breeze.optimize.AdaptiveGradientDescent

L1Regularization

class L1Regularization[T] extends StochasticGradientDescent[T]

Implements the L1 regularization update.

Each step is:

x_{t+1}i = sign(x_{t,i} - eta/s_i * g_ti) * (abs(x_ti - eta/s_ti * g_ti) - lambda * eta /s_ti))_+

where g_ti is the gradient and s_ti = \sqrt(\sum_t'{t} g_ti2)

Linear Supertypes
StochasticGradientDescent[T], FirstOrderMinimizer[T, StochasticDiffFunction[T]], Logging, Minimizer[T, StochasticDiffFunction[T]], AnyRef, Any
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Inherited
  1. L1Regularization
  2. StochasticGradientDescent
  3. FirstOrderMinimizer
  4. Logging
  5. Minimizer
  6. AnyRef
  7. Any
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  1. Public
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Instance Constructors

  1. new L1Regularization(lambda: Double = 1.0, delta: Double = 1.0E-5, eta: Double = 4, maxIter: Int = 100)(implicit vspace: MutableCoordinateSpace[T, Double])

Type Members

  1. case class History(sumOfSquaredGradients: T) extends Product with Serializable

    Definition Classes
    L1Regularization → FirstOrderMinimizer

  2. case class State(x: T, value: Double, grad: T, adjustedValue: Double, adjustedGradient: T, iter: Int, initialAdjVal: Double, history: History, fVals: IndexedSeq[Double] = ..., numImprovementFailures: Int = 0, searchFailed: Boolean = false) extends Product with Serializable

    Definition Classes
    FirstOrderMinimizer

Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  5. final def ==(arg0: Any): Boolean

    Definition Classes
    Any

  6. def adjust(newX: T, newGrad: T, newVal: Double): (Double, T)

    Attributes
    protected
    Definition Classes
    L1Regularization → FirstOrderMinimizer

  7. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  8. def chooseDescentDirection(state: State, fn: StochasticDiffFunction[T]): T

    Attributes
    protected
    Definition Classes
    StochasticGradientDescent → FirstOrderMinimizer

  9. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  10. val defaultStepSize: Double

    Definition Classes
    StochasticGradientDescent

  11. def determineStepSize(state: State, f: StochasticDiffFunction[T], dir: T): Double

    Choose a step size scale for this iteration.

    Choose a step size scale for this iteration.

    Default is eta / math.pow(state.iter + 1,2.0 / 3.0)

    Definition Classes
    L1Regularization → StochasticGradientDescent → FirstOrderMinimizer

  12. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  13. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  14. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  15. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any

  16. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  17. def initialHistory(f: StochasticDiffFunction[T], init: T): History

    Definition Classes
    L1Regularization → FirstOrderMinimizer

  18. def initialState(f: StochasticDiffFunction[T], init: T): State

    Attributes
    protected
    Definition Classes
    FirstOrderMinimizer

  19. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  20. def iterations(f: StochasticDiffFunction[T], init: T): Iterator[State]

    Definition Classes
    FirstOrderMinimizer

  21. val lambda: Double

  22. lazy val logger: Logger

    Attributes
    protected
    Definition Classes
    Logging

  23. val minImprovementWindow: Int

    Definition Classes
    FirstOrderMinimizer

  24. def minimize(f: StochasticDiffFunction[T], init: T): T

    Definition Classes
    FirstOrderMinimizer → Minimizer

  25. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  26. final def notify(): Unit

    Definition Classes
    AnyRef

  27. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  28. val numberOfImprovementFailures: Int

    Definition Classes
    FirstOrderMinimizer

  29. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef

  30. def takeStep(state: State, dir: T, stepSize: Double): T

    Projects the vector x onto whatever ball is needed.

    Projects the vector x onto whatever ball is needed. Can also incorporate regularization, or whatever.

    Default just takes a step

    Attributes
    protected
    Definition Classes
    L1Regularization → StochasticGradientDescent → FirstOrderMinimizer

  31. def toString(): String

    Definition Classes
    AnyRef → Any

  32. def updateFValWindow(oldState: State, newAdjVal: Double): IndexedSeq[Double]

    Attributes
    protected
    Definition Classes
    StochasticGradientDescent → FirstOrderMinimizer

  33. def updateHistory(newX: T, newGrad: T, newValue: Double, oldState: State): History

    Definition Classes
    L1Regularization → FirstOrderMinimizer

  34. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  35. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  36. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from StochasticGradientDescent[T]

Inherited from FirstOrderMinimizer[T, StochasticDiffFunction[T]]

Inherited from Logging

Inherited from Minimizer[T, StochasticDiffFunction[T]]

Inherited from AnyRef

Inherited from Any

Ungrouped