The potential of recovering the topology of a grid using solely publicly available market data is explored here. In contemporary whole-sale electricity markets, real-time prices are typically determined by solving the network-constrained economic dispatch problem. Under a linear DC model, locational marginal prices (LMPs) correspond to the Lagrange multipliers of the linear program involved. The interesting observation here is that the matrix of spatiotemporally varying LMPs exhibits the following property: Once premultiplied by the weighted grid Laplacian, it yields a low-rank and sparse matrix. Leveraging this rich structure, a regularized maximum likelihood estimator (MLE) is developed to recover the grid Laplacian from the LMPs. The convex optimization problem formulated includes low rank- and sparsity-promoting regularizers, and it is solved using a scalable algorithm. Numerical tests on prices generated for the IEEE 14-bus benchmark provide encouraging topology recovery results.

We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that a top-down sensing procedure can identify these partitions, and hence the activations, using few measurements. By exploiting the cluster structure, we are able to provide localization guarantees at weaker signal to noise ratios than in the unstructured setting. We complement this performance guarantee with an information theoretic lower bound, providing a necessary signal-to-noise ratio for any algorithm to successfully localize the cluster. We verify our analysis with some simulations, demonstrating the practicality of our algorithm.

The Generalized Traveling Salesman Problem (GTSP) is one of the NP-hard combinatorial optimization problems. A variant of GTSP is E-GTSP where E, meaning equality, has the constraint: exactly one node from a cluster of a graph partition is visited. The main objective of the E-GTSP is to find a minimum cost tour passing through exactly one node from each cluster of an undirected graph. Agent-based approaches involving are successfully used nowadays for solving real life complex problems. The aim of the current paper is to illustrate some variants of agent-based algorithms including ant-based models with specific properties for solving E-GTSP.

We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian manifolds, where non-analytic ordinary differential equations are involved in virtually all computations. The probabilistic formulation permits marginalising the uncertainty of the numerical solution such that statistics are less sensitive to inaccuracies. This leads to new Riemannian algorithms for mean value computations and principal geodesic analysis. Marginalisation also means results can be less precise than point estimates, enabling a noticeable speed-up over the state of the art. Our approach is an argument for a wider point that uncertainty caused by numerical calculations should be tracked throughout the pipeline of machine learning algorithms.

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come.

This article addresses prediction problems where covariate information is missing during model construction and is also missing in future observations for which we are obligated to generate a forecast. Our aim is to innovate a nonparametric statistical learning extension which incorporates missingness into both the training and the forecasting phases. In the spirit of nonparametric learning, we wish to incorporate the missingness in both phases automatically, without the need for pre-specified modeling. We limit our focus to tree-based statistical learning, which has demonstrated strong predictive performance and has consequently received considerable attention in recent years. State-of-the-art algorithms include Random Forests (RF, Breiman, 2001b), stochastic gradient boosting (Friedman, 2002), and Bayesian Additive and Regression Trees (BART, Chipman et al., 2010), the algorithm of interest in this study.

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a necessity in such setting. Deviating from this paradigm, we show that non-negativity constraints on the regression coefficients may be similarly effective as explicit regularization if the design matrix has additional properties, which are met in several applications of non-negative least squares (NNLS). We show that for these designs, the performance of NNLS with regard to prediction and estimation is comparable to that of the lasso. We argue further that in specific cases, NNLS may have a better $\ell_{\infty}$-rate in estimation and hence also advantages with respect to support recovery when combined with thresholding. From a practical point of view, NNLS does not depend on a regularization parameter and is hence easier to use.

We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research interest of this paper is to find the vectors as close to the vertices as possible in a situation in which noise is added to the data points. Our algorithm is designed to capture the shape of the convex hull of data points by using its enclosing ellipsoid. We show that the algorithm has correctness and robustness properties from theoretical and practical perspectives; correctness here means that if the data points do not contain any noise, the algorithm can find the vertices of their convex hull; robustness means that if the data points contain noise, the algorithm can find the near-vertices. Finally, we apply the algorithm to document clustering, and report the experimental results.

This chapter overviews a recently introduced network-based model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a graph having as vertices the local optima and as edges the possible weighted transitions between them. Two definitions of edges have been proposed: basin-transition and escape-edges, which capture relevant topological features of the underlying search spaces. This network model brings a new set of metrics to characterize the structure of combinatorial landscapes, those associated with the science of complex networks. These metrics are described, and results are presented of local optima network extraction and analysis for two selected combinatorial landscapes: NK landscapes and the quadratic assignment problem. Network features are found to correlate with and even predict the performance of heuristic search algorithms operating on these problems.

We describe a probabilistic framework for synthesizing control policies for general multi-robot systems, given environment and sensor models and a cost function. Decentralized, partially observable Markov decision processes (Dec-POMDPs) are a general model of decision processes where a team of agents must cooperate to optimize some objective (specified by a shared reward or cost function) in the presence of uncertainty, but where communication limitations mean that the agents cannot share their state, so execution must proceed in a decentralized fashion. While Dec-POMDPs are typically intractable to solve for real-world problems, recent research on the use of macro-actions in Dec-POMDPs has significantly increased the size of problem that can be practically solved as a Dec-POMDP. We describe this general model, and show how, in contrast to most existing methods that are specialized to a particular problem class, it can synthesize control policies that use whatever opportunities for coordination are present in the problem, while balancing off uncertainty in outcomes, sensor information, and information about other agents. We use three variations on a warehouse task to show that a single planner of this type can generate cooperative behavior using task allocation, direct communication, and signaling, as appropriate.