455 research outputs found

    Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation

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    In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real-world datasets. Furthermore, we extend the models with the Bayesian automatic relevance determination prior, allowing the models to perform automatic model selection, and demonstrate its efficiency

    Temporally adaptive monitoring procedures with applications in enterprise cyber-security

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    Due to the perpetual threat of cyber-attacks, enterprises must employ and develop new methods of detection as attack vectors evolve and advance. Enterprise computer networks produce a large volume and variety of data including univariate data streams, time series and network graph streams. Motivated by cyber-security, this thesis develops adaptive monitoring tools for univariate and network graph data streams, however, they are not limited to this domain. In all domains, real data streams present several challenges for monitoring including trend, periodicity and change points. Streams often also have high volume and frequency. To deal with the non-stationarity in the data, the methods applied must be adaptive. Adaptability in the proposed procedures throughout the thesis is introduced using forgetting factors, weighting the data accordingly to recency. Secondly, methods applied must be computationally fast with a small or fixed computation burden and fixed storage requirements for timely processing. Throughout this thesis, sequential or sliding window approaches are employed to achieve this. The first part of the thesis is centred around univariate monitoring procedures. A sequential adaptive parameter estimator is proposed using a Bayesian framework. This procedure is then extended for multiple change point detection, where, unlike existing change point procedures, the proposed method is capable of detecting abrupt changes in the presence of trend. We additionally present a time series model which combines short-term and long-term behaviours of a series for improved anomaly detection. Unlike existing methods which primarily focus on point anomalies detection (extreme outliers), our method is capable of also detecting contextual anomalies, when the data deviates from persistent patterns of the series such as seasonality. Finally, a novel multi-type relational clustering methodology is proposed. As multiple relations exist between the different entities within a network (computers, users and ports), multiple network graphs can be generated. We propose simultaneously clustering over all graphs to produce a single clustering for each entity using Non-Negative Matrix Tri-Factorisation. Through simplifications, the proposed procedure is fast and scalable for large network graphs. Additionally, this methodology is extended for graph streams. This thesis provides an assortment of tools for enterprise network monitoring with a focus on adaptability and scalability making them suitable for intrusion detection and situational awareness.Open Acces

    A novel augmented graph approach for estimation in localisation and mapping

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    This thesis proposes the use of the augmented system form - a generalisation of the information form representing both observations and states. In conjunction with this, this thesis proposes a novel graph representation for the estimation problem together with a graph based linear direct solving algorithm. The augmented system form is a mathematical description of the estimation problem showing the states and observations. The augmented system form allows a more general range of factorisation orders among the observations and states, which is essential for constraints and is beneficial for sparsity and numerical reasons. The proposed graph structure is a novel sparse data structure providing more symmetric access and faster traversal and modification operations than the compressed-sparse-column (CSC) sparse matrix format. The graph structure was developed as a fundamental underlying structure for the formulation of sparse estimation problems. This graph-theoretic representation replaces conventional sparse matrix representations for the estimation states, observations and their interconnections. This thesis contributes a new implementation of the indefinite LDL factorisation algorithm based entirely in the graph structure. This direct solving algorithm was developed in order to exploit the above new approaches of this thesis. The factorisation operations consist of accessing adjacencies and modifying the graph edges. The developed solving algorithm demonstrates the significant differences in the form and approach of the graph-embedded algorithm compared to a conventional matrix implementation. The contributions proposed in this thesis improve estimation methods by providing novel mathematical data structures used to represent states, observations and the sparse links between them. These offer improved flexibility and capabilities which are exploited in the solving algorithm. The contributions constitute a new framework for the development of future online and incremental solving, data association and analysis algorithms for online, large scale localisation and mapping

    Learning Density Models via Structured Latent Variables

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    As one principal approach to machine learning and cognitive science, the probabilistic framework has been continuously developed both theoretically and practically. Learning a probabilistic model can be thought of as inferring plausible models to explain observed data. The learning process exploits random variables as building blocks which are held together with probabilistic relationships. The key idea behind latent variable models is to introduce latent variables as powerful attributes (setting/instrument) to reveal data structures and explore underlying features which can sensitively describe the real-world data. The classical research approaches engage shallow architectures, including latent feature models and finite mixtures of latent variable models. Within the classical frameworks, we should make certain assumptions about the form, structure, and distribution of the data. Since the shallow form may not describe the data structures sufficiently, new types of latent structures are promptly developed with the probabilistic frameworks. In this line, three main research interests are sparked, including infinite latent feature models, mixtures of the mixture models, and deep models. This dissertation summarises our work which is advancing the state-of-the-art in both classical and emerging areas. In the first block, a finite latent variable model with the parametric priors is presented for clustering and is further extended into a two-layer mixture model for discrimination. These models embed the dimensionality reduction in their learning tasks by designing a latent structure called common loading. Referred to as the joint learning models, these models attain more appropriate low-dimensional space that better matches the learning task. Meanwhile, the parameters are optimised simultaneously for both the low-dimensional space and model learning. However, these joint learning models must assume the fixed number of features as well as mixtures, which are normally tuned and searched using a trial and error approach. In general, the simpler inference can be performed by fixing more parameters. However, the fixed parameters will limit the flexibility of models, and false assumptions could even derive incorrect inferences from the data. Thus, a richer model is allowed for reducing the number of assumptions. Therefore an infinite tri-factorisation structure is proposed with non-parametric priors in the second block. This model can automatically determine an optimal number of features and leverage the interrelation between data and features. In the final block, we introduce how to promote the shallow latent structures model to deep structures to handle the richer structured data. This part includes two tasks: one is a layer-wise-based model, another is a deep autoencoder-based model. In a deep density model, the knowledge of cognitive agents can be modelled using more complex probability distributions. At the same time, inference and parameter computation procedure are straightforward by using a greedy layer-wise algorithm. The deep autoencoder-based joint learning model is trained in an end-to-end fashion which does not require pre-training of the autoencoder network. Also, it can be optimised by standard backpropagation without the inference of maximum a posteriori. Deep generative models are much more efficient than their shallow architectures for unsupervised and supervised density learning tasks. Furthermore, they can also be developed and used in various practical applications

    Integration of multi-scale protein interactions for biomedical data analysis

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    With the advancement of modern technologies, we observe an increasing accumulation of biomedical data about diseases. There is a need for computational methods to sift through and extract knowledge from the diverse data available in order to improve our mechanistic understanding of diseases and improve patient care. Biomedical data come in various forms as exemplified by the various omics data. Existing studies have shown that each form of omics data gives only partial information on cells state and motivated jointly mining multi-omics, multi-modal data to extract integrated system knowledge. The interactome is of particular importance as it enables the modelling of dependencies arising from molecular interactions. This Thesis takes a special interest in the multi-scale protein interactome and its integration with computational models to extract relevant information from biomedical data. We define multi-scale interactions at different omics scale that involve proteins: pairwise protein-protein interactions, multi-protein complexes, and biological pathways. Using hypergraph representations, we motivate considering higher-order protein interactions, highlighting the complementary biological information contained in the multi-scale interactome. Based on those results, we further investigate how those multi-scale protein interactions can be used as either prior knowledge, or auxiliary data to develop machine learning algorithms. First, we design a neural network using the multi-scale organization of proteins in a cell into biological pathways as prior knowledge and train it to predict a patient's diagnosis based on transcriptomics data. From the trained models, we develop a strategy to extract biomedical knowledge pertaining to the diseases investigated. Second, we propose a general framework based on Non-negative Matrix Factorization to integrate the multi-scale protein interactome with multi-omics data. We show that our approach outperforms the existing methods, provide biomedical insights and relevant hypotheses for specific cancer types

    Deep Multi-View Learning for Visual Understanding

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    PhD ThesisMulti-view data is the result of an entity being perceived or represented from multiple perspectives. Plenty of applications in visual understanding contain multi-view data. For example, the face images for training a recognition system are usually captured by different devices from multiple angles. This thesis focuses on the cross-view visual recognition problems, e.g., identifying the face images of the same person across different cameras. Several representative multi-view settings, from the supervised multi-view learning to the more challenging unsupervised domain adaptive (UDA) multi-view learning, are investigated. Novel multi-view learning algorithms are proposed correspondingly. To be more specific, the proposed methods are based on the advanced deep neural network (DNN) architectures for better handling visual data. However, directly combining the multi-view learning objectives with DNN can result in different issues, e.g., on scalability, and limit the application scenarios and model performance. Corresponding novelties in DNN methods are thus required to solve them. This thesis is organised into three parts. Each chapter focuses on a multi-view learning setting with novel solutions and is detailed as follows: Chapter 3 A supervised multi-view learning setting with two different views are studied. To recognise the data samples across views, one strategy is aligning them in a common feature space via correlation maximisation. It is also known as canonical correlation analysis (CCA). Deep CCA has been proposed for better performance with the non-linear projection via deep neural networks. Existing deep CCA models typically decorrelate the deep feature dimensions of each view before their Euclidean distances are minimised in the common space. This feature decorrelation is achieved by enforcing an exact decorrelation constraint which is computationally expensive due to the matrix inversion or SVD operations. Therefore, existing deep CCA models are inefficient and have scalability issues. Furthermore, the exact decorrelation is incompatible with the gradient based deep model training and results in sub-optimal solution. To overcome these aforementioned issues, a novel deep CCA model Soft CCA is introduced in this thesis. Specifically, the exact decorrelation is replaced by soft decorrelation via a mini-batch based Stochastic Decorrelation Loss (SDL). It can be jointly optimised with the other training objectives. In addition, our SDL loss can be applied to other deep models beyond multi-view learning. Chapter 4 The supervised multi-view learning setting, whereby more than two views exist, are studied in this chapter. Recently developed deep multi-view learning algorithms either learn a latent visual representation based on a single semantic level and/or require laborious human annotation of these factors as attributes. A novel deep neural network architecture, called Multi- Level Factorisation Net (MLFN), is proposed to automatically factorise the visual appearance into latent discriminative factors at multiple semantic levels without manual annotation. The main purpose is forcing different views share the same latent factors so that they are can be aligned at all layers. Specifically, MLFN is composed of multiple stacked blocks. Each block contains multiple factor modules to model latent factors at a specific level, and factor selection modules that dynamically select the factor modules to interpret the content of each input image. The outputs of the factor selection modules also provide a compact latent factor descriptor that is complementary to the conventional deeply learned feature, and they can be fused efficiently. The effectiveness of the proposed MLFN is demonstrated by not only the large-scale cross-view recognition problems but also the general object categorisation tasks. Chapter 5 The last problem is a special unsupervised domain adaptation setting called unsupervised domain adaptive (UDA) multi-view learning. It contains a fully annotated dataset as the source domain and another unsupervised dataset with relevant tasks as the target domain. The main purpose is to improve the performance of the unlabelled dataset with the annotated data from the other dataset. More importantly, this setting further requires both the source and target domains are multi-view datasets with relevant tasks. Therefore, the assumption of the aligned label space across domains is inappropriate in the UDA multi-view learning. For example, the person re-identification (Re-ID) datasets built on different surveillance scenarios are with images of different people captured and should be given disjoint person identity labels. Existing methods for UDA multi-view learning problems are aligning different domains either in the raw image space or a feature embedding space for domain alignment. In this thesis, a different framework, multi-task learning, is adopted with the domain specific objectives for a common space learning. Specifically, such common space is proposed to enable the knowledge transfer. The conventional supervised losses can be used for the labelled source data while the unsupervised objectives for the target domain play the key roles in domain adaptation. Two novel unsupervised objectives are introduced for UDA multi-view learning and result in two models as below. The first model, termed common factorised space model (CFSM), is built on the assumptions that the semantic latent attributes are shared between the source and target domains since they are relevant multi-view learning tasks. Different from the existing methods that based on domain alignment, CFSM emphasizes on transferring the information across domains via discovering discriminative latent factors in the proposed common space. However, the multi-view data from target domain is without labels. Therefore, an unsupervised factorisation loss is derived and applied on the common space for latent factors discovery across domains. The second model still learns a shared embedding space with multi-view data from both domains but with a different assumption. It attempts to discover the latent correspondence of multi-view data in the unsupervised target data. The target data’s contribution comes from a clustering process. Each cluster thus reveals the underlying cross-view correspondences across multiple views in target domain. To this end, a novel Stochastic Inference for Deep Clustering (SIDC) method is proposed. It reduces self-reinforcing errors that lead to premature convergence to a sub-optimal solution by changing the conventional deterministic cluster assignment to a stochastic one
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