Gaussian process approximations of stochastic differential equations

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations. The method is applied to two simple problems: the Ornstein-Uhlenbeck process, of which the exact solution is known and can be compared to, and the double-well system, for which standard approaches such as the ensemble Kalman smoother fail to provide a satisfactory result. Experiments show that our variational approximation is viable and that the results are very promising as the variational approximate solution outperforms standard Gaussian process regression for non-Gaussian Markov processes.

Short-term electricity demand and gas price forecasts using wavelet transforms and adaptive models

This paper presents some forecasting techniques for energy demand and price prediction, one day ahead. These techniques combine wavelet transform (WT) with fixed and adaptive machine learning/time series models (multi-layer perceptron (MLP), radial basis functions, linear regression, or GARCH). To create an adaptive model, we use an extended Kalman filter or particle filter to update the parameters continuously on the test set. The adaptive GARCH model is a new contribution, broadening the applicability of GARCH methods. We empirically compared two approaches of combining the WT with prediction models: multicomponent forecasts and direct forecasts. These techniques are applied to large sets of real data (both stationary and non-stationary) from the UK energy markets, so as to provide comparative results that are statistically stronger than those previously reported. The results showed that the forecasting accuracy is significantly improved by using the WT and adaptive models. The best models on the electricity demand/gas price forecast are the adaptive MLP/GARCH with the multicomponent forecast; their MSEs are 0.02314 and 0.15384 respectively.

Data visualisation and exploration with prior knowledge

Visualising data for exploratory analysis is a major challenge in many applications. Visualisation allows scientists to gain insight into the structure and distribution of the data, for example finding common patterns and relationships between samples as well as variables. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are employed. These methods are favoured because of their simplicity, but they cannot cope with missing data and it is difficult to incorporate prior knowledge about properties of the variable space into the analysis; this is particularly important in the high-dimensional, sparse datasets typical in geochemistry. In this paper we show how to utilise a block-structured correlation matrix using a modification of a well known non-linear probabilistic visualisation model, the Generative Topographic Mapping (GTM), which can cope with missing data. The block structure supports direct modelling of strongly correlated variables. We show that including prior structural information it is possible to improve both the data visualisation and the model fit. These benefits are demonstrated on artificial data as well as a real geochemical dataset used for oil exploration, where the proposed modifications improved the missing data imputation results by 3 to 13%.

Probabilistic methods for drug discovery

This thesis introduces a flexible visual data exploration framework which combines advanced projection algorithms from the machine learning domain with visual representation techniques developed in the information visualisation domain to help a user to explore and understand effectively large multi-dimensional datasets. The advantage of such a framework to other techniques currently available to the domain experts is that the user is directly involved in the data mining process and advanced machine learning algorithms are employed for better projection. A hierarchical visualisation model guided by a domain expert allows them to obtain an informed segmentation of the input space. Two other components of this thesis exploit properties of these principled probabilistic projection algorithms to develop a guided mixture of local experts algorithm which provides robust prediction and a model to estimate feature saliency simultaneously with the training of a projection algorithm.Local models are useful since a single global model cannot capture the full variability of a heterogeneous data space such as the chemical space. Probabilistic hierarchical visualisation techniques provide an effective soft segmentation of an input space by a visualisation hierarchy whose leaf nodes represent different regions of the input space. We use this soft segmentation to develop a guided mixture of local experts (GME) algorithm which is appropriate for the heterogeneous datasets found in chemoinformatics problems. Moreover, in this approach the domain experts are more involved in the model development process which is suitable for an intuition and domain knowledge driven task such as drug discovery. We also derive a generative topographic mapping (GTM) based data visualisation approach which estimates feature saliency simultaneously with the training of a visualisation model.

Induction by a Hilbert hypercube representation

This thesis describes a novel connectionist machine utilizing induction by a Hilbert hypercube representation. This representation offers a number of distinct advantages which are described. We construct a theoretical and practical learning machine which lies in an area of overlap between three disciplines - neural nets, machine learning and knowledge acquisition - hence it is refered to as a "coalesced" machine. To this unifying aspect is added the various advantages of its orthogonal lattice structure as against less structured nets. We discuss the case for such a fundamental and low level empirical learning tool and the assumptions behind the machine are clearly outlined. Our theory of an orthogonal lattice structure the Hilbert hypercube of an n-dimensional space using a complemented distributed lattice as a basis for supervised learning is derived from first principles on clearly laid out scientific principles. The resulting "subhypercube theory" was implemented in a development machine which was then used to test the theoretical predictions again under strict scientific guidelines. The scope, advantages and limitations of this machine were tested in a series of experiments. Novel and seminal properties of the machine include: the "metrical", deterministic and global nature of its search; complete convergence invariably producing minimum polynomial solutions for both disjuncts and conjuncts even with moderate levels of noise present; a learning engine which is mathematically analysable in depth based upon the "complexity range" of the function concerned; a strong bias towards the simplest possible globally (rather than locally) derived "balanced" explanation of the data; the ability to cope with variables in the network; and new ways of reducing the exponential explosion. Performance issues were addressed and comparative studies with other learning machines indicates that our novel approach has definite value and should be further researched.

Finding structures in information networks using the affinity network

This thesis proposes a novel graphical model for inference called the Affinity Network,which displays the closeness between pairs of variables and is an alternative to Bayesian Networks and Dependency Networks. The Affinity Network shares some similarities with Bayesian Networks and Dependency Networks but avoids their heuristic and stochastic graph construction algorithms by using a message passing scheme. A comparison with the above two instances of graphical models is given for sparse discrete and continuous medical data and data taken from the UCI machine learning repository. The experimental study reveals that the Affinity Network graphs tend to be more accurate on the basis of an exhaustive search with the small datasets. Moreover, the graph construction algorithm is faster than the other two methods with huge datasets. The Affinity Network is also applied to data produced by a synchronised system. A detailed analysis and numerical investigation into this dynamical system is provided and it is shown that the Affinity Network can be used to characterise its emergent behaviour even in the presence of noise.

Gaussian process quantile regression using expectation propagation

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the expected tilted loss function. The integration required in learning is not analytically tractable so to speed up the learning we employ the Expectation Propagation algorithm. We describe how this work relates to other quantile regression methods and apply the method on both synthetic and real data sets. The method is shown to be competitive with state of the art methods whilst allowing for the leverage of the full Gaussian process probabilistic framework.

Guiding local regression using visualisation

Solving many scientific problems requires effective regression and/or classification models for large high-dimensional datasets. Experts from these problem domains (e.g. biologists, chemists, financial analysts) have insights into the domain which can be helpful in developing powerful models but they need a modelling framework that helps them to use these insights. Data visualisation is an effective technique for presenting data and requiring feedback from the experts. A single global regression model can rarely capture the full behavioural variability of a huge multi-dimensional dataset. Instead, local regression models, each focused on a separate area of input space, often work better since the behaviour of different areas may vary. Classical local models such as Mixture of Experts segment the input space automatically, which is not always effective and it also lacks involvement of the domain experts to guide a meaningful segmentation of the input space. In this paper we addresses this issue by allowing domain experts to interactively segment the input space using data visualisation. The segmentation output obtained is then further used to develop effective local regression models.

Visualisation of heterogeneous data with the generalised generative topographic mapping

Heterogeneous and incomplete datasets are common in many real-world visualisation applications. The probabilistic nature of the Generative Topographic Mapping (GTM), which was originally developed for complete continuous data, can be extended to model heterogeneous (i.e. containing both continuous and discrete values) and missing data. This paper describes and assesses the resulting model on both synthetic and real-world heterogeneous data with missing values.

Experiments with two Approaches for Tracking Drifting Concepts

This paper addresses the task of learning classifiers from streams of labelled data. In this case we can face the problem that the underlying concepts can change over time. The paper studies two mechanisms developed for dealing with changing concepts. Both are based on the time window idea. The first one forgets gradually, by assigning to the examples weight that gradually decreases over time. The second one uses a statistical test to detect changes in concept and then optimizes the size of the time window, aiming to maximise the classification accuracy on the new examples. Both methods are general in nature and can be used with any learning algorithm. The objectives of the conducted experiments were to compare the mechanisms and explore whether they can be combined to achieve a synergetic e ect. Results from experiments with three basic learning algorithms (kNN, ID3 and NBC) using four datasets are reported and discussed.

An improved memory management scheme for large scale graph computing engine GraphChi

GraphChi is the first reported disk-based graph engine that can handle billion-scale graphs on a single PC efficiently. GraphChi is able to execute several advanced data mining, graph mining and machine learning algorithms on very large graphs. With the novel technique of parallel sliding windows (PSW) to load subgraph from disk to memory for vertices and edges updating, it can achieve data processing performance close to and even better than those of mainstream distributed graph engines. GraphChi mentioned that its memory is not effectively utilized with large dataset, which leads to suboptimal computation performances. In this paper we are motivated by the concepts of 'pin ' from TurboGraph and 'ghost' from GraphLab to propose a new memory utilization mode for GraphChi, which is called Part-in-memory mode, to improve the GraphChi algorithm performance. The main idea is to pin a fixed part of data inside the memory during the whole computing process. Part-in-memory mode is successfully implemented with only about 40 additional lines of code to the original GraphChi engine. Extensive experiments are performed with large real datasets (including Twitter graph with 1.4 billion edges). The preliminary results show that Part-in-memory mode memory management approach effectively reduces the GraphChi running time by up to 60% in PageRank algorithm. Interestingly it is found that a larger portion of data pinned in memory does not always lead to better performance in the case that the whole dataset cannot be fitted in memory. There exists an optimal portion of data which should be kept in the memory to achieve the best computational performance.

An Approach to Variable Aggregation in Efficiency Analysis

In the nonparametric framework of Data Envelopment Analysis the statistical properties of its estimators have been investigated and only asymptotic results are available. For DEA estimators results of practical use have been proved only for the case of one input and one output. However, in the real world problems the production process is usually well described by many variables. In this paper a machine learning approach to variable aggregation based on Canonical Correlation Analysis is presented. This approach is applied for efficiency estimation of all the farms in Terceira Island of the Azorean archipelago.

Parallel Semi-supervised EM-algorithm (MT-SSEM)

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013