GAUSSIAN PROCESS REGRESSION WITHIN AN ACTIVE LEARNING SCHEME

1. University of Trento Dept. of Information Engineering and Computer Science Italy GAUSSIAN PROCESS REGRESSION WITHINAN ACTIVE LEARNING SCHEME EdoardoPasolli pasolli@disi.unitn.it FaridMelgani melgani@disi.unitn.it IGARSS 2011

2. Introduction • Supervised regression approach Pre-processing Featureextraction Regression Image/ Signal Prediction Training sample collection Human expert Training samplequality/quantity Impact onpredictionerrors

3. Introduction • Active learning approach for classification problems f2 f2 Class 1 Class 3 Class 2 f1 f1 Training (labeled) set Learning (unlabeled) set f2 f2 Training of classifier Active learning method f1 f1 Model of classifier Selected samples from learning (unlabeled) set f2 Insertion in training set Labeling of selected samples Human expert f1 Selected samples after labeling

4. Objective • Propose GP-based active learning strategies for biophysical parameter estimation problems

5. Gaussian Processes (GPs) • Predictive distribution covariance matrix defined by covariance function noise variance

6. Gaussian Processes (GPs) • Example of predicted function : training sample : predicted value : standard deviation of predicted value

7. Proposed Strategies GP Regression U: Learning set L: Training set Insertion in training set Selection Human expert L’s: Labeled samples U’s: Selected unlabeled samples Labeling

8. Proposed Strategies • Minimize covariance measure in feature space (Cov) : squared exponential covariance function : training sample signal variance length-scale : covariance function with respect to training sample

9. Proposed Strategies • Minimize covariance measure in feature space (Cov) : training sample : covariance function with respect to training sample : covariance measure with respect to all training samples : selection of samples with minimum values of

10. Proposed Strategies • Maximize variance of predicted value (Var) : training sample : predicted value : standard deviation of predicted value

11. Proposed Strategies • Maximize variance of predicted value (Var) : training sample : variance : selection of samples with maximum values of

12. Experimental Results • Data set description (MERIS) • Simulated acquisitions • Objective: estimation of chlorophyll concentration in subsurface case I + case II (open and coastal) waters • Sensor: MEdium Resolution Imaging Spectrometer (MERIS) • # channels: 8 (412-618 nm) • Range of chlorophyll concentration: 0.02-54 mg/m3

13. Experimental Results • Data set description (SeaBAM) • Real aquisitions • Objective: estimation of chlorophyll concentration mostly in subsurface case I (open) waters • Sensor: Sea-viewing Wide Field-of-view (SeaWiFS) • # channels: 5 (412-555 nm) • Range of chlorophyll concentration: 0.02-32.79 mg/m3

14. Experimental Results • Mean Squared Error MERIS SeaBAM

15. Experimental Results • Standard Deviation of Mean Squared Error MERIS SeaBAM

16. Experimental Results • Detailed results MERIS Accuracies on 4000 test samples

17. Experimental Results • Detailed results MERIS Accuracies on 4000 test samples

18. Experimental Results • Detailed results SeaBAM Accuracies on 459 test samples

19. Experimental Results • Detailed results SeaBAM Accuracies on 459 test samples

20. Conclusions • In this work, GP-based active learning strategies for regression problems are proposed • Encouraging performances in terms of • convergence speed • stability • Future developments • extension to other regression approaches

21. University of Trento Dept. of Information Engineering and Computer Science Italy GAUSSIAN PROCESS REGRESSION WITHINAN ACTIVE LEARNING SCHEME EdoardoPasolli pasolli@disi.unitn.it FaridMelgani melgani@disi.unitn.it IGARSS 2011