Structured PCA Model
X
The matrix of data
n
The number of samples
k
Latent dimensionality
d
Simensionality of observations
beta
Covariance function hyperparameters
K
covariance matrix generated from the covariance function and hyperparameters
KD
Partial derivatived of K w.r.t each of the hyperparameters
locs
Locations (t_i)
covFn
Covariance function
covFnD
Function giving partial derivatives of covariance function w.r.t hyperparameters
muHat
MAP estimate of mu
WHat
MAP estimate of W
sigSqHat
MAP estimate of sigSq
Vmean
The posterior mean of each latent variable
VVar
The posterior variance around each latent variable
logEvidence
log of the approximate evidence
logPosteriors
sequence of posteriors obtained in fitting. Un-normalised if sparse
logEvidenceD
Partial derivatives of evidence w.r.t hyperparameters
H
The precision matrix for the gaussian approximation to the posterior around each w
maxim
the maximisation object returned in hyperparameter tuning
thetaConv
Whether theta has been optimised to convergence (if false, beta has probably converged, not theta)
theta
betaHist history of betas in optimisation
convergence
History of logEvidence and logPosteror; used to assess convergence
sparse
whether this is a sparse stpca model
b
The sparsity hyperparameter in a sparse model.
crossvalidate(nFolds = 3, nThreads = 1)
Perform k-fold cross-validation (possibly multithreaded) to determine the held out log likelihood of examples. This could be used as an alternative to computing the approximate evidence in model selection.
decode(Vnew)
Decode points in the latent space into observations
encode(Xnew)
Encode a matrix of observations into latent distributions.
set_b(bNew)
Setter for 'b'
set_beta(betaNew)
Sets beta to a new value, recomputes K, KD and H.
set_locs(locsNew)
Sets the locations, and recomputes K. Be careful with this method. Does not update theta
set_sparse(spNew, b)
Setter for 'sparse'
set_X(Xnew)
Sets X, updates mu. Does not opdate anything else so it is recommended to call update() or something. Be careful with this method.
simulate(n = 1, Wknown = TRUE)
Simulates new synthetic data from a fitted model.
update(tune.maxit = 10, tune.tol = 1e-05, EM.maxit = 500,
EM.bftol = 1e-05, ...)
The major method for performing inference. This iterates between updating theta (using update_theta) and updating beta (using update_beta).
update_beta(...)
Optimises the approximate evidence with respect to the hyperparameters.
update_theta(maxit = 500, bftol = 1e-05)
Finds the MAP theta using EM.
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