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]], SerializableLogging, Serializable, Serializable, Minimizer[T, StochasticDiffFunction[T]], AnyRef, Any
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Inherited
  1. L1Regularization
  2. StochasticGradientDescent
  3. FirstOrderMinimizer
  4. SerializableLogging
  5. Serializable
  6. Serializable
  7. Minimizer
  8. AnyRef
  9. Any
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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 space: MutableFiniteCoordinateField[T, _, Double], rand: RandBasis = breeze.stats.distributions.Rand)

Type Members

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

    Any history the derived minimization function needs to do its updates.

  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

    Tracks the information about the optimizer, including the current point, its value, gradient, and then any history.

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. def adjustFunction(f: StochasticDiffFunction[T]): StochasticDiffFunction[T]

    Attributes
    protected
    Definition Classes
    FirstOrderMinimizer

  8. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  9. def calculateObjective(f: StochasticDiffFunction[T], x: T, history: History): (Double, T)

    Attributes
    protected
    Definition Classes
    FirstOrderMinimizer

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

    Attributes
    protected
    Definition Classes
    StochasticGradientDescent → FirstOrderMinimizer

  11. def clone(): AnyRef

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

  12. val defaultStepSize: Double

    Definition Classes
    StochasticGradientDescent

  13. 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

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

    Definition Classes
    AnyRef

  15. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  16. def finalize(): Unit

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

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

    Definition Classes
    AnyRef → Any

  18. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  19. def infiniteIterations(f: StochasticDiffFunction[T], init: T): Iterator[State]

    Definition Classes
    FirstOrderMinimizer

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

    Definition Classes
    L1Regularization → FirstOrderMinimizer

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

    Attributes
    protected
    Definition Classes
    FirstOrderMinimizer

  22. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    FirstOrderMinimizer

  24. val lambda: Double

  25. def logger: LazyLogger

    Attributes
    protected
    Definition Classes
    SerializableLogging

  26. val minImprovementWindow: Int

    Definition Classes
    FirstOrderMinimizer

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

    Definition Classes
    FirstOrderMinimizer → Minimizer

  28. def minimizeAndReturnState(f: StochasticDiffFunction[T], init: T): State

    Definition Classes
    FirstOrderMinimizer

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

    Definition Classes
    AnyRef

  30. final def notify(): Unit

    Definition Classes
    AnyRef

  31. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  32. val numberOfImprovementFailures: Int

    Definition Classes
    FirstOrderMinimizer

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

    Definition Classes
    AnyRef

  34. 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

  35. def toString(): String

    Definition Classes
    AnyRef → Any

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

    Attributes
    protected
    Definition Classes
    StochasticGradientDescent → FirstOrderMinimizer

  37. def updateHistory(newX: T, newGrad: T, newValue: Double, f: StochasticDiffFunction[T], oldState: State): History

    Definition Classes
    L1Regularization → FirstOrderMinimizer

  38. implicit val vspace: NormedModule[T, Double]

    Attributes
    protected
    Definition Classes
    StochasticGradientDescent

  39. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from StochasticGradientDescent[T]

Inherited from FirstOrderMinimizer[T, StochasticDiffFunction[T]]

Inherited from SerializableLogging

Inherited from Serializable

Inherited from Serializable

Inherited from Minimizer[T, StochasticDiffFunction[T]]

Inherited from AnyRef

Inherited from Any

Ungrouped