Tensor-variate machine learning on graphs

Traditional machine learning algorithms are facing significant challenges as the world enters the era of big data, with a dramatic expansion in volume and range of applications and an increase in the variety of data sources. The large- and multi-dimensional nature of data often increases the computational costs associated with their processing and raises the risks of model over-fitting - a phenomenon known as the curse of dimensionality. To this end, tensors have become a subject of great interest in the data analytics community, owing to their remarkable ability to super-compress high-dimensional data into a low-rank format, while retaining the original data structure and interpretability. This leads to a significant reduction in computational costs, from an exponential complexity to a linear one in the data dimensions. An additional challenge when processing modern big data is that they often reside on irregular domains and exhibit relational structures, which violates the regular grid assumptions of traditional machine learning models. To this end, there has been an increasing amount of research in generalizing traditional learning algorithms to graph data. This allows for the processing of graph signals while accounting for the underlying relational structure, such as user interactions in social networks, vehicle flows in traffic networks, transactions in supply chains, chemical bonds in proteins, and trading data in financial networks, to name a few. Although promising results have been achieved in these fields, there is a void in literature when it comes to the conjoint treatment of tensors and graphs for data analytics. Solutions in this area are increasingly urgent, as modern big data is both large-dimensional and irregular in structure. To this end, the goal of this thesis is to explore machine learning methods that can fully exploit the advantages of both tensors and graphs. In particular, the following approaches are introduced: (i) Graph-regularized tensor regression framework for modelling high-dimensional data while accounting for the underlying graph structure; (ii) Tensor-algebraic approach for computing efficient convolution on graphs; (iii) Graph tensor network framework for designing neural learning systems which is both general enough to describe most existing neural network architectures and flexible enough to model large-dimensional data on any and many irregular domains. The considered frameworks were employed in several real-world applications, including air quality forecasting, protein classification, and financial modelling. Experimental results validate the advantages of the proposed methods, which achieved better or comparable performance against state-of-the-art models. Additionally, these methods benefit from increased interpretability and reduced computational costs, which are crucial for tackling the challenges posed by the era of big data.Open Acces

Information fusion between knowledge and data in Bayesian network structure learning

Bayesian Networks (BNs) have become a powerful technology for reasoning under uncertainty, particularly in areas that require causal assumptions that enable us to simulate the effect of intervention. The graphical structure of these models can be determined by causal knowledge, learnt from data, or a combination of both. While it seems plausible that the best approach in constructing a causal graph involves combining knowledge with machine learning, this approach remains underused in practice. We implement and evaluate 10 knowledge approaches with application to different case studies and BN structure learning algorithms available in the open-source Bayesys structure learning system. The approaches enable us to specify pre-existing knowledge that can be obtained from heterogeneous sources, to constrain or guide structure learning. Each approach is assessed in terms of structure learning effectiveness and efficiency, including graphical accuracy, model fitting, complexity, and runtime; making this the first paper that provides a comparative evaluation of a wide range of knowledge approaches for BN structure learning. Because the value of knowledge depends on what data are available, we illustrate the results both with limited and big data. While the overall results show that knowledge becomes less important with big data due to higher learning accuracy rendering knowledge less important, some of the knowledge approaches are actually found to be more important with big data. Amongst the main conclusions is the observation that reduced search space obtained from knowledge does not always imply reduced computational complexity, perhaps because the relationships implied by the data and knowledge are in tension

Generating realistic scaled complex networks

Research on generative models is a central project in the emerging field of network science, and it studies how statistical patterns found in real networks could be generated by formal rules. Output from these generative models is then the basis for designing and evaluating computational methods on networks, and for verification and simulation studies. During the last two decades, a variety of models has been proposed with an ultimate goal of achieving comprehensive realism for the generated networks. In this study, we (a) introduce a new generator, termed ReCoN; (b) explore how ReCoN and some existing models can be fitted to an original network to produce a structurally similar replica, (c) use ReCoN to produce networks much larger than the original exemplar, and finally (d) discuss open problems and promising research directions. In a comparative experimental study, we find that ReCoN is often superior to many other state-of-the-art network generation methods. We argue that ReCoN is a scalable and effective tool for modeling a given network while preserving important properties at both micro- and macroscopic scales, and for scaling the exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the paper was presented at the 5th International Workshop on Complex Networks and their Application

Local-Aggregate Modeling for Big-Data via Distributed Optimization: Applications to Neuroimaging

Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging scans. This is an ultra-high-dimensional problem that consists of a matrix of covariates (brain locations by time points) for each subject; few methods currently exist to fit supervised models directly to this tensor data. We propose a novel modeling and algorithmic strategy to apply generalized linear models (GLMs) to this massive tensor data in which one set of variables is associated with locations. Our method begins by fitting GLMs to each location separately, and then builds an ensemble by blending information across locations through regularization with what we term an aggregating penalty. Our so called, Local-Aggregate Model, can be fit in a completely distributed manner over the locations using an Alternating Direction Method of Multipliers (ADMM) strategy, and thus greatly reduces the computational burden. Furthermore, we propose to select the appropriate model through a novel sequence of faster algorithmic solutions that is similar to regularization paths. We will demonstrate both the computational and predictive modeling advantages of our methods via simulations and an EEG classification problem.Comment: 41 pages, 5 figures and 3 table