Enhancing Predictive Modeling of Nested Spatial Data through Group-Level Feature Disaggregation

Multilevel modeling and multi-task learning are two widely used approaches for modeling nested (multi-level) data, which contain observations that can be clustered into groups, characterized by their group-level features. Despite the similarity of the problems they address, the explicit relationship between multilevel modeling and multi-task learning has not been carefully examined. In this paper, we present a comparative analysis between the two methods to illustrate their strengths and limitations when applied to two-level nested data. We provide a detailed analysis demonstrating the equivalence of their formulations under a mild condition from an optimization perspective. We also demonstrate their limitations in terms of their predictive performance and especially, their difficulty in identifying potential cross-scale interactions between the local and group-level features when applied to datasets with either a small number of groups or limited training examples per group. To overcome these limitations, we propose a novel method for disaggregating the coarse-scale values of the group-level features in the nested data. Experimental results on both synthetic and real-world data show that the disaggregated group-level features can help enhance the prediction accuracy of the models significantly and identify the cross-scale interactions more effectively.

[1]  P. Soranno,et al.  Cross‐scale interactions: quantifying multi‐scaled cause–effect relationships in macrosystems , 2014 .

[2]  Herman Aguinis,et al.  Best-Practice Recommendations for Estimating Cross-Level Interaction Effects Using Multilevel Modeling , 2013 .

[3]  Brandon K. Vaughn,et al.  Data analysis using regression and multilevel/hierarchical models, by Gelman, A., & Hill, J. , 2008 .

[4]  Jieping Ye,et al.  Multi-Task Feature Learning Via Efficient l2, 1-Norm Minimization , 2009, UAI.

[5]  Jiayu Zhou,et al.  Clustered Multi-Task Learning Via Alternating Structure Optimization , 2011, NIPS.

[6]  Jiayu Zhou,et al.  Multi-level Multi-task Learning for Modeling Cross-Scale Interactions in Nested Geospatial Data , 2017, 2017 IEEE International Conference on Data Mining (ICDM).

[7]  Massimiliano Pontil,et al.  Multi-Task Feature Learning , 2006, NIPS.

[8]  Donald Eugene. Farrar,et al.  Multicollinearity in Regression Analysis; the Problem Revisited , 2011 .

[9]  Christopher Higgins,et al.  Cross-Scale Responses of Biodiversity to Hurricane and Anthropogenic Disturbance in a Tropical Forest , 2007, Ecosystems.

[10]  Pang-Ning Tan,et al.  Building a multi-scaled geospatial temporal ecology database from disparate data sources: fostering open science and data reuse , 2015, GigaScience.

[11]  K. Knuth,et al.  What Is a Question , 2004, physics/0403089.

[12]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[13]  Kendra Spence Cheruvelil,et al.  Multiscale landscape and wetland drivers of lake total phosphorus and water color , 2011 .

[14]  N. Laird,et al.  Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. , 1997, Statistics in medicine.

[15]  Jiayu Zhou,et al.  Multi-Task Feature Interaction Learning , 2016, KDD.

[16]  Jiayu Zhou,et al.  A multi-task learning formulation for predicting disease progression , 2011, KDD.

[17]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[18]  Aurelie C. Lozano,et al.  Multi-level Lasso for Sparse Multi-task Regression , 2012, ICML.

[19]  R. Darrell Bock,et al.  Multilevel analysis of educational data , 1989 .

[20]  Jiayu Zhou,et al.  Integrating low-rank and group-sparse structures for robust multi-task learning , 2011, KDD.

[21]  W. Tobler.  A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[22]  Y. Nesterov.  Gradient methods for minimizing composite objective function , 2007 .

[23]  J. Hox,et al.  Sufficient Sample Sizes for Multilevel Modeling , 2005 .

[24]  J. Mathieu,et al.  Understanding and estimating the power to detect cross-level interaction effects in multilevel modeling. , 2012, The Journal of applied psychology.

[25]  G. A. Marcoulides.  Multilevel Analysis Techniques and Applications , 2002 .

[26]  Roger D. Peng,et al.  What is the question? , 2015, Science.

[27]  M. Kenward,et al.  Small sample inference for fixed effects from restricted maximum likelihood. , 1997, Biometrics.

[28]  P. Tseng.  Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization , 2001 .

[29]  Songlin Fei,et al.  Cross-scale contradictions in ecological relationships , 2015, Landscape Ecology.

[30]  Feiping Nie,et al.  Efficient and Robust Feature Selection via Joint ℓ2, 1-Norms Minimization , 2010, NIPS.

[31]  Mirjam Moerbeek,et al.  Multilevel Analysis : Techniques and Applications, Third Edition , 2017 .

[32]  Craig A. Stow,et al.  The statistical power to detect cross-scale interactions at macroscales , 2016 .

[33]  Brandon T Bestelmeyer,et al.  Cross-scale interactions, nonlinearities, and forecasting catastrophic events. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Jiayu Zhou,et al.  GSpartan: a Geospatio-Temporal Multi-task Learning Framework for Multi-location Prediction , 2016, SDM.

[35]  Rich Caruana,et al.  Multitask Learning , 1998, Encyclopedia of Machine Learning and Data Mining.