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Beyond trees: classification with sparse pairwise dependencies

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2020年第1期21卷 7728-7760页

作者： Yaniv Tenzer Amit Moscovich Mary Frances Dorn Boaz Nadler Clifford Spiegelman Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ Los Alamos National Laboratory Los Alamos NM Department of Statistics Texas A&M University College Station TX

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attaining low classification errors. In this setting, the optimal classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criterion, and finally construct a linear SVM using the retained log-transformed densities. We demonstrate on synthetic and real data sets, that our classifier, named SLB (sparse log-bivariate density), is competitive with other popular classification methods.

关键词： binary classification graphical model Bayesian network sparsity semi-parametric

On the cross-validation bias due to unsupervised preprocessing

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arXiv 2019年

作者： Moscovich, Amit Rosset, Saharon Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistics and Operations Research Tel-Aviv University Tel-Aviv Israel

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centering, rescaling, dimensionality reduction, and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or response values) are generally safe to do prior to cross-validation. In this paper, we study three commonly-practiced preprocessing procedures prior to a regression analysis: (i) variance-based feature selection;(ii) grouping of rare categorical features;and (iii) feature rescaling. We demonstrate that unsupervised preprocessing can, in fact, introduce a substantial bias into cross-validation estimates and potentially hurt model selection. This bias may be either positive or negative and its exact magnitude depends on all the parameters of the problem in an intricate manner. Further research is needed to understand the real-world impact of this bias across different application domains, particularly when dealing with small sample sizes and high-dimensional *** Codes 62-07 Copyright © 2019, The Authors. All rights reserved.

关键词： Regression analysis

Some results in optimal hierarchical estimation

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Some results in optimal hierarchical estimation

IEEE Conference on Decision and Control

作者： S. Roy P. Bhimasankaram R. A. Iltis Department of Electrical and Computer Engineering University of California Santa Barbara CA USA Statistics and Applied probability program University of California Santa Barbara CA USA

The primary objective of this paper is to review several results available in the statistical literature pertaining to the problem of hierarchical estimation. Some relevant extensions are derived for the problem of reconstructing the globally optimal estimate based on local estimates transmitted by feeder nodes. Their utilisty is next demonstrated with characterizations and examples pertaining to common scenarios in decentralized estimation problems.

关键词： Sensor systems Noise measurement Optimal control Sensor phenomena and characterization Signal processing Costs Fault tolerant systems Sensor fusion Particle measurements statistics

Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

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arXiv 2024年

作者： Wang, Kesen Kim, Minwoo Castruccio, Stefano Genton, Marc G. Statistics Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics Pusan National University Busan46241 Korea Republic of Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modeling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behavior is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model. © 2024, CC BY.

关键词： Clean energy

Towards a legal compliance verification approach on the procurement process of IT solutions for the Brazilian Federal Public Administration

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Towards a legal compliance verification approach on the proc...

Requirements Engineering and Law, RELAW

作者： Lamartine da Silva Barboza Gilberto A. de A. Cysneiros Filho Ricardo A. C. de Souza Master's Program in Applied Informatics Federal Rural University of Pemambuco Recife Brazil Department of Statistics and Informatics Federal Rural University of Pernambuco Recife Brazil

The Brazilian federal government regulates the process for procurement of Information Technology (IT) solutions through specific legislation named Regulatory Instruction - RI N° 04/2010. This process consists of three phases: procurement planning, supplier selection and contract management. This work helps (i) specify and validate an approach for traceability between legal requirements and documents created in the procurement process of IT solutions; (ii) reduce manual work for the verification of legal compliance in the set of artifacts produced; and (iii) support activities of auditing and inspection during and after the procurement of IT solutions by the Brazilian federal government.

关键词： Procurement Law Educational institutions Government Visualization

Regularized matrix data clustering and its application to image analysis

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arXiv 2018年

作者： Gao, Xu Shen, Weining Ombao, Hernando Department of Statistics University of California IrvineCA United States Program on Applied Mathematics & Computational Science King Abdullah University of Science and Technology Saudi Arabia

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing regularization terms into the likelihood function. Through a modified EM algorithm, our method achieves the optimal solution with low computational cost. Theoretical results are also provided to establish the consistency of the proposed estimators. Simulations show the advantages of the proposed method over other existing methods. We also apply the approach to two real datasets from different experiments. Promising results imply that the proposed method successfully characterizes signals with different patterns while yielding insightful scientific interpretation. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

Machine-learning-based non-Newtonian fluid model with molecular fidelity

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Physical Review E 2020年第4期102卷 043309-043309页

作者： Huan Lei Lei Wu Weinan E Department of Computational Mathematics Science & Engineering and Department of Statistics & Probability Michigan State University East Lansing Michigan 48824 USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN2 where models based on empirical closures show limitations.

关键词： Learning Neuronal networks Complex fluids Non-Newtonian fluids Rheology Viscoelasticity Multiscale modeling

Assessing alternatives for meeting water demand: A case study of water resource management in the Brazilian Semiarid region

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Assessing alternatives for meeting water demand: A case stud...

作者： de Andrade Santana, Rosinele Marques Bezerra, Saulo de Tarso Melo dos Santos, Sylvana Paiva Coutinho, Artur Lopes Coelho, Isabela Carolina Silva Pessoa, Ruben Vivaldi Postgraduation Program in Civil and Environmental Engineering Universidade Federal de Pernambuco CaruaruPE Brazil Department of Technology Universidade Federal de Pernambuco Avenida Campina Grande S/N CaruaruPE55014-900 Brazil Department of Civil and Environmental Engineering Universidade Federal de Pernambuco RecifePE Brazil Postgraduation Program in Biometry and Applied Statistics Universidade Federal Rural de Pernambuco RecifePE Brazil

Population growth, climate change, and the occurrence of droughts have intensified the water supply crises in the Brazilian Semiarid region. The objective of this study was to identify the most relevant measures for the improvement of the water supply of Caruaru, Brazil. The research involved five steps: the selection of experts, comprehension of variables, application of Delphi research, statistical analyses, and consolidation of results. Projects to expand the system and reduce real losses are the most recommended measures. It is also important to implement an integrated water resources management approach that embraces alternative technological and governance strategies. © 2019 Elsevier Ltd

关键词： Water supply

Assessing the reliability of wind power operations under a changing climate with a non-Gaussian bias correction

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arXiv 2020年

作者： Zhang, Jiachen Crippa, Paola Genton, Marc G. Castruccio, Stefano Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Civid and Environmental Engineering and Geoscience University of Notre Dame United States Statistics Program King Abdullah University of Science and Technology Saudi Arabia

Facing increasing societal and economic pressure, many countries have established strategies to develop renewable energy portfolios, whose penetration in the market can alleviate the dependence on fossil fuels. In the case of wind, there is a fundamental question related to the resilience, and hence profitability, of future wind farms to a changing climate, given that current wind turbines have lifespans of up to thirty years. In this work we develop a new non-Gaussian method to adjust assimilated observational data to simulations and to estimate future wind, predicated on a trans-Gaussian transformation and a cluster-wise minimization of the Kullback-Leibler divergence. Future winds abundance will be determined for Saudi Arabia, a country with a recently established plan to develop a portfolio of up to 16 GW of wind energy. Further, we estimate the change in profits over future decades using additional high-resolution simulations, an improved method for vertical wind extrapolation and power curves from a collection of popular wind turbines. We find an overall increase in daily profit of $272,000 for the wind energy market for the optimal locations for wind farming in the country. Copyright © 2020, The Authors. All rights reserved.

关键词： Wind power