breeze

optimize

package optimize

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Type Members

  1. class AdaDeltaGradientDescent[T] extends StochasticGradientDescent[T]

    Created by jda on 3/17/15.

  2. class ApproximateGradientFunction[K, T] extends DiffFunction[T]

    Approximates a gradient by finite differences.

  3. trait ApproximateLineSearch extends MinimizingLineSearch

    A line search optimizes a function of one variable without analytic gradient information.

  4. class BacktrackingLineSearch extends ApproximateLineSearch

    Implements the Backtracking Linesearch like that in LBFGS-C (which is (c) 2007-2010 Naoaki Okazaki under BSD)

  5. trait BatchDiffFunction[T] extends DiffFunction[T] with (T, IndexedSeq[Int]) ⇒ Double

    A diff function that supports subsets of the data.

  6. case class BatchSize(size: Int) extends OptimizationOption with Product with Serializable

  7. class CachedBatchDiffFunction[T] extends BatchDiffFunction[T]

  8. class CachedDiffFunction[T] extends DiffFunction[T]

  9. class CompactHessian extends NumericOps[CompactHessian]

  10. abstract class CubicLineSearch extends SerializableLogging with MinimizingLineSearch

  11. trait DiffFunction[T] extends StochasticDiffFunction[T] with NumericOps[DiffFunction[T]]

    Represents a differentiable function whose output is guaranteed to be consistent

  12. sealed trait DiffFunctionOpImplicits extends AnyRef

  13. class EmpiricalHessian[T] extends AnyRef

    The empirical hessian evaluates the derivative for multiplcation.

  14. sealed class FirstOrderException extends RuntimeException

  15. abstract class FirstOrderMinimizer[T, DF <: StochasticDiffFunction[T]] extends Minimizer[T, DF] with SerializableLogging

  16. class FisherDiffFunction[T] extends SecondOrderFunction[T, FisherMatrix[T]]

  17. class FisherMatrix[T] extends AnyRef

    The Fisher matrix approximates the Hessian by E[grad grad'].

  18. trait IterableOptimizationPackage[Function, Vector, State] extends OptimizationPackage[Function, Vector]

  19. case class L1Regularization(value: Double = 1.0) extends OptimizationOption with Product with Serializable

  20. case class L2Regularization(value: Double = 1.0) extends OptimizationOption with Product with Serializable

  21. class LBFGS[T] extends FirstOrderMinimizer[T, DiffFunction[T]] with SerializableLogging

    Port of LBFGS to Scala.

  22. class LBFGSB extends FirstOrderMinimizer[DenseVector[Double], DiffFunction[DenseVector[Double]]] with SerializableLogging

    This algorithm is refered the paper "A LIMITED MEMOR Y ALGORITHM F OR BOUND CONSTRAINED OPTIMIZA TION" written by Richard H.

  23. trait LineSearch extends ApproximateLineSearch

    A line search optimizes a function of one variable without analytic gradient information.

  24. class LineSearchFailed extends FirstOrderException

  25. case class MaxIterations(num: Int) extends OptimizationOption with Product with Serializable

  26. trait Minimizer[T, -F] extends AnyRef

    Anything that can minimize a function

  27. trait MinimizingLineSearch extends AnyRef

  28. class NaNHistory extends FirstOrderException

  29. class OWLQN[K, T] extends LBFGS[T] with SerializableLogging

    Implements the Orthant-wise Limited Memory QuasiNewton method, which is a variant of LBFGS that handles L1 regularization.

  30. sealed trait OptimizationOption extends (OptParams) ⇒ OptParams

  31. trait OptimizationPackage[Function, Vector] extends AnyRef

  32. sealed trait OptimizationPackageLowPriority extends OptimizationPackageLowPriority2

  33. sealed trait OptimizationPackageLowPriority2 extends AnyRef

  34. class ProjectedQuasiNewton extends FirstOrderMinimizer[DenseVector[Double], DiffFunction[DenseVector[Double]]] with Projecting[DenseVector[Double]] with SerializableLogging

  35. trait Projecting[T] extends AnyRef

  36. trait SecondOrderFunction[T, H] extends DiffFunction[T]

    Represents a function for which we can easily compute the Hessian.

  37. class SpectralProjectedGradient[T] extends FirstOrderMinimizer[T, DiffFunction[T]] with Projecting[T] with SerializableLogging

    SPG is a Spectral Projected Gradient minimizer; it minimizes a differentiable function subject to the optimum being in some set, given by the projection operator projection

  38. class StepSizeOverflow extends FirstOrderException

  39. case class StepSizeScale(alpha: Double = 1.0) extends OptimizationOption with Product with Serializable

  40. class StepSizeUnderflow extends FirstOrderException

  41. class StochasticAveragedGradient[T] extends FirstOrderMinimizer[T, BatchDiffFunction[T]]

  42. trait StochasticDiffFunction[T] extends (T) ⇒ Double with NumericOps[StochasticDiffFunction[T]]

    A differentiable function whose output is not guaranteed to be the same across consecutive invocations.

  43. abstract class StochasticGradientDescent[T] extends FirstOrderMinimizer[T, StochasticDiffFunction[T]] with SerializableLogging

    Minimizes a function using stochastic gradient descent

  44. class StrongWolfeLineSearch extends CubicLineSearch

  45. case class Tolerance(fvalTolerance: Double = 1.0E-5, gvalTolerance: Double = 1.0E-6) extends OptimizationOption with Product with Serializable

  46. class TruncatedNewtonMinimizer[T, H] extends Minimizer[T, SecondOrderFunction[T, H]] with SerializableLogging

    Implements a TruncatedNewton Trust region method (like Tron).

Value Members

  1. object AdaptiveGradientDescent

    Implements the L2^2 and L1 updates from Duchi et al 2010 Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.

  2. object BatchDiffFunction

  3. object DiffFunction extends DiffFunctionOpImplicits

  4. object EmpiricalHessian

  5. object FirstOrderMinimizer extends Serializable

  6. object FisherMatrix

  7. object GradientTester extends SerializableLogging

    Class that compares the computed gradient with an empirical gradient based on finite differences.

  8. object LBFGS extends Serializable

  9. object LBFGSB extends Serializable

  10. object LineSearch

  11. object OptimizationOption

  12. object OptimizationPackage extends OptimizationPackageLowPriority

  13. object PreferBatch extends OptimizationOption with Product with Serializable

  14. object PreferOnline extends OptimizationOption with Product with Serializable

  15. object ProjectedQuasiNewton extends SerializableLogging

  16. object SecondOrderFunction

  17. object StochasticGradientDescent extends Serializable

  18. package flow

  19. def iterations[Objective, Vector, State](fn: Objective, init: Vector, options: OptimizationOption*)(implicit optimization: IterableOptimizationPackage[Objective, Vector, State]): Iterator[State]

    Returns a sequence of states representing the iterates of a solver, given an breeze.optimize.IterableOptimizationPackage that knows how to minimize The actual state class varies with the kind of function passed in.

    Returns a sequence of states representing the iterates of a solver, given an breeze.optimize.IterableOptimizationPackage that knows how to minimize The actual state class varies with the kind of function passed in. Typically, they have a .x value of type Vector that is the current point being evaluated, and .value is the current objective value

    Objective
    Vector
    fn
    init
    options
    optimization
    returns

  20. package linear

  21. def minimize[Objective, Vector](fn: Objective, init: Vector, options: OptimizationOption*)(implicit optimization: OptimizationPackage[Objective, Vector]): Vector

    Minimizes a function, given an breeze.optimize.OptimizationPackage that knows how to minimize

    Minimizes a function, given an breeze.optimize.OptimizationPackage that knows how to minimize

    Objective
    Vector
    fn
    init
    options
    optimization
    returns

  22. package proximal

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