Dept of Computer Science, Michigan State University b

Transcription

1 CONTOUR REGRESSION: A distribution-regularized regression framework for climate modeling Zubin Abraham a, Pang-Ning Tan a, Julie A. Winkler b, Perdinan b, Shiyuan Zhong b, Malgorzata Liszewska c a Dept of Computer Science, Michigan State University b Dept of Geography, Michigan State University c Centre for Math and Comp Modeling, Univ of Warsaw

2 Introduction : Climate Modeling 2 Climate Change Modeling There are growing concerns about climate change and how it could impact natural resources and various sectors of economy and society Agriculture, Health, Hydrology, Population migration and conflict, etc. Climate change impact assessment studies require long-term projections of future climate scenarios. [1] [1] Julie W inkler et. al. Climate Scenario Development and Applications for Local/Regional Climate Change Impact Assessments: An Overview for the Non-Climate Scientist: Part I: Scenario Development Using Dow nscaling Methods Climate scenario development and applications I- In proceeding of Geography Compass 11

3 Introduction : Climate Modeling 3 Long Term Projection of Future Climate Warm bias Cold bias Histogram of daily maximum temperature at a weather station in Michigan

4 Introduction : Multiple Linear Regression 4 Example: Multiple Linear Regression Regression-based methods that minimize prediction error tend to have large distribution bias The cumulative distribution function (CDF) of observation variable

5 Introduction : Quantile Mapping 5 Example: Quantile Mapping (QM) Quantile mapping is a bias correction method. Eq. (1) Where, x is the RCM/GCM output and y the observed response variable. CDF of x and y Bias correction methods minimize bias but have large prediction error

6 Introduction : Climate Modeling 6 Comparison between QM and MLR Fig. Histogram of daily maximum temperature at a weather station in Michigan

7 [3] Zubin Abraham et al. Distribution regularized regression framework for climate modeling SDM 13 [4] Zubin Abraham et al. Contour regression: A distribution-regularized regression framework for climate modeling In proceeding of Statistical Analysis and Data Mining 14 Contour Regression 7 Contributions Present framework (Contour Regression) that maximizes prediction accuracy while minimizing bias in the distribution. [3,4] We also present a linear, a non-linear and a quantile regression based variations of contour regression The framework can incorporate predictor variables from heterogeneous data sources (semi-supervised) [4]

8 Contour Regression: Introduction 8 Contour Regression (CR) General framework for contour regression Minimize residual errors Minimize errors in CDF (2) Where, Regression line y x

9 Contour Regression: MLCR 9 Multiple Linear Contour Regression (MLCR) Eq. (5) Where, Eq. (6)

10 Contour Regression: Non-Linear Setting 10 Kernel Contour Regression (KCR) Ridge regression applied to CR. Kernel Contour regression (KCR). Eq. (7) Eq. (8) Where, Eq. (9)

11 Contour Regression: Conditional Quantiles 11 Quantile Regression (QR) W 1 =7.0, W 0 =-0.4 Regression line (Y) (X) Zubin Abraham et al. Extreme Value Prediction for Zero Inflated DataL-PAKDD 12

12 Contour Regression: Conditional Quantiles 12 Quantile Regression (QR) (10) Where, u = Residual (Observation-prediction)

13 Contour Regression: Conditional Quantiles 13 Quantile Contour Regression (QCR) Contour regression that uses a QR based loss function take the following form (11) Where The preceding optimization problem can be converted to the following form (12) Linear programming is used to solve the above loss function.

14 Zubin Abraham et al. Position Preserving Multi-Output Prediction ECML-PKDD 13 J. I. Marden. Positions and qq plots. Statistical Science 04 Contour Regression: Multi-Source Data 14 Contour Regression for Multi-Source Data Predictor variables: Response variable: Geometric Quantile Mapping: Geometric quantile is the multi-dimensional equivalent of a univariate quantile mapping function. Eq. (13) Eq. (14)

15 EXPERIMENTAL EVALUATION

16 Contour Regression ( CR) : Experimental Evaluation 16 Experimental Setup Predicting surface precipitation, maximum temperature and min temperature at a location using the following predictor variables obtained from regional climate models: Julie Winkler et. al. - Climate Scenario Development using Hybrid Downscaling: An Application to NARCCAP and ENSEMBLES simulations- In proceeding of AAG 12*

17 Data : RCM 17 Data Sources Predictor variables are obtained from NCEP-driven regional climate models. WRFG CRCM RCM3 Observation data obtained from 14 climate stations in Michigan. Daily data from Training: Testing:

18 Experimental Evaluation: Introduction 18 Experimental Evaluation Performance of CR when using least square loss function. Comparing residual error and distribution bias of MLR, QM, and MLCR Performance of CR when using QR based loss function. QCR versus QR Performance of CR when using predictor variables from multiple data sources. MLCR (in a semi-supervised setting)

19 Multiple Linear Contour Regression ( MLCR) : Experimental Results 19 MLCR Results (Accuracy) A bar plot of maximum temperature RMSE of the 14 station belonging to the WRFG dataset

20 Multiple Linear Contour Regression ( MLCR) : Experimental Results 20 MLCR Results (Distribution Bias) The CDF plots of maximum temperature and precipitation of a station belonging to WRFG dataset

21 Multiple Linear Contour Regression ( MLCR) : Experimental Results 21 Summary for MLCR Results Relative performance gain of MLCR over baseline approaches.. MLCR had lower distribution bias in 14/14 stations for each dataset

22 Multiple Linear Contour Regression ( MLCR) : Experimental Results 22 Summary for MLCR Results Relative performance gain of MLCR over baseline approaches..

23 Quantile Contour Regression ( QCR) : Experimental Results 23 Summary of QCR Results The CDF plots of minimum temperature and precipitation of a station belonging to WRFG dataset QCR had lower distribution bias than QR in 14/14 stations for each dataset

24 Quantile Contour Regression ( QCR) : Experimental Results 24 Summary of QCR Results Percentage of stations that QCR outperformed QR QCR had better accuracy than QR in 14/14 stations for each dataset

25 Multiple Linear Contour Regression ( MLCR) : Experimental Results 25 MLCR Results (Heterogeneous Data) The CDF plots of maximum temperature and precipitation of a station belonging to WRFG dataset

26 Contour Regression ( CR) : References 26 Summary We presented a framework for contour regression, that maximizes prediction accuracy while minimizing bias in the distribution. We show that the framework can be adapted to modeling non linear relationships and conditional quantiles. We empirically showed that the framework outperformed or was at least on par with baseline approaches on real world climate data. The framework can incorporate predictor variables from heterogeneous data sources

27 Contour Regression ( CR) : Summary 27 References [1] Julie Winkler et. al. Climate Scenario Development and Applications for Local/Regional Climate Change Impact Assessments: An Overview for the Non-Climate Scientist: Part I: Scenario Development Using Downscaling Methods Climate scenario development and applications I- In proceeding of Geography Compass 11 [2] Themeßl, Jakob, M., Gobiet, A. and Leuprecht, A. (2011), Empirical-statistical downscaling and error correction of daily precipitation from regional climate models. International Journal of Climatology, 31: [3] Zubin Abraham et al. Distribution regularized regression framework for climate modeling SDM 13 [4] Zubin Abraham et al. Contour regression: A distribution-regularized regression framework for climate modeling In proceeding of Statistical Analysis and Data Mining 14 [5] Zubin Abraham et al. Position Preserving Multi-Output Prediction ECML-PKDD 13 [6] Zubin Abraham et al. Extreme Value Prediction for Zero Inflated DataL-PAKDD 12 [7] Zubin Abraham et al. An Integrated Framework for Simultaneous Classification and Regression of Time-Series data. SDM 10 [8] Julie Winkler et. al. - Climate Scenario Development using Hybrid Downscaling: An Application to NARCCAP and ENSEMBLES simulations- In proceeding of AAG 12* [9] J. I. Marden. Positions and qq plots. Statistical Science 04 [10] X. He, Y. Yang, and J. Zhang. Bivariate downscaling with asynchronous measurements. Journal of agricultural, biological, and environmental statistics 12.

28 THANK YOU! This work is partially supported by NSF grant III and subcontract for NASA award NNX09AL60G. This work is also partly supported by National Science Foundation Dynamics of Coupled Natural and Human Systems competition Program (CNH Award No ).