for convenient modelling. We designed the glm-ie package to be simple, generic and easily expansible. Most of the code is written in Matlab including some MEX files to be fully compatible to both Matlab 7.x and GNU Octave 3.3.x. Large scale probabilistic classification as well as sparse linear modelling can be performed in a common algorithmical framework by the glm-ie toolkit. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2012. ( edit, beta )

NeurIPS Conference 2011 Conference Paper

Additive Gaussian Processes

• David Duvenaud
• Hannes Nickisch
• Carl Rasmussen

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.

JMLR Journal 2010 Journal Article

Gaussian Processes for Machine Learning (GPML) Toolbox

• Carl Edward Rasmussen
• Hannes Nickisch

The GPML toolbox provides a wide range of functionality for Gaussian process (GP) inference and prediction. GPs are specified by mean and covariance functions; we offer a library of simple mean and covariance functions and mechanisms to compose more complex ones. Several likelihood functions are supported including Gaussian and heavy-tailed for regression as well as others suitable for classification. Finally, a range of inference methods is provided, including exact and variational inference, Expectation Propagation, and Laplace's method dealing with non-Gaussian likelihoods and FITC for dealing with large regression tasks. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2010. ( edit, beta )

ICML Conference 2009 Conference Paper

Convex variational Bayesian inference for large scale generalized linear models

• Hannes Nickisch
• Matthias W. Seeger

We show how variational Bayesian inference can be implemented for very large generalized linear models. Our relaxation is proven to be a convex problem for any log-concave model. We provide a generic double loop algorithm for solving this relaxation on models with arbitrary super-Gaussian potentials. By iteratively decoupling the criterion, most of the work can be done by solving large linear systems, rendering our algorithm orders of magnitude faster than previously proposed solvers for the same problem. We evaluate our method on problems of Bayesian active learning for large binary classification models, and show how to address settings with many candidates and sequential inclusion steps.

JMLR Journal 2008 Journal Article

Approximations for Binary Gaussian Process Classification

• Hannes Nickisch
• Carl Edward Rasmussen

We provide a comprehensive overview of many recent algorithms for approximate inference in Gaussian process models for probabilistic binary classification. The relationships between several approaches are elucidated theoretically, and the properties of the different algorithms are corroborated by experimental results. We examine both 1) the quality of the predictive distributions and 2) the suitability of the different marginal likelihood approximations for model selection (selecting hyperparameters) and compare to a gold standard based on MCMC. Interestingly, some methods produce good predictive distributions although their marginal likelihood approximations are poor. Strong conclusions are drawn about the methods: The Expectation Propagation algorithm is almost always the method of choice unless the computational budget is very tight. We also extend existing methods in various ways, and provide unifying code implementing all approaches. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

NeurIPS Conference 2008 Conference Paper

Bayesian Experimental Design of Magnetic Resonance Imaging Sequences

• Hannes Nickisch
• Rolf Pohmann
• Bernhard Schölkopf
• Matthias Seeger

We show how improved sequences for magnetic resonance imaging can be found through automated optimization of Bayesian design scores. Combining recent advances in approximate Bayesian inference and natural image statistics with high-performance numerical computation, we propose the first scalable Bayesian experimental design framework for this problem of high relevance to clinical and brain research. Our solution requires approximate inference for dense, non-Gaussian models on a scale seldom addressed before. We propose a novel scalable variational inference algorithm, and show how powerful methods of numerical mathematics can be modified to compute primitives in our framework. Our approach is evaluated on a realistic setup with raw data from a 3T MR scanner.

ICML Conference 2008 Conference Paper

Compressed sensing and Bayesian experimental design

• Matthias W. Seeger
• Hannes Nickisch