mgplvm.models.bfa module

class mgplvm.models.bfa.Bfa(n, d, sigma=None, learn_sigma=True, Y=None, learn_neuron_scale=False, ard=False, learn_scale=None)

Bases: mgplvm.models.gp_base.GpBase

Bayesian Factor Analysis Assumes Gaussian observation noise Computes log_prob and posterior predictions exactly

property dim_scale

elbo(y, x, sample_idxs=None, m=None)

Parameters

yTensor

data tensor with dimensions (n_samples x n x m)

xTensor (single kernel) or Tensor list (product kernels)

input tensor(s) with dimensions (n_mc x n_samples x d x m)

Returns

lik, prior_klTuple[torch.Tensor, torch.Tensor]

lik has dimensions (n_mc x n) prior_kl has dimensions (n) and is zero

Return type

Tuple[Tensor, Tensor]

g0_parameters()

g1_parameters()

log_prob(y, x)

compute prior p(y) = N(y|0, X^T X)

property msg

name = 'Bfa'

property neuron_scale

predict(xstar, y, x, full_cov=False)

compute posterior p(f* | x, y)

property prms: torch.Tensor

Return type

Tensor

property scale

property sigma: torch.Tensor

Return type

Tensor

training: bool

class mgplvm.models.bfa.Bvfa(n, d, m, n_samples, likelihood, q_mu=None, q_sqrt=None, tied_samples=True, Y=None, learn_neuron_scale=False, ard=False, learn_scale=None, rel_scale=1, scale=None, dim_scale=None, neuron_scale=None)

Bases: mgplvm.models.gp_base.GpBase

property dim_scale

elbo(y, x, sample_idxs=None, m=None)

Parameters

yTensor

data tensor with dimensions (n_samples x n x m)

xTensor (single kernel) or Tensor list (product kernels)

input tensor(s) with dimensions (n_mc x n_samples x d x m)

mOptional int

used to scale the svgp likelihood. If not provided, self.m is used which is provided at initialization. This parameter is useful if we subsample data but want to weight the prior as if it was the full dataset. We use this e.g. in crossvalidation

Returns

lik, prior_klTuple[torch.Tensor, torch.Tensor]

lik has dimensions (n_mc x n) prior_kl has dimensions (n)

Return type

Tuple[Tensor, Tensor]

g0_parameters()

g1_parameters()

property msg

name = 'Bvfa'

property neuron_scale

predict(x, full_cov, sample_idxs=None)

Parameters

xTensor (single kernel) or Tensor list (product kernels)

test input tensor(s) with dimensions (n_b x n_samples x d x m)

full_covbool

returns full covariance if true otherwise returns the diagonal

Returns

muTensor

mean of predictive density at test inputs [ s ]

vTensor

variance/covariance of predictive density at test inputs [ s ] if full_cov is true returns full covariance, otherwise returns diagonal variance

Return type

Tuple[Tensor, Tensor]

prior_kl(p(f) || q(f))

property prms: Tuple[torch.Tensor, torch.Tensor]

Return type

Tuple[Tensor, Tensor]

property q_mu

property q_sqrt

sample(query, n_mc=1000, square=False, noise=True)

Parameters

queryTensor (single kernel)

test input tensor with dimensions (n_samples x d x m)

n_mcint

numper of samples to return

squarebool

determines whether to square the output

noisebool

determines whether we also sample explicitly from the noise model or simply return samples of the mean

Returns

y_sampsTensor

samples from the model (n_mc x n_samples x d x m)

property scale

training: bool

class mgplvm.models.bfa.Fa(n, d, sigma=None, learn_sigma=True, Y=None, C=None)

Bases: mgplvm.models.gp_base.GpBase

Standard non-Bayesian Factor Analysis Assumes Gaussian observation noise Computes log_prob and posterior predictions exactly

elbo(y, x, sample_idxs=None, m=None)

Parameters

yTensor

data tensor with dimensions (n_samples x n x m)

xTensor (single kernel) or Tensor list (product kernels)

input tensor(s) with dimensions (n_mc x n_samples x d x m)

Returns

lik, prior_klTuple[torch.Tensor, torch.Tensor]

lik has dimensions (n_mc x n) prior_kl has dimensions (n) and is zero

Return type

Tuple[Tensor, Tensor]

g0_parameters()

g1_parameters()

log_prob(y, x)

compute p(y|X) = N(y|CX, I) x is (n_mc x n_samples x d x m) y is (n_samples x n x m)

property msg

name = 'Fa'

predict(xstar, full_cov=False)

compute posterior p(f* | x, y, C) = N(C@x*, Sig)

property prms: torch.Tensor

Return type

Tensor

sample(query, n_mc=1000, square=False, noise=True)

Parameters

queryTensor (single kernel)

test input tensor with dimensions (n_samples x d x m)

n_mcint

numper of samples to return

squarebool

determines whether to square the output

noisebool

determines whether we also sample explicitly from the noise model or simply return samples of the mean

Returns

y_sampsTensor

samples from the model (n_mc x n_samples x d x m)

property sigma: torch.Tensor

Return type

Tensor

training: bool

mgplvm.models.bfa.batch_capacitance_tril(W, D)

Copied from pytorch source code Computes Cholesky of \(I + W.T @ inv(D) @ W\) for a batch of matrices \(W\) and a batch of vectors \(D\).

class mgplvm.models.bfa.vFa(n, d, m, n_samples, likelihood, Y=None, rel_scale=1, C=None)

Bases: mgplvm.models.gp_base.GpBase

Variational non-Bayesian Factor Analysis Allows for non-Gaussian noise

elbo(y, x, sample_idxs=None, m=None)

Parameters

yTensor

data tensor with dimensions (n_samples x n x m)

xTensor (single kernel) or Tensor list (product kernels)

input tensor(s) with dimensions (n_mc x n_samples x d x m)

Returns

lik, prior_klTuple[torch.Tensor, torch.Tensor]

lik has dimensions (n_mc x n) prior_kl has dimensions (n) and is zero

Return type

Tuple[Tensor, Tensor]

g0_parameters()

g1_parameters()

property msg

name = 'vFa'

predict(xstar, full_cov=False)

compute posterior p(f* | x, y, C) = N(C@x*, Sig)

property prms: torch.Tensor

Return type

Tensor

sample(query, n_mc=1000, square=False, noise=True)

Parameters

queryTensor (single kernel)

test input tensor with dimensions (n_samples x d x m)

n_mcint

numper of samples to return

squarebool

determines whether to square the output

noisebool

determines whether we also sample explicitly from the noise model or simply return samples of the mean

Returns

y_sampsTensor

samples from the model (n_mc x n_samples x d x m)

training: bool