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In this talk we discuss some recent limit laws for empirical optimal transport distances from a simulation perspective. On discrete spaces, this requires to solve another optimal transport problem in each simulation step, which reveals simulations of such limit laws computational demanding. We discuss an approximation strategy to overcome this burden. In particular, we examine empirically an upper bound for such limiting distributions on discrete spaces based on a spanning tree approximation which can be computed explicitly.

Multiple classification techniques have been employed for different business applications. In the particular case of credit scoring, a classifier which maximizes the total profit is preferable. The recently proposed expected maximum profit (EMP) measure for credit scoring allows to select the most profitable classifier. Taking the idea of the EMP one step further, it is desirable to integrate the measure into model construction, and thus obtain a profit maximizing model.

Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are developed for scalar functions supported on undirected graphs. We propose both a generalization of the underlying graph and a class of linear operations for stochastic (time-varying) processes on directed (or undirected) graphs to be used in graph convolutional networks.

Network science provides valuable insights across
numerous disciplines including sociology, biology, neuroscience
and engineering. A task of major practical importance in these
application domains is inferring the network structure from
noisy observations at a subset of nodes. Available methods for
topology inference typically assume that the process over the
network is observed at all nodes. However, application-specific
constraints may prevent acquiring network-wide observations.

False discovery rate (FDR) control is highly desirable in several high-dimensional estimation problems. While solving such problems, it is observed that traditional approaches such as the Lasso select a high number of false positives, which increase with higher noise and correlation levels in the dataset. Stability selection is a procedure which uses randomization with the Lasso to reduce the number of false positives.

We consider the problem of localizing point sources on an interval from possibly noisy measurements. In the absence of noise, we show that measurements from Chebyshev sys- tems are an injective map for non-negative sparse measures, and therefore non-negativity is sufficient to ensure unique- ness for sparse measures. Moreover, we characterize non- negative solutions from inexact measurements and show that any non-negative solution consistent with the measurements is proportionally close to the solution of the system with ex- act measurements.

We consider the problem of predicting power outages in an electrical power grid due to hazards produced by convective storms. These storms produce extreme weather phenomena such as intense wind, tornadoes and lightning over a small area. In this paper, we discuss the application of state-of-the-art machine learning techniques, such as random forest classifiers and deep neural networks, to predict the amount of damage caused by storms.