Package org.drip.learning.bound
Class DiagonalOperatorCoveringBound
java.lang.Object
org.drip.learning.bound.DiagonalOperatorCoveringBound
public class DiagonalOperatorCoveringBound
extends java.lang.Object
DiagonalOperatorCoveringBound implements the Behavior of the Bound on the Covering Number of the
Diagonal Scaling Operator. The Asymptote is set as either
log [e_n(A)] ~ O {(1/log n)^alpha}
- OR -
e_n(A) ~ O {(1/log n)^alpha}
The References are:
log [e_n(A)] ~ O {(1/log n)^alpha}
- OR -
e_n(A) ~ O {(1/log n)^alpha}
The References are:
- Ash, R. (1965): Information Theory Inter-science New York
- Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators Cambridge University Press Cambridge UK
- Gordon, Y., H. Konig, and C. Schutt (1987): Geometric and Probabilistic Estimates of Entropy and Approximation Numbers of Operators Journal of Approximation Theory 49 219-237
- Konig, H. (1986): Eigenvalue Distribution of Compact Operators Birkhauser Basel, Switzerland
- Smola, A. J., A. Elisseff, B. Scholkopf, and R. C. Williamson (2000): Entropy Numbers for Convex Combinations and mlps, in: Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B. Scholkopf, and D. Schuurmans - editors MIT Press Cambridge, MA
- Williamson, R. C., A. J. Smola, and B. Scholkopf (2001): Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators IEEE Transactions on Information Theory 47 (6) 2516-2532
- Module = Computational Core Module
- Library = Statistical Learning
- Project = Agnostic Learning Bounds under Empirical Loss Minimization Schemes
- Package = Covering Numbers, Concentration, Lipschitz Bounds
- Author:
- Lakshmi Krishnamurthy
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Field Summary
Fields Modifier and Type Field Description static int
BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
Asymptote on the Base Diagonal Operator Entropy Numberstatic int
LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
Asymptote on the Log of the Diagonal Operator Entropy Number -
Constructor Summary
Constructors Constructor Description DiagonalOperatorCoveringBound(int iOperatorEntropyAsymptoteBase, double dblOperatorEntropyAsymptoteExponent)
DiagonalOperatorCoveringBound Constructor -
Method Summary
Modifier and Type Method Description double
entropyNumberAsymptoteExponent()
Retrieve the Entropy Number Asymptote Exponentint
entropyNumberAsymptoteType()
Retrieve the Entropy Number Asymptote TypeMethods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Field Details
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BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
public static final int BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENTAsymptote on the Base Diagonal Operator Entropy Number- See Also:
- Constant Field Values
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LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
public static final int LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENTAsymptote on the Log of the Diagonal Operator Entropy Number- See Also:
- Constant Field Values
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Constructor Details
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DiagonalOperatorCoveringBound
public DiagonalOperatorCoveringBound(int iOperatorEntropyAsymptoteBase, double dblOperatorEntropyAsymptoteExponent) throws java.lang.ExceptionDiagonalOperatorCoveringBound Constructor- Parameters:
iOperatorEntropyAsymptoteBase
- Indicate the Asymptote is on the Base Value or Log ValuedblOperatorEntropyAsymptoteExponent
- The Entropy Number Asymptote Exponent- Throws:
java.lang.Exception
- Throws if the Inputs are Invalid
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Method Details
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entropyNumberAsymptoteType
public int entropyNumberAsymptoteType()Retrieve the Entropy Number Asymptote Type- Returns:
- The Entropy Number Asymptote Type
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entropyNumberAsymptoteExponent
public double entropyNumberAsymptoteExponent()Retrieve the Entropy Number Asymptote Exponent- Returns:
- The Entropy Number Asymptote Exponent
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