torch_openreml.covariance.CovariancePropagation¶

class torch_openreml.covariance.CovariancePropagation(*args, **kwargs)[source]¶

Bases: Operator

Covariance propagation operator.

\[\symbf{V} = \symbf{Z} \symbf{G} \symbf{Z}^\top\]

Propagates the covariance matrix \(\symbf{G}\) through the design matrix \(\symbf{Z}\). The first operand is treated as \(\symbf{Z}\) and the second as \(\symbf{G}\). Either or both may be trainable Matrix instances or fixed torch.Tensor values.

This structure arises naturally in linear mixed-effects models where \(\symbf{Z}\) is the random-effect design matrix and \(\symbf{G}\) is the random-effect covariance matrix, giving the random-effect contribution \(\symbf{Z}\symbf{G}\symbf{Z}^\top\) to the marginal covariance.

Initialize a covariance propagation operator from exactly two operands.

Parameters:

*args – Exactly two operands as positional arguments or a single dict. The first is \(\symbf{Z}\), the second \(\symbf{G}\).
**kwargs – Exactly two operands as keyword arguments.

Raises:

ValueError – If the number of operands is not exactly two.

Example:

import torch
from torch_openreml.covariance import DummyMatrix, DiagonalMatrix, CovariancePropagation

z = DummyMatrix(["a", "b", "c", "a"])
z()

tensor([[1., 0., 0.],
        [0., 1., 0.],
        [0., 0., 1.],
        [1., 0., 0.]])

g = DiagonalMatrix(3)
op = CovariancePropagation(z=z, g=g)
free_params = torch.tensor([0.0, 0.5, 1.0])
op(free_params)

tensor([[1.0000, 0.0000, 0.0000, 1.0000],
        [0.0000, 2.7183, 0.0000, 0.0000],
        [0.0000, 0.0000, 7.3891, 0.0000],
        [1.0000, 0.0000, 0.0000, 1.0000]])

Methods

`__call__`([free_params])	Construct the matrix from a flat parameter tensor.
`auto_grad`([free_params])	Compute the Jacobian of `build()` with respect to free parameters using automatic differentiation.
`build_operands`([free_params])	Evaluate each operand at the current free parameters.
`build_params`([free_params, include_fixed, ...])	Construct the full parameter tensor by delegating to each operand.
`disable_cache`()	Disable intermediate caching on this operator and its operands.
`enable_cache`()	Enable intermediate caching on this operator and its operands.
`get_default_dtype_device`()	Get the dtype and the device of the parameter defaults.
`get_intermediates`(params)	Retrieve cached intermediate computation results if still valid.
`grad`([free_params])	Compute the Jacobian of `__call__()` with respect to trainable parameters.
`grad_tree`([free_params])	Compute the gradient of this operator and of every nested operand, returning each keyed by its path.
`inverse`([free_params])	Construct the matrix and return its inverse.
`manual_grad`([free_params])	Compute the Jacobian of `__call__()` with respect to trainable parameters using a closed-form analytic expression.
`operands_grad`([free_params])	Compute the Jacobian of each operand with respect to its parameters.
`operands_inverse`([free_params])	Compute the inverse of each operand at the current free parameters.
`reset_intermediates`()	Clear the intermediate caches of this operator and its operands.
`resolve_dim`(n)	Resolve a matrix dimension from an integer or a vector of levels.
`set_intermediates`(params, intermediates)	Cache intermediate computation results keyed by the parameter values.
`set_param_specs`(key, *[, fixed, default, trans])	Update the fields of one or more parameter specifications in place.
`trans_grad`([free_params])	Compute the element-wise derivative of the free parameter transforms.
`tree`([free_params])	Evaluate this operator and every nested operand, returning each result keyed by its path.

Attributes

`fixed_param_defaults`	Fixed parameter defaults.
`fixed_param_index`	Index of fixed parameters.
`fixed_param_names`	Fixed parameter names.
`fixed_param_trans`	Transforms for fixed parameters.
`free_param_defaults`	Free parameter defaults.
`free_param_index`	Index of free parameters.
`free_param_names`	Free parameter names.
`free_param_trans`	Transforms for free parameters.
`num_fixed_params`	Total number of fixed parameters.
`num_free_params`	Total number of free parameters.
`num_params`	Total number of parameters.
`operands`	Mapping from operand names to operand matrices or tensors.
`param_defaults`	Parameter defaults.
`param_names`	Parameter names.
`param_specs`	Parameter specifications, returned as stored rather than copied.
`param_trans`	Parameter transforms.
`repr_dict`	Key-value pairs used to build the string representation.
`shape`	Output matrix shape.
`grad_mode`	Gradient computation mode.
`jacobian_method`	Jacobian method used by `auto_grad()`, one of `"jacrev"`, `"jacfwd"`, or `"jacobian"`.
`jacobian_chunk_size`	Number of outputs held per batch when `auto_grad()` differentiates with `"jacrev"`, or `None` to compute the Jacobian in a single batch.
`cache`	Whether intermediate computation results are cached, toggled by `enable_cache()` and `disable_cache()`.

__call__(free_params=None)[source]¶

Construct the matrix from a flat parameter tensor.

Must be implemented by subclasses. Implementations should convert free_params via build_params() to validate, include fixed parameters, and apply transforms before any computation.

Parameters:: free_params (torch.Tensor or dict) – Flat 1D parameter tensor or parameter dictionary. If omitted, default values are used. Default: None.
Returns:: Constructed matrix of shape shape.
Return type:: torch.Tensor

manual_grad(free_params=None)[source]¶

Compute the Jacobian of __call__() with respect to trainable parameters using a closed-form analytic expression.

Applies the product rule to \(\symbf{V} = \symbf{Z} \symbf{G} \symbf{Z}^\top\):

With respect to \(\theta_{\symbf{Z}}\): \(\frac{\partial \symbf{V}}{\partial \theta} = \frac{\partial \symbf{Z}}{\partial \theta} \symbf{G} \symbf{Z}^\top + \symbf{Z} \symbf{G} \frac{\partial \symbf{Z}^\top}{\partial \theta}\) (two terms because \(\symbf{Z}\) appears twice).
With respect to \(\theta_{\symbf{G}}\): \(\frac{\partial \symbf{V}}{\partial \theta} = \symbf{Z} \frac{\partial \symbf{G}}{\partial \theta} \symbf{Z}^\top\) (linear in \(\symbf{G}\)).

Per-operand Jacobians from operands_grad() are propagated through the same structure.

Parameters:

free_params (torch.Tensor or dict) – Flat 1D parameter tensor or parameter dictionary. If omitted, default values are used. Default: None.

Returns:

(grad, grad_names), where grad is a 3D tensor of shape (num_free_params, *shape) and grad_names is a list of the corresponding parameter names. Returns (None, []) if all parameters are fixed.

Return type:

tuple

Raises:

TypeError – If free_params is not a Torch tensor.
ValueError – If free_params is not a 1D tensor or has the wrong length, or if free_params is a dict with missing or unexpected keys.

Example:

import torch
from torch_openreml.covariance import DummyMatrix, DiagonalMatrix, CovariancePropagation

z = DummyMatrix(["a", "b", "c", "a"])
z()

tensor([[1., 0., 0.],
        [0., 1., 0.],
        [0., 0., 1.],
        [1., 0., 0.]])

g = DiagonalMatrix(3)
op = CovariancePropagation(z=z, g=g)
free_params = torch.tensor([0.0, 0.5, 1.0])
grad, grad_names = op.manual_grad(free_params)
grad

tensor([[[ 2.0000,  0.0000,  0.0000,  2.0000],
         [ 0.0000,  0.0000,  0.0000,  0.0000],
         [ 0.0000,  0.0000,  0.0000,  0.0000],
         [ 2.0000,  0.0000,  0.0000,  2.0000]],

        [[ 0.0000,  0.0000,  0.0000,  0.0000],
         [ 0.0000,  5.4366,  0.0000,  0.0000],
         [ 0.0000,  0.0000,  0.0000,  0.0000],
         [ 0.0000,  0.0000,  0.0000,  0.0000]],

        [[ 0.0000,  0.0000,  0.0000,  0.0000],
         [ 0.0000,  0.0000,  0.0000,  0.0000],
         [ 0.0000,  0.0000, 14.7781,  0.0000],
         [ 0.0000,  0.0000,  0.0000,  0.0000]]])

grad_names

['g/sigma^2_0', 'g/sigma^2_1', 'g/sigma^2_2']