bf.dist.low_rank_multivariate_normal: Low Rank Multivariate Normal Distribution

In BayesForge: Bayesian Inference using 'numpyro' and 'XLA'

Low Rank Multivariate Normal Distribution

Description

The *Low-Rank Multivariate Normal* (LRMVN) distribution is a parameterizaton of the multivariate normal distribution where the covariance matrix is expressed as a low-rank plus diagonal decomposition:

\Sigma = F F^\top + D

where $F$ is a low-rank matrix (capturing correlations) and $D$ is a diagonal matrix (capturing independent noise). This representation is often used in probabilistic modeling and variational inference to efficiently handle high-dimensional Gaussian distributions with structured covariance.

Usage

bf.dist.low_rank_multivariate_normal(
  loc,
  cov_factor,
  cov_diag,
  validate_args = py_none(),
  name = "x",
  obs = py_none(),
  mask = py_none(),
  sample = FALSE,
  seed = py_none(),
  shape = c(),
  event = 0,
  create_obj = FALSE,
  to_jax = TRUE
)

Arguments

loc	A numeric vector representing the mean vector.
cov_factor	A numeric vector or matrix used to construct the covariance matrix.
cov_diag	A numeric vector representing the diagonal elements of the covariance matrix.
validate_args	Logical: Whether to validate parameter values. Defaults to 'reticulate::py_none()'.
name	A character string representing the name of the random variable within a model. This is used to uniquely identify the variable. Defaults to 'x'.
obs	A numeric vector or array of observed values. If provided, the random variable is conditioned on these values. If 'NULL', the variable is treated as a latent (unobserved) variable. Defaults to 'NULL'.
mask	Logical vector. Optional boolean array to mask observations.
sample	A logical value that controls the function's behavior. If 'TRUE', the function will directly draw samples from the distribution. If 'FALSE', it will create a random variable within a model. Defaults to 'FALSE'.
seed	An integer used to set the random seed for reproducibility when 'sample = TRUE'. This argument has no effect when 'sample = FALSE', as randomness is handled by the model's inference engine. Defaults to 0.
shape	Numeric vector. A multi-purpose argument for shaping. When ‘sample=False' (model building), this is used with '.expand(shape)' to set the distribution’s batch shape. When 'sample=True' (direct sampling), this is used as 'sample_shape' to draw a raw JAX array of the given shape.
event	Integer. The number of batch dimensions to reinterpret as event dimensions (used in model building).
create_obj	Logical. If True, returns the raw BI distribution object instead of creating a sample site. This is essential for building complex distributions like 'MixtureSameFamily'.
to_jax	Boolean. Indicates whether to return a JAX array or not.

Value

- When sample=FALSE, a BI Low Rank Multivariate Normal distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the Low Rank Multivariate Normal distribution (for direct sampling).

- When create_obj=TRUE, the raw BI distribution object (for advanced use cases).

See Also

This is a wrapper of https://num.pyro.ai/en/stable/distributions.html#lowrankmultivariatenormal

Examples

library(BayesForge)
m=importBF(platform='cpu')
event_size = 10
rank = 5
bf.dist.low_rank_multivariate_normal(
  loc = bf.dist.normal(0,1,shape = c(event_size), sample = TRUE)*2,
  cov_factor = bf.dist.normal(0,1,shape = c(event_size, rank), sample = TRUE),
  cov_diag = bf.dist.normal(10,0.5,shape = c(event_size), sample = TRUE),
  sample = TRUE)

BayesForge documentation built on June 9, 2026, 1:09 a.m.