Class/Object

scalismo.statisticalmodel

LowRankGaussianProcess

Related Docs: object LowRankGaussianProcess | package statisticalmodel

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class LowRankGaussianProcess[D <: Dim, DO <: Dim] extends GaussianProcess[D, DO]

A gaussian process which is represented in terms of a (small) finite set of basis functions. The basis functions are the orthonormal basis functions given by a mercers' decomposition.

D

The dimensionality of the input space

DO

The dimensionality of the output space

Linear Supertypes
GaussianProcess[D, DO], AnyRef, Any
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Inherited
  1. LowRankGaussianProcess
  2. GaussianProcess
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Instance Constructors

  1. new LowRankGaussianProcess(mean: VectorField[D, DO], klBasis: KLBasis[D, DO])(implicit arg0: NDSpace[D], arg1: NDSpace[DO])

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    mean

    The mean function

    klBasis

    A set of basis functions

Value Members

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

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  5. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  6. def coefficients(trainingData: IndexedSeq[(Point[D], Vector[DO])], sigma2: Double): DenseVector[Float]

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    Returns the sample of the coefficients of the sample that best explains the given training data.

    Returns the sample of the coefficients of the sample that best explains the given training data. It is assumed that the training data (values) are subject to 0 mean Gaussian noise

  7. def coefficients(trainingData: IndexedSeq[(Point[D], Vector[DO], NDimensionalNormalDistribution[DO])]): DenseVector[Float]

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    Returns the sample of the coefficients of the sample that best explains the given training data.

    Returns the sample of the coefficients of the sample that best explains the given training data. It is assumed that the training data (values) are subject to 0 mean Gaussian noise

  8. val cov: MatrixValuedPDKernel[D, DO]

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    The covariance function.

    The covariance function. Needs to be positive definite

    Definition Classes
    GaussianProcess
  9. val dimOps: NDSpace[DO]

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    Attributes
    protected[this]
    Definition Classes
    GaussianProcess
  10. def discretize(domain: DiscreteDomain[D]): DiscreteLowRankGaussianProcess[D, DO]

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    Discretize the gaussian process on the given points.

  11. def domain: Domain[D]

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    Definition Classes
    GaussianProcess
  12. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  13. def equals(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  14. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  15. final def getClass(): Class[_]

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    Definition Classes
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  16. def hashCode(): Int

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    Definition Classes
    AnyRef → Any
  17. def instance(c: DenseVector[Float]): VectorField[D, DO]

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    an instance of the gaussian process, which is formed by a linear combination of the klt basis using the given coefficients c.

    an instance of the gaussian process, which is formed by a linear combination of the klt basis using the given coefficients c.

    c

    Coefficients that determine the linear combination. Are assumed to be N(0,1) distributed.

  18. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  19. val klBasis: KLBasis[D, DO]

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    A set of basis functions

  20. def logpdf(coefficients: DenseVector[Float]): Double

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    Returns the log of the probability density of the instance produced by the x coefficients.

    Returns the log of the probability density of the instance produced by the x coefficients.

    If you are interested in ordinal comparisons of PDFs, use this as it is numerically more stable

  21. def marginal(pt: Point[D]): NDimensionalNormalDistribution[DO]

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    Compute the marginal distribution at a single point.

    Compute the marginal distribution at a single point.

    Definition Classes
    GaussianProcess
  22. def marginal(domain: DiscreteDomain[D]): DiscreteGaussianProcess[D, DO]

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    Compute the marginal distribution for the given points.

    Compute the marginal distribution for the given points. The result is again a Gaussian process, whose domain is defined by the given points.

    Definition Classes
    GaussianProcess
  23. val mean: VectorField[D, DO]

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    The mean function

    The mean function

    Definition Classes
    GaussianProcess
  24. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  25. final def notify(): Unit

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    Definition Classes
    AnyRef
  26. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  27. def pdf(coefficients: DenseVector[Float]): Double

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    Returns the probability density of the instance produced by the x coefficients

  28. def posterior(trainingData: IndexedSeq[(Point[D], Vector[DO], NDimensionalNormalDistribution[DO])]): LowRankGaussianProcess[D, DO]

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    The posterior distribution of the gaussian process, with respect to the given trainingData.

    The posterior distribution of the gaussian process, with respect to the given trainingData. It is computed using Gaussian process regression.

    Definition Classes
    LowRankGaussianProcessGaussianProcess
  29. def posterior(trainingData: IndexedSeq[(Point[D], Vector[DO])], sigma2: Double): LowRankGaussianProcess[D, DO]

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    The posterior distribution of the gaussian process, with respect to the given trainingData.

    The posterior distribution of the gaussian process, with respect to the given trainingData. It is computed using Gaussian process regression. We assume that the trainingData is subject to isotropic Gaussian noise with variance sigma2.

    Definition Classes
    LowRankGaussianProcessGaussianProcess
  30. def project(trainingData: IndexedSeq[(Point[D], Vector[DO], NDimensionalNormalDistribution[DO])]): VectorField[D, DO]

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    Returns the sample of the gaussian process that best explains the given training data.

    Returns the sample of the gaussian process that best explains the given training data. It is assumed that the training data (values) are subject to 0 mean gaussian noise

    trainingData

    Point/value pairs where that the sample should approximate, together with the variance of the noise model at each point.

  31. def project(trainingData: IndexedSeq[(Point[D], Vector[DO])], sigma2: Double = 1e-6): VectorField[D, DO]

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    Returns the sample of the gaussian process that best explains the given training data.

    Returns the sample of the gaussian process that best explains the given training data. It is assumed that the training data (values) are subject to 0 mean Gaussian noise

    trainingData

    Point/value pairs where that the sample should approximate.

    sigma2

    variance of a Gaussian noise that is assumed on every training point

  32. def rank: Int

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    the rank (i.e.

    the rank (i.e. number of basis functions)

  33. def sample: VectorField[D, DO]

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    A random sample of the gaussian process

  34. def sampleAtPoints(domain: DiscreteDomain[D]): DiscreteVectorField[D, DO]

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    A random sample evaluated at the given points

    A random sample evaluated at the given points

    Definition Classes
    LowRankGaussianProcessGaussianProcess
  35. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  36. def toString(): String

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    Definition Classes
    AnyRef → Any
  37. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  38. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  39. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from GaussianProcess[D, DO]

Inherited from AnyRef

Inherited from Any

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