We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient descent, we sample and evaluate possible "moves" in a sphere of fixed radius for each point in the embedded space. A fixed-point convergence guarantee can be shown by formulating the proposed algorithm as an instance of General Pattern Search (GPS) framework. Evaluation on both clean and noisy synthetic datasets shows that pattern search MDS can accurately infer the intrinsic geometry of manifolds embedded in high-dimensional spaces. Additionally, experiments on real data, even under noisy conditions, demonstrate that the proposed pattern search MDS yields state-of-the-art results.

Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM) problems remains challenging. In this paper, we make the first attempt to extend the emerging technique named screening in large-scale sparse learning to SFM for accelerating its optimization process. We first conduct a careful studying of the relationships between SFM and the corresponding convex proximal problems, as well as the accurate primal optimum estimation of the proximal problems. Relying on this study, we subsequently propose a novel safe screening method to quickly identify the elements guaranteed to be included (we refer to them as active) or excluded (inactive) in the final optimal solution of SFM during the optimization process. By removing the inactive elements and fixing the active ones, the problem size can be dramatically reduced, leading to great savings in the computational cost without sacrificing any accuracy. To the best of our knowledge, the proposed method is the first screening method in the fields of SFM and even combinatorial optimization, thus pointing out a new direction for accelerating SFM algorithms. Experiment results on both synthetic and real datasets demonstrate the significant speedups gained by our approach.

Bayesian On-line Changepoint Detection is extended to on-line model selection and non-stationary spatio-temporal processes. We propose spatially structured Vector Autoregressions (VARs) for modelling the process between changepoints (CPs) and give an upper bound on the approximation error of such models. The resulting algorithm performs prediction, model selection and CP detection on-line. Its time complexity is linear and its space complexity constant, and thus it is two orders of magnitudes faster than its closest competitor. In addition, it outperforms the state of the art for multivariate data.

In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms, each method incorporates different physics-based assumptions in order to reduce the computational complexity while maintaining the physics as much as possible. This work specifically focuses on using the ML approaches to model a 2D concrete sample under low strain rate pure tensile loading conditions with 20 preexisting cracks present. A high-fidelity finite element-discrete element model is used to both produce a training dataset of 150 simulations and an additional 35 simulations for validation. Results from the ML approaches are directly compared against the results from the high-fidelity model. Strengths and weaknesses of each approach are discussed and the most important conclusion is that a combination of physics-informed and data-driven features are necessary for emulating the physics of crack propagation, interaction and coalescence. All of the models presented here have runtimes that are orders of magnitude faster than the original high-fidelity model and pave the path for developing accurate reduced order models that could be used to inform larger length-scale models with important sub-scale physics that often cannot be accounted for due to computational cost.

This Ph.D. thesis deals with the optimization of several renewable energy resources development as well as the improvement of facilities management in oceanic engineering and airports, using computational hybrid methods belonging to AI to this end. Energy is essential to our society in order to ensure a good quality of life. This means that predictions over the characteristics on which renewable energies depend are necessary, in order to know the amount of energy that will be obtained at any time. The second topic tackled in this thesis is related to the basic parameters that influence in different marine activities and airports, whose knowledge is necessary to develop a proper facilities management in these environments. Within this work, a study of the state-of-the-art Machine Learning have been performed to solve the problems associated with the topics above-mentioned, and several contributions have been proposed: One of the pillars of this work is focused on the estimation of the most important parameters in the exploitation of renewable resources. The second contribution of this thesis is related to feature selection problems. The proposed methodologies are applied to multiple problems: the prediction of $H_s$, relevant for marine energy applications and marine activities, the estimation of WPREs, undesirable variations in the electric power produced by a wind farm, the prediction of global solar radiation in areas from Spain and Australia, really important in terms of solar energy, and the prediction of low-visibility events at airports. All of these practical issues are developed with the consequent previous data analysis, normally, in terms of meteorological variables.

We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the responses for a small subset of the points that are then used to construct linear predictions for all points in the dataset. The performance of the predictions is evaluated by the total square loss on all responses (the attained as well as the hidden ones). We show that a good approximate solution to this least squares problem can be obtained from just dimension $d$ many responses by using a joint sampling technique called volume sampling. Moreover, the least squares solution obtained for the volume sampled subproblem is an unbiased estimator of optimal solution based on all n responses. This unbiasedness is a desirable property that is not shared by other common subset selection techniques. Motivated by these basic properties, we develop a theoretical framework for studying volume sampling, resulting in a number of new matrix expectation equalities and statistical guarantees which are of importance not only to least squares regression but also to numerical linear algebra in general. Our methods also lead to a regularized variant of volume sampling, and we propose the first efficient algorithms for volume sampling which make this technique a practical tool in the machine learning toolbox. Finally, we provide experimental evidence which confirms our theoretical findings.

Normative modeling has recently been proposed as an alternative for the case-control approach in modeling heterogeneity within clinical cohorts. Normative modeling is based on single-output Gaussian process regression that provides coherent estimates of uncertainty required by the method but does not consider spatial covariance structure. Here, we introduce a scalable multi-task Gaussian process regression (S-MTGPR) approach to address this problem. To this end, we exploit a combination of a low-rank approximation of the spatial covariance matrix with algebraic properties of Kronecker product in order to reduce the computational complexity of Gaussian process regression in high-dimensional output spaces. On a public fMRI dataset, we show that S-MTGPR: 1) leads to substantial computational improvements that allow us to estimate normative models for high-dimensional fMRI data whilst accounting for spatial structure in data; 2) by modeling both spatial and across-sample variances, it provides higher sensitivity in novelty detection scenarios.

Healthcare is a natural arena for the application of machine learning, especially as modern electronic health records (EHRs) provide increasingly large amounts of data to answer clinically meaningful questions. However, clinical data and practice present unique challenges that complicate the use of common methodologies. This article serves as a primer on addressing these challenges and highlights opportunities for members of the machine learning and data science communities to contribute to this growing domain.

We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known randomized online coordinate descent algorithms. Furthermore, the proposed algorithms for stochastic optimization exhibit as good convergence rates as the best known randomized coordinate descent algorithms. We also show simulation results to demonstrate performance of the proposed algorithms.

In the age of globalization with fierce competition, dynamic marketplaces and changing customer demands, it is critical that business organizations understand their structures and processses, align business strategy and organization's capabilities and investment, detect and reorganize redundant business capabilities (especially after mergers and acquisitions), and recognize business innovations. Consequently, great efforts have been made to design and improve Business Architecture (BA) models for solving those challenges. Business Architecture (BA) is a blueprint of the enterprise that provides a common understanding of the organization and is used to align strategic objectives and tactical demands, which articulates the structure of an enterprise in terms of its capabilities, governance structure, business processes, and business information [1]. In the past few decades, various BA models have been developed, of which some major models including: ArchiMate [2] that is maintained by the Archimate Foundation and approved as technical standard by the Open Group, and can be used to formally describe business operations; Business Architecture Working Group (BAWG) [3] that is founded as a part of the Objected Management Group (OMG) for establishing industry standards, supporting the creation, and alignment of business blueprints; Business driven analytics is implemented in CBM and explore what and how business insights can be obtained through the data-driven analytics. We conclude the paper by summarizing our current work, and discussing future directions.