Tensor-on-tensor regression

We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L_2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression .Comment: 33 pages, 3 figure

Data-Driven Framework for Understanding & Modeling Ride-Sourcing Transportation Systems

Ride-sourcing transportation services offered by transportation network companies (TNCs) like Uber and Lyft are disrupting the transportation landscape. The growing demand on these services, along with their potential short and long-term impacts on the environment, society, and infrastructure emphasize the need to further understand the ride-sourcing system. There were no sufficient data to fully understand the system and integrate it within regional multimodal transportation frameworks. This can be attributed to commercial and competition reasons, given the technology-enabled and innovative nature of the system. Recently, in 2019, the City of Chicago the released an extensive and complete ride-sourcing trip-level data for all trips made within the city since November 1, 2018. The data comprises the trip ends (pick-up and drop-off locations), trip timestamps, trip length and duration, fare including tipping amounts, and whether the trip was authorized to be shared (pooled) with another passenger or not. Therefore, the main goal of this dissertation is to develop a comprehensive data-driven framework to understand and model the system using this data from Chicago, in a reproducible and transferable fashion. Using data fusion approach, sociodemographic, economic, parking supply, transit availability and accessibility, built environment and crime data are collected from open sources to develop this framework. The framework is predicated on three pillars of analytics: (1) explorative and descriptive analytics, (2) diagnostic analytics, and (3) predictive analytics. The dissertation research framework also provides a guide on the key spatial and behavioral explanatory variables shaping the utility of the mode, driving the demand, and governing the interdependencies between the demand’s willingness to share and surge price. Thus, the key findings can be readily challenged, verified, and utilized in different geographies. In the explorative and descriptive analytics, the ride-sourcing system’s spatial and temporal dimensions of the system are analyzed to achieve two objectives: (1) explore, reveal, and assess the significance of spatial effects, i.e., spatial dependence and heterogeneity, in the system behavior, and (2) develop a behavioral market segmentation and trend mining of the willingness to share. This is linked to the diagnostic analytics layer, as the revealed spatial effects motivates the adoption of spatial econometric models to analytically identify the ride-sourcing system determinants. Multiple linear regression (MLR) is used as a benchmark model against spatial error model (SEM), spatially lagged X (SLX) model, and geographically weighted regression (GWR) model. Two innovative modeling constructs are introduced deal with the ride-sourcing system’s spatial effects and multicollinearity: (1) Calibrated Spatially Lagged X Ridge Model (CSLXR) and Calibrated Geographically Weighted Ridge Regression (CGWRR) in the diagnostic analytics layer. The identified determinants in the diagnostic analytics layer are then fed into the predictive analytics one to develop an interpretable machine learning (ML) modeling framework. The system’s annual average weekday origin-destination (AAWD OD) flow is modeled using the following state-of-the-art ML models: (1) Multilayer Perceptron (MLP) Regression, (2) Support Vector Machines Regression (SVR), and (3) Tree-based ensemble learning methods, i.e., Random Forest Regression (RFR) and Extreme Gradient Boosting (XGBoost). The innovative modeling construct of CGWRR developed in the diagnostic analytics is then validated in a predictive context and is found to outperform the state-of-the-art ML models in terms of testing score of 0.914, in comparison to 0.906 for XGBoost, 0.84 for RFR, 0.89 for SVR, and 0.86 for MLP. The CGWRR exhibits outperformance as well in terms of the root mean squared error (RMSE) and mean average error (MAE). The findings of this dissertation partially bridge the gap between the practice and the research on ride-sourcing transportation systems understanding and integration. The empirical findings made in the descriptive and explorative analytics can be further utilized by regional agencies to fill practice and policymaking gaps on regulating ride-sourcing services using corridor or cordon toll, optimally allocating standing areas to minimize deadheading, especially during off-peak periods, and promoting the ride-share willingness in disadvantage communities. The CGWRR provides a reliable modeling and simulation tool to researchers and practitioners to integrate the ride-sourcing system in multimodal transportation modeling frameworks, simulation testbed for testing long-range impacts of policies on ride-sourcing, like improved transit supply, congestions pricing, or increased parking rates, and to plan ahead for similar futuristic transportation modes, like the shared autonomous vehicles

Machine learning in international trade research - evaluating the impact of trade agreements

Modern trade agreements contain a large number of provisions in addition to tariff reductions, in areas as diverse as services trade, competition policy, trade-related investment measures, or public procurement. Existing research has struggled with overfitting and severe multicollinearity problems when trying to estimate the effects of these provisions on trade flows. Building on recent developments in the machine learning and variable selection literature, this paper proposes data-driven methods for selecting the most important provisions and quantifying their impact on trade flows, without the need of making ad hoc assumptions on how to aggregate individual provisions. The analysis finds that provisions related to antidumping, competition policy, technical barriers to trade, and trade facilitation are associated with enhancing the trade-increasing effect of trade agreements

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Otimização eficiente global dirigida por metamodelos combinados : novos caminhos abertos pela aproximação por mínimos quadrados

Orientador: Alberto Luiz SerpaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O presente trabalho representa a compilação dos resultados anteriores dessa pesquisa no campo de metamodelos combinados e otimização eficiente global (EGO), os quais foram sumetidos para publicação em periódicos especializados. Recentemente foi implementado nesse trabalho de doutorado o algoritmo LSEGO que é uma abordagem para conduzir algoritmos tipo EGO, baseando-se em metamodelos combinados através da aproximação por mínimos quadrados (metamodelos combinados LS). Através dos metamodelos combinados LS é possível estimar a incerteza da aproximação usando qualquer tipo de metamodelagem (e não somente do tipo kriging), permitindo estimar a função de expectativa de melhora para a função objetivo. Nos experimentos computacionais anteriores em problemas de otimização sem restrições, a abordagem LSEGO mostrou-se como uma alternativa viável para conduzir otimização eficiente global usando metamodelos combinados, sem se restringir a somente um ponto adicional por ciclo de otimização iterativa. Na presente tese o algoritmo LSEGO foi extendido de modo a tratar também problemas de otimização com restrições. Os resultados de testes numéricos com problemas analíticos e de referência e também em um estudo de caso de engenharia em escala industrial mostraram-se bastante promissores e competitivos em relação aos trabalhos similares encontrados na literaturaAbstract: In this work we review and compile the results of our previous research in the fields of ensemble of metamodels and efficient global optimization (EGO). Recently we implemented LSEGO that is an approach to drive EGO algorithms, based on LS (least squares) ensemble of metamodels. By means of LS ensemble of metamodels, it is possible to estimate the uncertainty of the prediction by using any kind of model (not only kriging) and provide an estimate for the expected improvement function. In previous numerical experiments with unconstrained optimization problems, LSEGO approach has shown to be a feasible alternative to drive efficient global optimization by using multiple or ensemble of metamodels, not restricted to kriging approximation or single infill point per optimization cycles. In the present work we extended the previous LSEGO algorithm to handle constrained optimization problems as well. Some numerical experiments were performed with analytical benchmark functions and also for industry scale engineering problems with competitive resultsDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânic

Variable selection in varying coefficient models for mapping quantitative trait loci

The Collaborative Cross (CC), a renewable mouse resource that mimics the genetic diversity in humans, provides great data sources for mapping Quantitative Trait Loci (QTL). The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines have several attractive features and can be produced repeatedly. Many quantitative traits are inherently complex and change with other covariates. To map such complex traits, phenotypes are measured across multiple values of covariates on each subject. In the first topic, we propose a more flexible nonparametric varying coefficient QTL mapping method for RIX data. This model lets the QTL effects evolve with certain covariates, and naturally extends classical parametric QTL mapping methods. Simulation results indicate that the varying coefficient QTL mapping has substantially higher power and higher mapping precision compared to parametric models when the assumption of constant genetic effects fails. We model the time-varying genetic effects with functional approximation using B-spline basis. We apply a nested permutation method to obtain threshold values for QTL detection. In the second topic, we extend the single marker QTL mapping to multiple QTL mapping. We treat multiple QTL mapping as a model/variable selection problem and propose a penalized mixed effects model. We apply a penalty function for the group selection of coefficients associated with each gene. We propose new selection procedures for tuning parameters. Simulations showed that the new mapping method performs better than the single marker analysis when multiple QTL exist. Last, in the third topic, we extend the multiple QTL mapping method to longitudinal data. We pay special attention to modeling the covariance structure of repeated measurements. Popular stationary assumptions on variance and covariance structures may not be realistic for many longitudinal traits. The structured antedependence (SAD) model is a parsimonious covariance model that allows for both nonstationary variance and correlation. We propose a penalized likelihood method for multiple QTL mapping using the SAD model. Simulation results showed the model selection method outperforms the single marker analysis. Furthermore, the performance of multiple QTL mapping will be affected if the covariance model is misspecified

Multi-city time series analyses of air pollution and mortality data using generalized geoadditive mixed models

Background Here we introduce the generalized geoadditive mixed model (GGAMM), a combination of generalized additive model and linear mixed model with unified model structure for more flexible applications, to alternatively examine the influence of air pollution to human health. Methods Extant air pollution and mortality data came from the National Morbidity, Mortality, and Air Pollution Study for 15 U.S. cities in 1991-1995. The PM10 main model, distributed lag model and four co-pollutant models used the GGAMM approach to analyze the effect of PM10, lag effects and co-pollutants on several mortalities, adjusting for day-of-week, calendar time and temperature. Objectives First, the effects of PM10 on mortality are preliminarily examined; second, a jackknife-bootstrap method and a principal component analysis are proposed to handle potential convergence problems; third, some missing data imputation methods are evaluated in the GGAMM; fourth, the issues of multicollinearity and concurvity in our models are examined; fifth, comparisons of the GGAMM and 2-stage Bayesian hierarchical model are performed; sixth, three simulations are accomplished for investigating the influence of concurvity, multicollinearity and missing data imputation methods on estimates and smoothing functions. Results First, the effects of PM10 on mortality are preliminarily examined; second, a jackknife-bootstrap method and a principal component analysis are proposed to handle potential convergence problems; third, some missing data imputation methods are evaluated in the GGAMM; fourth, the issues of multicollinearity and concurvity in our models are examined; fifth, comparisons of the GGAMM and 2-stage Bayesian hierarchical model are performed; sixth, three simulations are accomplished for investigating the influence of concurvity, multicollinearity and missing data imputation methods on estimates and smoothing functions. Conclusions The GGAMM provides an integrate model structure to concern national average estimates, city-specific estimates, smoothing and spatial functions simultaneously. Geographical data can immediately be used in the GGAMM without being affected by missing data, and nation-level smoothing functions can be fitted well by enough valid observations from all cities. These properties are not offered by 2-stage Bayesian hierarchical models, and recommended by using spatio-temporal data