The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

On-line learning with adaptive back-propagation in two-layer networks

An adaptive back-propagation algorithm parameterized by an inverse temperature 1/T is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, we analyse these learning algorithms in both the symmetric and the convergence phase for finite learning rates in the case of uncorrelated teachers of similar but arbitrary length T. These analyses show that adaptive back-propagation results generally in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

Upper and lower bounds on the learning curve for Gaussian processes

In this paper we introduce and illustrate non-trivial upper and lower bounds on the learning curves for one-dimensional Gaussian Processes. The analysis is carried out emphasising the effects induced on the bounds by the smoothness of the random process described by the Modified Bessel and the Squared Exponential covariance functions. We present an explanation of the early, linearly-decreasing behavior of the learning curves and the bounds as well as a study of the asymptotic behavior of the curves. The effects of the noise level and the lengthscale on the tightness of the bounds are also discussed.

miniDVMS v1.8 : A user manual(The data visualization and modeling system)

Today, the data available to tackle many scientific challenges is vast in quantity and diverse in nature. The exploration of heterogeneous information spaces requires suitable mining algorithms as well as effective visual interfaces. miniDVMS v1.8 provides a flexible visual data mining framework which combines advanced projection algorithms developed in the machine learning domain and visual techniques developed in the information visualisation domain. The advantage of this interface is that the user is directly involved in the data mining process. Principled projection methods, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), are integrated with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates, and user interaction facilities, to provide this integrated visual data mining framework. The software also supports conventional visualisation techniques such as principal component analysis (PCA), Neuroscale, and PhiVis. This user manual gives an overview of the purpose of the software tool, highlights some of the issues to be taken care while creating a new model, and provides information about how to install and use the tool. The user manual does not require the readers to have familiarity with the algorithms it implements. Basic computing skills are enough to operate the software.

Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

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.

Protein-protein interactions classification from text via local learning with class priors

Text classification is essential for narrowing down the number of documents relevant to a particular topic for further pursual, especially when searching through large biomedical databases. Protein-protein interactions are an example of such a topic with databases being devoted specifically to them. This paper proposed a semi-supervised learning algorithm via local learning with class priors (LL-CP) for biomedical text classification where unlabeled data points are classified in a vector space based on their proximity to labeled nodes. The algorithm has been evaluated on a corpus of biomedical documents to identify abstracts containing information about protein-protein interactions with promising results. Experimental results show that LL-CP outperforms the traditional semisupervised learning algorithms such as SVMand it also performs better than local learning without incorporating class priors.

Improving scheduling techniques in heterogeneous systems with dynamic, on-line optimisations

Computational performance increasingly depends on parallelism, and many systems rely on heterogeneous resources such as GPUs and FPGAs to accelerate computationally intensive applications. However, implementations for such heterogeneous systems are often hand-crafted and optimised to one computation scenario, and it can be challenging to maintain high performance when application parameters change. In this paper, we demonstrate that machine learning can help to dynamically choose parameters for task scheduling and load-balancing based on changing characteristics of the incoming workload. We use a financial option pricing application as a case study. We propose a simulation of processing financial tasks on a heterogeneous system with GPUs and FPGAs, and show how dynamic, on-line optimisations could improve such a system. We compare on-line and batch processing algorithms, and we also consider cases with no dynamic optimisations.

The evolution of learning systems:to Bayes or not to be

Bayesian algorithms pose a limit to the performance learning algorithms can achieve. Natural selection should guide the evolution of information processing systems towards those limits. What can we learn from this evolution and what properties do the intermediate stages have? While this question is too general to permit any answer, progress can be made by restricting the class of information processing systems under study. We present analytical and numerical results for the evolution of on-line algorithms for learning from examples for neural network classifiers, which might include or not a hidden layer. The analytical results are obtained by solving a variational problem to determine the learning algorithm that leads to maximum generalization ability. Simulations using evolutionary programming, for programs that implement learning algorithms, confirm and expand the results. The principal result is not just that the evolution is towards a Bayesian limit. Indeed it is essentially reached. In addition we find that evolution is driven by the discovery of useful structures or combinations of variables and operators. In different runs the temporal order of the discovery of such combinations is unique. The main result is that combinations that signal the surprise brought by an example arise always before combinations that serve to gauge the performance of the learning algorithm. This latter structures can be used to implement annealing schedules. The temporal ordering can be understood analytically as well by doing the functional optimization in restricted functional spaces. We also show that there is data suggesting that the appearance of these traits also follows the same temporal ordering in biological systems. © 2006 American Institute of Physics.

Learning user and product distributed representations using a sequence model for sentiment analysis

In product reviews, it is observed that the distribution of polarity ratings over reviews written by different users or evaluated based on different products are often skewed in the real world. As such, incorporating user and product information would be helpful for the task of sentiment classification of reviews. However, existing approaches ignored the temporal nature of reviews posted by the same user or evaluated on the same product. We argue that the temporal relations of reviews might be potentially useful for learning user and product embedding and thus propose employing a sequence model to embed these temporal relations into user and product representations so as to improve the performance of document-level sentiment analysis. Specifically, we first learn a distributed representation of each review by a one-dimensional convolutional neural network. Then, taking these representations as pretrained vectors, we use a recurrent neural network with gated recurrent units to learn distributed representations of users and products. Finally, we feed the user, product and review representations into a machine learning classifier for sentiment classification. Our approach has been evaluated on three large-scale review datasets from the IMDB and Yelp. Experimental results show that: (1) sequence modeling for the purposes of distributed user and product representation learning can improve the performance of document-level sentiment classification; (2) the proposed approach achieves state-of-The-Art results on these benchmark datasets.