Efficient learning of neighbor representations for boundary trees and forests

We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large datasets. While boundary trees use an Euclidean measure of similarity, the Differentiable Boundary Tree algorithm by Zoran et al.(2017) was introduced to learn low-dimensional representations of complex input data, on which semantic similarity can be calculated to train boundary trees. As is pointed out by its authors, the differentiable boundary tree approach contains a few limitations that prevents it from scaling to large datasets. In this paper, we introduce Differentiable Boundary Sets, an algorithm that overcomes the computational issues of the differentiable boundary tree scheme and also improves its classification accuracy and data representability. Our algorithm is efficiently implementable with existing tools and offers a significant reduction in training time. We test and compare the algorithms on the well known MNIST handwritten digits dataset and the newer Fashion-MNIST dataset by Xiao et al.(2017).Comment: 9 pages, 2 figure

Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial datasets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article is submitted to the Practice section of the journal with the aim of developing massively scalable Bayesian approaches that can rapidly deliver Bayesian inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (e.g., a standard desktop or laptop) using easily available statistical software packages without requiring message-parsing interfaces or parallel programming paradigms. Key insights are offered regarding assumptions and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table

Applied Sensor Fault Detection, Identification and Data Reconstruction

Sensor fault detection and identification (SFD/I) has attracted considerable attention in military applications, especially when safety- or mission-critical issues are of paramount importance. Here, two readily implementable approaches for SFD/I are proposed through hierarchical clustering and self-organizing map neural networks. The proposed methodologies are capable of detecting sensor faults from a large group of sensors measuring different physical quantities and achieve SFD/I in a single stage. Furthermore, it is possible to reconstruct the measurements expected from the faulted sensor and thereby facilitate improved unit availability. The efficacy of the proposed approaches is demonstrated through the use of measurements from experimental trials on a gas turbine. Ultimately, the underlying principles are readily transferable to other complex industrial and military systems

A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization

We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility, possibly degenerate. Our backward scheme, based on least-squares regressions, takes advantage of high-dimensional properties of Monte-Carlo methods, and also provides a parametric estimate in feedback form for the optimal control. A partial analysis of the error of the scheme is provided, as well as numerical tests on the problem of superreplication of option with uncertain volatilities and/or correlations, including a detailed comparison with the numerical results from the alternative scheme proposed in [7]