azula.linalg.covariance¶

Covariance matrices.

Classes¶

`Covariance`	Abstract covariance matrix.
`IsotropicCovariance`	Isotropic covariance matrix.
`DiagonalCovariance`	Diagonal covariance matrix.
`FullCovariance`	Full covariance matrix.
`DPLRCovariance`	Diagonal plus low-rank (DPLR) covariance matrix.
`DMLRCovariance`	Diagonal minus low-rank (DMLR) covariance matrix.
`KroneckerCovariance`	Kronecker-factorized covariance matrix.

class azula.linalg.covariance.Covariance¶[source]: Abstract covariance matrix.

class azula.linalg.covariance.IsotropicCovariance(lmbda)¶[source]

Isotropic covariance matrix.

\[C = \lambda I\]

class azula.linalg.covariance.DiagonalCovariance(D)¶[source]

Diagonal covariance matrix.

\[C = \mathrm{diag}(D)\]

class azula.linalg.covariance.FullCovariance(Q, L)¶[source]

Full covariance matrix.

\[C = Q \mathrm{diag}(L) Q^\top\]

where \(Q\) is an orthonormal matrix.

class azula.linalg.covariance.DPLRCovariance(D, V)¶[source]

Diagonal plus low-rank (DPLR) covariance matrix.

\[\mathrm{diag}(D) + V V^\top\]

Wikipedia

static from_data(X, rank=1, iterations=0)¶[source]

References

The EM Algorithm for Mixtures of Factor Analyzers (Zoubin et al., 1996)

class azula.linalg.covariance.DMLRCovariance(D, V)¶[source]

Diagonal minus low-rank (DMLR) covariance matrix.

\[\mathrm{diag}(D) - V V^\top\]

class azula.linalg.covariance.KroneckerCovariance(Qs, L)¶[source]

Kronecker-factorized covariance matrix.

\[C = (Q_1 \otimes \dots \otimes Q_n) \, L \, (Q_1 \otimes \dots \otimes Q_n)^\top\]

where \(Q_i\) are orthonormal matrices for each dimension and \(\otimes\) denotes the Kronecker product.

Wikipedia