com.github.gradientgmm.components
GConcaveGaussian
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package components
Compute augmented parameter matrix
data dimensionality
data dimensionality
Returns the covariance matrix' determinant
Returns the covariance matrix' determinant
Returns the g-concave reformulation's density evaluated on x
Augmented parameter block matrix inverse [A B; C D].
Augmented parameter block matrix inverse [A B; C D]. Its blocks are:
A = sigmaInv
B = sigmaInv * mu
C = mu.t * sigmaInv
D = 1/s + mu.t * sigmaInv * mu
Returns the covariance matrix' log-determinant
Returns the covariance matrix' log-determinant
Returns the distribution's log-density function evaluated on x
Returns the distribution's log-density function evaluated on x
Returns the distribution's log-density function evaluated on x
Returns the distribution's log-density function evaluated on x
Augmented parameter block matrix [A B; C D].
Augmented parameter block matrix [A B; C D]. The blocks are:
A = sigma + s * mu * mu.t
B = s * mu
C = s * mu.t
D = s
Returns the distribution's density function evaluated on x
Returns the distribution's density function evaluated on x
Returns the distribution's density function evaluated on x
Returns the distribution's density function evaluated on x
square root of the covariance matrix inverse, and the density's constant term
square root of the covariance matrix inverse, and the density's constant term
Positive scalar
square root of the covariance matrix inverse, and the density's constant term
square root of the covariance matrix inverse, and the density's constant term
Multivariate Gaussian Distribution reformulation that produces a g-concave loss function in An Alternative to EM for Gaussian Mixture Models: Batch and Stochastic Riemannian Optimization]]
For an arbitrary Gaussian distribution, its g-concave reformulation have zero mean and an augmented covariance matrix which is a function of the original mean, covariance matrix and an additional positive scalar s. Original data points x are mapped to y = [x 1] to be evaluated under the new distribution. When s = 1, the density of the original distribution and the reformulation coincide.