Gaussian Processes for Machine Learning

The code provided here originally demonstrated the main algorithms from Rasmussen and Williams: Gaussian Processes for Machine Learning. It has since grown to allow more likelihood functions, further inference methods and a flexible framework for specifying GPs.

Methodological implications of critical realism for mixed-methods research

Building on recent developments in mixed methods, we discuss the methodological implications of critical realism and explore how these can guide dynamic mixed-methods research design in information systems. Specifically, we examine the core ontological assumptions of CR in order to gain some perspective on key epistemological issues such as causation and validity, and illustrate how these shape our logic of inference in the research process through what is known as retroduction. We demonstrate the value of a CR-led mixed-methods research approach by drawing on a study that examines the impact of ICT adoption in the financial services sector. In doing so, we provide insight into the interplay between qualitative and quantitative methods and the particular value of applying mixed methods guided by CR methodological principles. Our positioning of demi-regularities within the process of retroduction contributes a distinctive development in this regard. We argue that such a research design enables us to better address issues of validity and the development of more robust meta-inferences.

A dependent partition-valued process for multitask clustering and time evolving network modelling

The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree structured covariate spaces. We define a partition-valued process on an arbitrary covariate space using Gaussian processes. We use the process to construct a multitask clustering model which partitions datapoints in a similar way across multiple data sources, and a time series model of network data which allows cluster assignments to vary over time. We describe sampling algorithms for inference and apply our method to defining cancer subtypes based on different types of cellular characteristics, finding regulatory modules from gene expression data from multiple human populations, and discovering time varying community structure in a social network.

A Hierarchical Model for Ordinal Matrix Factorization

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in the factorization of very large matrices with missing entries. The model is evaluated on a collaborative filtering task, where users have rated a collection of movies and the system is asked to predict their ratings for other movies. The Netflix data set is used for evaluation, which consists of around 100 million ratings. Using root mean-squared error (RMSE) as an evaluation metric, results show that the suggested model outperforms alternative factorization techniques. Results also show how Gibbs sampling outperforms variational Bayes on this task, despite the large number of ratings and model parameters. Matlab implementations of the proposed algorithms are available from cogsys.imm.dtu.dk/ordinalmatrixfactorization.

Scaling the Indian Buffet Process via Submodular Maximization

Inference for latent feature models is inherently difficult as the inference space grows exponentially with the size of the input data and number of latent features. In this work, we use Kurihara & Welling (2008)'s maximization-expectation framework to perform approximate MAP inference for linear-Gaussian latent feature models with an Indian Buffet Process (IBP) prior. This formulation yields a submodular function of the features that corresponds to a lower bound on the model evidence. By adding a constant to this function, we obtain a nonnegative submodular function that can be maximized via a greedy algorithm that obtains at least a one-third approximation to the optimal solution. Our inference method scales linearly with the size of the input data, and we show the efficacy of our method on the largest datasets currently analyzed using an IBP model.

Dopamine and performance in a reinforcement learning task: evidence from Parkinson's disease.

The role dopamine plays in decision-making has important theoretical, empirical and clinical implications. Here, we examined its precise contribution by exploiting the lesion deficit model afforded by Parkinson's disease. We studied patients in a two-stage reinforcement learning task, while they were ON and OFF dopamine replacement medication. Contrary to expectation, we found that dopaminergic drug state (ON or OFF) did not impact learning. Instead, the critical factor was drug state during the performance phase, with patients ON medication choosing correctly significantly more frequently than those OFF medication. This effect was independent of drug state during initial learning and appears to reflect a facilitation of generalization for learnt information. This inference is bolstered by our observation that neural activity in nucleus accumbens and ventromedial prefrontal cortex, measured during simultaneously acquired functional magnetic resonance imaging, represented learnt stimulus values during performance. This effect was expressed solely during the ON state with activity in these regions correlating with better performance. Our data indicate that dopamine modulation of nucleus accumbens and ventromedial prefrontal cortex exerts a specific effect on choice behaviour distinct from pure learning. The findings are in keeping with the substantial other evidence that certain aspects of learning are unaffected by dopamine lesions or depletion, and that dopamine plays a key role in performance that may be distinct from its role in learning.

Altruistic learning.

The origin of altruism remains one of the most enduring puzzles of human behaviour. Indeed, true altruism is often thought either not to exist, or to arise merely as a miscalculation of otherwise selfish behaviour. In this paper, we argue that altruism emerges directly from the way in which distinct human decision-making systems learn about rewards. Using insights provided by neurobiological accounts of human decision-making, we suggest that reinforcement learning in game-theoretic social interactions (habitisation over either individuals or games) and observational learning (either imitative of inference based) lead to altruistic behaviour. This arises not only as a result of computational efficiency in the face of processing complexity, but as a direct consequence of optimal inference in the face of uncertainty. Critically, we argue that the fact that evolutionary pressure acts not over the object of learning ('what' is learned), but over the learning systems themselves ('how' things are learned), enables the evolution of altruism despite the direct threat posed by free-riders.

Dopamine and performance in a reinforcement learning task: Evidence from Parkinson's disease

The role dopamine plays in decision-making has important theoretical, empirical and clinical implications. Here, we examined its precise contribution by exploiting the lesion deficit model afforded by Parkinson's disease. We studied patients in a two-stage reinforcement learning task, while they were ON and OFF dopamine replacement medication. Contrary to expectation, we found that dopaminergic drug state (ON or OFF) did not impact learning. Instead, the critical factor was drug state during the performance phase, with patients ON medication choosing correctly significantly more frequently than those OFF medication. This effect was independent of drug state during initial learning and appears to reflect a facilitation of generalization for learnt information. This inference is bolstered by our observation that neural activity in nucleus accumbens and ventromedial prefrontal cortex, measured during simultaneously acquired functional magnetic resonance imaging, represented learnt stimulus values during performance. This effect was expressed solely during the ON state with activity in these regions correlating with better performance. Our data indicate that dopamine modulation of nucleus accumbens and ventromedial prefrontal cortex exerts a specific effect on choice behaviour distinct from pure learning. The findings are in keeping with the substantial other evidence that certain aspects of learning are unaffected by dopamine lesions or depletion, and that dopamine plays a key role in performance that may be distinct from its role in learning. © 2012 The Author.

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is, where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples. © Taylor & Francis Group, LLC.

Dynamic Covariance Models for Multivariate Financial Time Series

The accurate prediction of time-changing covariances is an important problem in the modeling of multivariate financial data. However, some of the most popular models suffer from a) overfitting problems and multiple local optima, b) failure to capture shifts in market conditions and c) large computational costs. To address these problems we introduce a novel dynamic model for time-changing covariances. Over-fitting and local optima are avoided by following a Bayesian approach instead of computing point estimates. Changes in market conditions are captured by assuming a diffusion process in parameter values, and finally computationally efficient and scalable inference is performed using particle filters. Experiments with financial data show excellent performance of the proposed method with respect to current standard models.

Bayesian Learning of Noisy Markov Decision Processes

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.

Bayesian Structured Prediction Using Gaussian Processes

We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M3N), and structured support vector machines (SVMstruct), which embody only a subset of its properties. We present an inference procedure based on Markov Chain Monte Carlo. The framework can be instantiated for a wide range of structured objects such as linear chains, trees, grids, and other general graphs. As a proof of concept, the model is benchmarked on several natural language processing tasks and a video gesture segmentation task involving a linear chain structure. We show prediction accuracies for GPstruct which are comparable to or exceeding those of CRFs and SVMstruct.

Determinantal Clustering Processes - A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel matrix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyperparameter learning. The model is implemented on a variety of synthetic and real world data sets.

The Supervised IBP: Neighbourhood Preserving Infinite Latent Feature Models

We propose a probabilistic model to infer supervised latent variables in the Hamming space from observed data. Our model allows simultaneous inference of the number of binary latent variables, and their values. The latent variables preserve neighbourhood structure of the data in a sense that objects in the same semantic concept have similar latent values, and objects in different concepts have dissimilar latent values. We formulate the supervised infinite latent variable problem based on an intuitive principle of pulling objects together if they are of the same type, and pushing them apart if they are not. We then combine this principle with a flexible Indian Buffet Process prior on the latent variables. We show that the inferred supervised latent variables can be directly used to perform a nearest neighbour search for the purpose of retrieval. We introduce a new application of dynamically extending hash codes, and show how to effectively couple the structure of the hash codes with continuously growing structure of the neighbourhood preserving infinite latent feature space.

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a 'high-lift' and an 'ultra high-lift' turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in 'ultra high-lift' design when compared to the 'high-lift' design. Stronger 'Klebanoff streaks' are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The 'part-span' Kelvin-Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging. © 2013 Elsevier Inc.