Packages

  • package root
    Definition Classes
    root
  • package breeze
    Definition Classes
    root
  • package optimize

    Definition Classes
    breeze
  • object AdaptiveGradientDescent

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

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

    Basically, we use "forward regularization" and an adaptive step size based on the previous gradients.

    Definition Classes
    optimize
  • L1Regularization
  • L2Regularization

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, Minimizer[T, StochasticDiffFunction[T]], AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. L1Regularization
  2. StochasticGradientDescent
  3. FirstOrderMinimizer
  4. SerializableLogging
  5. Serializable
  6. Minimizer
  7. AnyRef
  8. Any
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new L1Regularization(lambda: Double = 1.0, delta: Double = 1E-5, eta: Double = 4, maxIter: Int = 100)(implicit space: MutableFiniteCoordinateField[T, _, Double], rand: RandBasis)

Type Members

  1. case class History(sumOfSquaredGradients: T) extends Product with Serializable
  2. type State = FirstOrderMinimizer.State[T, Info, History]
    Definition Classes
    FirstOrderMinimizer

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. def adjust(newX: T, newGrad: T, newVal: Double): (Double, T)
    Attributes
    protected
    Definition Classes
    L1Regularization → FirstOrderMinimizer
  5. def adjustFunction(f: StochasticDiffFunction[T]): StochasticDiffFunction[T]
    Attributes
    protected
    Definition Classes
    FirstOrderMinimizer
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. def calculateObjective(f: StochasticDiffFunction[T], x: T, history: History): (Double, T)
    Attributes
    protected
    Definition Classes
    FirstOrderMinimizer
  8. def chooseDescentDirection(state: State, fn: StochasticDiffFunction[T]): T
    Attributes
    protected
    Definition Classes
    StochasticGradientDescent → FirstOrderMinimizer
  9. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  10. val convergenceCheck: ConvergenceCheck[T]
    Definition Classes
    FirstOrderMinimizer
  11. val defaultStepSize: Double
    Definition Classes
    StochasticGradientDescent
  12. 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
  13. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  14. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  15. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  16. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  17. def infiniteIterations(f: StochasticDiffFunction[T], state: State): Iterator[State]
    Definition Classes
    FirstOrderMinimizer
  18. def initialHistory(f: StochasticDiffFunction[T], init: T): History
    Definition Classes
    L1Regularization → FirstOrderMinimizer
  19. def initialState(f: StochasticDiffFunction[T], init: T): State
    Attributes
    protected
    Definition Classes
    FirstOrderMinimizer
  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. def iterations(f: StochasticDiffFunction[T], init: T): Iterator[State]
    Definition Classes
    FirstOrderMinimizer
  22. val lambda: Double
  23. def logger: LazyLogger
    Attributes
    protected
    Definition Classes
    SerializableLogging
  24. val maxIter: Int
    Definition Classes
    StochasticGradientDescent
  25. def minimize(f: StochasticDiffFunction[T], init: T): T
    Definition Classes
    FirstOrderMinimizer → Minimizer
  26. def minimizeAndReturnState(f: StochasticDiffFunction[T], init: T): State
    Definition Classes
    FirstOrderMinimizer
  27. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  28. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  29. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  30. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  31. 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
  32. def toString(): String
    Definition Classes
    AnyRef → Any
  33. def updateHistory(newX: T, newGrad: T, newValue: Double, f: StochasticDiffFunction[T], oldState: State): History
    Definition Classes
    L1Regularization → FirstOrderMinimizer
  34. implicit val vspace: NormedModule[T, Double]
    Attributes
    protected
    Definition Classes
    StochasticGradientDescent
  35. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  36. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  37. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated

Inherited from StochasticGradientDescent[T]

Inherited from FirstOrderMinimizer[T, StochasticDiffFunction[T]]

Inherited from SerializableLogging

Inherited from Serializable

Inherited from Minimizer[T, StochasticDiffFunction[T]]

Inherited from AnyRef

Inherited from Any

Ungrouped