Package org.drip.learning.rxtor1

Interface EmpiricalLearningMetricEstimator

All Known Implementing Classes:
ApproximateLipschitzLossLearner, GeneralizedLearner, L1LossLearner, LipschitzLossLearner, LpLossLearner
public interface EmpiricalLearningMetricEstimator
EmpiricalLearningMetricEstimator is the Estimator of the Empirical Loss and Risk, as well as the corresponding Covering Numbers.

The References are:

  • Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform Convergence, and Learnability Journal of Association of Computational Machinery 44 (4) 615-631
  • Anthony, M., and P. L. Bartlett (1999): Artificial Neural Network Learning - Theoretical Foundations Cambridge University Press Cambridge, UK
  • Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): Towards Efficient Agnostic Learning Machine Learning 17 (2) 115-141
  • Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with Squared Loss IEEE Transactions on Information Theory 44 1974-1980
  • Vapnik, V. N. (1998): Statistical learning Theory Wiley New York


Author:
Lakshmi Krishnamurthy

  • Method Details

    • functionClass

      NormedRxToNormedR1Finite functionClass()
      Retrieve the Underlying Learner Function Class
      Returns:
      The Underlying Learner Function Class

    • regularizerFunction

      RegularizationFunction regularizerFunction()
      Retrieve the Regularizer Function
      Returns:
      The Regularizer Function

    • lossSampleCoveringNumber

      double lossSampleCoveringNumber​(GeneralizedValidatedVector gvvi, double dblEpsilon, boolean bSupremum) throws java.lang.Exception
      Retrieve the Loss Class Sample Covering Number - L-Infinity or L-p based Based
      Parameters:
      gvvi - The Validated Instance Vector Sequence
      dblEpsilon - The Deviation of the Empirical Mean from the Population Mean
      bSupremum - TRUE To Use the Supremum Metric in place of the Built-in Metric
      Returns:
      The Loss Class Sample Covering Number - L-Infinity or L-p based Based
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • empiricalLoss

      double empiricalLoss​(R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Empirical Sample Loss
      Parameters:
      funcLearnerR1ToR1 - The R^1 To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Empirical Loss
      Throws:
      java.lang.Exception - Thrown if the Empirical Loss cannot be computed

    • empiricalLoss

      double empiricalLoss​(RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Empirical Sample Loss
      Parameters:
      funcLearnerRdToR1 - The R^d To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Empirical Loss
      Throws:
      java.lang.Exception - Thrown if the Empirical Loss cannot be computed

    • supremumEmpiricalLoss

      EmpiricalPenaltySupremum supremumEmpiricalLoss​(GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Empirical Sample Loss
      Parameters:
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Empirical Sample Loss
      Throws:
      java.lang.Exception - Thrown if the Supremum Empirical Sample Loss cannot be computed

    • structuralLoss

      double structuralLoss​(R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvvi) throws java.lang.Exception
      Compute the Structural Sample Loss
      Parameters:
      funcLearnerR1ToR1 - The R^1 To R^1 Learner Function
      gvvi - The Validated Predictor Instance
      Returns:
      The Structural Loss
      Throws:
      java.lang.Exception - Thrown if the Structural Loss cannot be computed

    • structuralLoss

      double structuralLoss​(RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvvi) throws java.lang.Exception
      Compute the Structural Sample Loss
      Parameters:
      funcLearnerRdToR1 - The R^d To R^1 Learner Function
      gvvi - The Validated Predictor Instance
      Returns:
      The Structural Loss
      Throws:
      java.lang.Exception - Thrown if the Structural Loss cannot be computed

    • supremumStructuralLoss

      EmpiricalPenaltySupremum supremumStructuralLoss​(GeneralizedValidatedVector gvviX) throws java.lang.Exception
      Compute the Supremum Structural Sample Loss
      Parameters:
      gvviX - The Validated Predictor Instance
      Returns:
      The Supremum Structural Sample Loss
      Throws:
      java.lang.Exception - Thrown if the Supremum Structural Sample Loss cannot be computed

    • regularizedLoss

      double regularizedLoss​(R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Regularized Sample Loss (Empirical + Structural)
      Parameters:
      funcLearnerR1ToR1 - The R^1 To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Regularized Loss
      Throws:
      java.lang.Exception - Thrown if the Regularized Loss cannot be computed

    • regularizedLoss

      double regularizedLoss​(RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Regularized Sample Loss (Empirical + Structural)
      Parameters:
      funcLearnerRdToR1 - The R^d To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Regularized Loss
      Throws:
      java.lang.Exception - Thrown if the Regularized Loss cannot be computed

    • supremumRegularizedLoss

      EmpiricalPenaltySupremum supremumRegularizedLoss​(GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Regularized Sample Loss
      Parameters:
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Regularized Sample Loss
      Throws:
      java.lang.Exception - Thrown if the Supremum Regularized Sample Loss cannot be computed

    • empiricalRisk

      double empiricalRisk​(R1R1 distR1R1, R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Empirical Sample Risk
      Parameters:
      distR1R1 - R^1 R^1 Multivariate Measure
      funcLearnerR1ToR1 - The R^1 To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Empirical Sample Risk
      Throws:
      java.lang.Exception - Thrown if the Empirical Sample Risk cannot be computed

    • empiricalRisk

      double empiricalRisk​(RdR1 distRdR1, RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Empirical Sample Risk
      Parameters:
      distRdR1 - R^d R^1 Multivariate Measure
      funcLearnerRdToR1 - The R^d To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Empirical Sample Risk
      Throws:
      java.lang.Exception - Thrown if the Empirical Sample Risk cannot be computed

    • supremumEmpiricalRisk

      EmpiricalPenaltySupremum supremumEmpiricalRisk​(R1R1 distR1R1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Empirical Sample Risk
      Parameters:
      distR1R1 - R^1 R^1 Multivariate Measure
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Empirical Sample Loss
      Throws:
      java.lang.Exception - Thrown if the Supremum Empirical Sample Loss cannot be computed

    • supremumEmpiricalRisk

      EmpiricalPenaltySupremum supremumEmpiricalRisk​(RdR1 distRdR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Empirical Sample Risk
      Parameters:
      distRdR1 - R^d R^1 Multivariate Measure
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Empirical Sample Loss
      Throws:
      java.lang.Exception - Thrown if the Supremum Empirical Sample Loss cannot be computed

    • structuralRisk

      double structuralRisk​(R1R1 distR1R1, R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Structural Sample Risk
      Parameters:
      distR1R1 - R^1 R^1 Multivariate Measure
      funcLearnerR1ToR1 - The R^1 To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Structural Risk
      Throws:
      java.lang.Exception - Thrown if the Structural Risk cannot be computed

    • structuralRisk

      double structuralRisk​(RdR1 distRdR1, RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Structural Sample Risk
      Parameters:
      distRdR1 - R^d R^1 Multivariate Measure
      funcLearnerRdToR1 - The R^d To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Structural Risk
      Throws:
      java.lang.Exception - Thrown if the Structural Risk cannot be computed

    • supremumStructuralRisk

      EmpiricalPenaltySupremum supremumStructuralRisk​(R1R1 distR1R1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Structural Sample Risk
      Parameters:
      distR1R1 - R^1 R^1 Multivariate Measure
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Structural Sample Loss
      Throws:
      java.lang.Exception - Thrown if the Supremum Structural Sample Risk cannot be computed

    • supremumStructuralRisk

      EmpiricalPenaltySupremum supremumStructuralRisk​(RdR1 distRdR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Structural Sample Risk
      Parameters:
      distRdR1 - R^d R^1 Multivariate Measure
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Structural Sample Risk
      Throws:
      java.lang.Exception - Thrown if the Supremum Structural Sample Risk cannot be computed

    • regularizedRisk

      double regularizedRisk​(R1R1 distR1R1, R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Regularized Sample Risk (Empirical + Structural)
      Parameters:
      distR1R1 - R^1 R^1 Multivariate Measure
      funcLearnerR1ToR1 - The R^1 To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Regularized Sample Risk
      Throws:
      java.lang.Exception - Thrown if the Regularized Sample Risk cannot be computed

    • regularizedRisk

      double regularizedRisk​(RdR1 distRdR1, RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Regularized Sample Risk (Empirical + Structural)
      Parameters:
      distRdR1 - R^d R^1 Multivariate Measure
      funcLearnerRdToR1 - The R^d To R^1 Learner Function
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Regularized Sample Risk
      Throws:
      java.lang.Exception - Thrown if the Regularized Sample Risk cannot be computed

    • supremumRegularizedRisk

      EmpiricalPenaltySupremum supremumRegularizedRisk​(R1R1 distR1R1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Regularized Sample Risk
      Parameters:
      distR1R1 - R^1 R^1 Multivariate Measure
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Regularized Sample Risk
      Throws:
      java.lang.Exception - Thrown if the Supremum Regularized Sample Risk cannot be computed

    • supremumRegularizedRisk

      EmpiricalPenaltySupremum supremumRegularizedRisk​(RdR1 distRdR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) throws java.lang.Exception
      Compute the Supremum Regularized Sample Risk
      Parameters:
      distRdR1 - R^d R^1 Multivariate Measure
      gvviX - The Validated Predictor Instance
      gvviY - The Validated Response Instance
      Returns:
      The Supremum Regularized Sample Risk
      Throws:
      java.lang.Exception - Thrown if the Supremum Regularized Sample Risk cannot be computed