Roman Garnett

A universal noise removal algorithm with an impulse detector

We introduce a local image statistic for identifying noise pixels in images corrupted with impulse noise of random values. The statistical values quantify how different in intensity the particular pixels are from their most similar neighbors. We continue to demonstrate how this statistic may be incorporated into a filter designed to remove additive Gaussian noise. The result is a new filter capable of reducing both Gaussian and impulse noises from noisy images effectively, which performs remarkably well, both in terms of quantitative measures of signal restoration and qualitative judgements of image quality. Our approach is extended to automatically remove any mix of Gaussian and impulse noise.

Bayesian optimization for sensor set selection

We consider the problem of selecting an optimal set of sensors, as determined, for example, by the predictive accuracy of the resulting sensor network. Given an underlying metric between pairs of set elements, we introduce a natural metric between sets of sensors for this task. Using this metric, we can construct covariance functions over sets, and thereby perform Gaussian process inference over a function whose domain is a power set. If the function has additional inputs, our covariances can be readily extended to incorporate them---allowing us to consider, for example, functions over both sets and time. These functions can then be optimized using Gaussian process global optimization (GPGO). We use the root mean squared error (RMSE) of the predictions made using a set of sensors at a particular time as an example of such a function to be optimized; the optimal point specifies the best choice of sensor locations. We demonstrate the resulting method by dynamically selecting the best subset of a given set of weather sensors for the prediction of the air temperature across the United Kingdom.

Multi-scale inference of interaction rules in animal groups using Bayesian model selection.

Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical ‘phase transition’, whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have ‘memory’ of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture the observed locality of interactions. Traditional self-propelled particle models fail to capture the fine scale dynamics of the system. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics, while maintaining a biologically plausible perceptual range. We conclude that prawns’ movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.

Sequential Bayesian Prediction in the Presence of Changepoints and Faults

We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We introduce nonstationary covariance functions to be used in Gaussian process prediction that model such changes, and then proceed to demonstrate how to effectively manage the hyperparameters associated with those covariance functions. We further introduce covariance functions to be used in situations where our observation model undergoes changes, as is the case for sensor faults. By using Bayesian quadrature, we can integrate out the hyperparameters, allowing us to calculate the full marginal predictive distribution. Furthermore, if desired, the posterior distribution over putative changepoint locations can be calculated as a natural byproduct of our prediction algorithm.

Efficient graph kernels by randomization

Learning from complex data is becoming increasingly important, and graph kernels have recently evolved into a rapidly developing branch of learning on structured data. However, previously proposed kernels rely on having discrete node label information. In this paper, we explore the power of continuous node-level features for propagation-based graph kernels. Specifically, propagation kernels exploit node label distributions from propagation schemes like label propagation, which naturally enables the construction of graph kernels for partially labeled graphs. In order to efficiently extract graph features from continuous node label distributions, and in general from continuous vector-valued node attributes, we utilize randomized techniques, which easily allow for deriving similarity measures based on propagated information. We show that propagation kernels utilizing locality-sensitive hashing reduce the runtime of existing graph kernels by several orders of magnitude. We evaluate the performance of various propagation kernels on real-world bioinformatics and image benchmark datasets.

Sequential Bayesian prediction in the presence of changepoints

We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We introduce nonstationary covariance functions to be used in Gaussian process prediction that model such changes, then proceed to demonstrate how to effectively manage the hyperparameters associated with those covariance functions. By using Bayesian quadrature, we can integrate out the hyperparameters, allowing us to calculate the marginal predictive distribution. Furthermore, if desired, the posterior distribution over putative changepoint locations can be calculated as a natural byproduct of our prediction algorithm.

Objectively identifying landmark use and predicting flight trajectories of the homing pigeon using Gaussian processes.

Pigeons home along idiosyncratic habitual routes from familiar locations. It has been suggested that memorized visual landmarks underpin this route learning. However, the inability to experimentally alter the landscape on large scales has hindered the discovery of the particular features to which birds attend. Here, we present a method for objectively classifying the most informative regions of animal paths. We apply this method to flight trajectories from homing pigeons to identify probable locations of salient visual landmarks. We construct and apply a Gaussian process model of flight trajectory generation for pigeons trained to home from specific release sites. The model shows increasing predictive power as the birds become familiar with the sites, mirroring the animals learning process. We subsequently find that the most informative elements of the flight trajectories coincide with landscape features that have previously been suggested as important components of the homing task.

Active Data Selection for Sensor Networks with Faults and Changepoints

We describe a Bayesian formalism for the intelligent selection of observations from sensor networks that may intermittently undergo faults or changepoints. Such active data selection is performed with the goal of taking as few observations as necessary in order to maintain a reasonable level of uncertainty about the variables of interest. The presence of faults/changepoints is not always obvious and therefore our algorithm must first detect their occurrence. Having done so, our selection of observations must be appropriately altered. Faults corrupt our observations, reducing their impact; changepoints (abrupt changes in the characteristics of data) may require the transition to an entirely different sampling schedule. Our solution is to employ a Gaussian process formalism that allows for sequential time-series prediction about variables of interest along with a decision theoretic approach to the problem of selecting observations.

Active search on graphs

Active search is an increasingly important learning problem in which we use a limited budget of label queries to discover as many members of a certain class as possible. Numerous real-world applications may be approached in this manner, including fraud detection, product recommendation, and drug discovery. Active search has model learning and exploration/exploitation features similar to those encountered in active learning and bandit problems, but algorithms for those problems do not fit active search. Previous work on the active search problem [5] showed that the optimal algorithm requires a lookahead evaluation of expected utility that is exponential in the number of selections to be made and proposed a truncated lookahead heuristic. Inspired by the success of myopic methods for active learning and bandit problems, we propose a myopic method for active search on graphs. We suggest selecting points by maximizing a score considering the potential impact of selecting a node, meant to emulate lookahead while avoiding exponential search. We test the proposed algorithm empirically on real-world graphs and show that it outperforms popular approaches for active learning and bandit problems as well as truncated lookahead of a few steps.

Propagation kernels: efficient graph kernels from propagated information

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage early-stage distributions from propagation schemes such as random walks to capture structural information encoded in node labels, attributes, and edge information. This has two benefits. First, off-the-shelf propagation schemes can be used to naturally construct kernels for many graph types, including labeled, partially labeled, unlabeled, directed, and attributed graphs. Second, by leveraging existing efficient and informative propagation schemes, propagation kernels can be considerably faster than state-of-the-art approaches without sacrificing predictive performance. We will also show that if the graphs at hand have a regular structure, for instance when modeling image or video data, one can exploit this regularity to scale the kernel computation to large databases of graphs with thousands of nodes. We support our contributions by exhaustive experiments on a number of real-world graphs from a variety of application domains.