Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces

We model a problem motivated by road design as a feasibility problem. Projections onto the constraint sets are obtained, and projection methods for solving the feasibility problem are studied. We present results of numerical experiments which demonstrate the efficacy of projection methods even for challenging nonconvex problems

Computational statistics using the Bayesian Inference Engine

This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimised software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organise and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasises hybrid tempered MCMC schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE is implements a full persistence or serialisation system that stores the full byte-level image of the running inference and previously characterised posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU GPL.Comment: Resubmitted version. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU GP

Fortschritte im unüberwachten Lernen und Anwendungsbereiche: Subspace Clustering mit Hintergrundwissen, semantisches Passworterraten und erlernte Indexstrukturen

Over the past few years, advances in data science, machine learning and, in particular, unsupervised learning have enabled significant progress in many scientific fields and even in everyday life. Unsupervised learning methods are usually successful whenever they can be tailored to specific applications using appropriate requirements based on domain expertise. This dissertation shows how purely theoretical research can lead to circumstances that favor overly optimistic results, and the advantages of application-oriented research based on specific background knowledge. These observations apply to traditional unsupervised learning problems such as clustering, anomaly detection and dimensionality reduction. Therefore, this thesis presents extensions of these classical problems, such as subspace clustering and principal component analysis, as well as several specific applications with relevant interfaces to machine learning. Examples include password guessing using semantic word embeddings and learning spatial index structures using statistical models. In essence, this thesis shows that application-oriented research has many advantages for current and future research.In den letzten Jahren haben Fortschritte in der Data Science, im maschinellen Lernen und insbesondere im unüberwachten Lernen zu erheblichen Fortentwicklungen in vielen Bereichen der Wissenschaft und des täglichen Lebens geführt. Methoden des unüberwachten Lernens sind in der Regel dann erfolgreich, wenn sie durch geeignete, auf Expertenwissen basierende Anforderungen an spezifische Anwendungen angepasst werden können. Diese Dissertation zeigt, wie rein theoretische Forschung zu Umständen führen kann, die allzu optimistische Ergebnisse begünstigen, und welche Vorteile anwendungsorientierte Forschung hat, die auf spezifischem Hintergrundwissen basiert. Diese Beobachtungen gelten für traditionelle unüberwachte Lernprobleme wie Clustering, Anomalieerkennung und Dimensionalitätsreduktion. Daher werden in diesem Beitrag Erweiterungen dieser klassischen Probleme, wie Subspace Clustering und Hauptkomponentenanalyse, sowie einige spezifische Anwendungen mit relevanten Schnittstellen zum maschinellen Lernen vorgestellt. Beispiele sind das Erraten von Passwörtern mit Hilfe semantischer Worteinbettungen und das Lernen von räumlichen Indexstrukturen mit Hilfe statistischer Modelle. Im Wesentlichen zeigt diese Arbeit, dass anwendungsorientierte Forschung viele Vorteile für die aktuelle und zukünftige Forschung hat

Extracting information from informal communication

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (leaves 89-93).This thesis focuses on the problem of extracting information from informal communication. Textual informal communication, such as e-mail, bulletin boards and blogs, has become a vast information resource. However, such information is poorly organized and difficult for a computer to understand due to lack of editing and structure. Thus, techniques which work well for formal text, such as newspaper articles, may be considered insufficient on informal text. One focus of ours is to attempt to advance the state-of-the-art for sub-problems of the information extraction task. We make contributions to the problems of named entity extraction, co-reference resolution and context tracking. We channel our efforts toward methods which are particularly applicable to informal communication. We also consider a type of information which is somewhat unique to informal communication: preferences and opinions. Individuals often expression their opinions on products and services in such communication. Others' may read these "reviews" to try to predict their own experiences. However, humans do a poor job of aggregating and generalizing large sets of data. We develop techniques that can perform the job of predicting unobserved opinions.(cont.) We address both the single-user case where information about the items is known, and the multi-user case where we can generalize opinions without external information. Experiments on large-scale rating data sets validate our approach.by Jason D.M. Rennie.Ph.D

Building Deep Networks on Grassmann Manifolds

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches.Comment: AAAI'18 pape

An order fitting rule for optimal subspace averaging

The problem of estimating a low-dimensional subspace from a collection of experimentally measured subspaces arises in many applications of statistical signal processing. In this paper we address this problem, and give a solution for the average subspace that minimizes an extrinsic mean-squared error, defined by the squared Frobenius norm between projection matrices. The solution automatically returns the dimension of the optimal average subspace, which is the novel result of the paper. The proposed order fitting rule is based on thresholding the eigenvalues of the average projection matrix, and thus it is free of penalty terms or other tuning parameters commonly used by other rank estimation techniques. Several numerical examples demonstrate the usefulness and applicability of the proposed criterion, showing how the dimension of the average subspace captures the variability of the measured subspaces.The work of I. Santamaría was supported by the Spanish Government through grants PRX14/0028 (Estancias de Movilidad de Profesores, Ministerio de Educación) and by project RACHEL (TEC2013-47141-C4-3-R) funded by the Ministerio de Economía y Competitividad (MINECO). The work of L. L. Scharf was supported by the National Science Foundation (NSF) under grant CCF-1018472