torch_openreml.covariance.AR1Matrix

class torch_openreml.covariance.AR1Matrix(n, param_names=None, trans=None, no_grad_index=None)

Bases: Matrix

First-order autoregressive covariance matrix.

\[\symbf{V}_{ij} = \sigma^2 \rho^{|i - j|}\]

Covariance decays geometrically with the lag between observations. The variance \(\sigma^2 > 0\) is enforced by TransformExpPow2 and the correlation \(\rho \in (-1, 1)\) is enforced by a sigmoid scaled to \((-1, 1)\) by default.

Initialize an AR(1) covariance matrix of size n x n.

Parameters:

• n (int) – Matrix dimension.

• param_names (list of str, optional) – Names for the variance and correlation parameters. Defaults to ["sigma^2", "rho"].

• trans (list of Transform, optional) – Transforms applied to each parameter. Defaults to TransformExpPow2 for \(\sigma^2\) and a sigmoid scaled to \((-1, 1)\) for \(\rho\).

• no_grad_index (list of int, optional) – Indices of parameters to exclude from gradient computation.

Example:

import torch
from torch_openreml.covariance import AR1Matrix

mat = AR1Matrix(4)
params = torch.tensor([0.5, 0.0])
mat(params)

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

Methods

__call__(params)	Construct the matrix from a flat parameter tensor.
auto_grad(params)	Compute the Jacobian of build() with respect to trainable parameters using automatic differentiation.
check_params(params)	Validate a parameter tensor and return its device and dtype.
from_param_dict(param_dict)	Extract parameter tensors from a dictionary into a flat 1D tensor.
get_intermediates(params)	Retrieve cached intermediate computation results if still valid.
grad(params)	Compute the Jacobian of __call__() with respect to trainable parameters.
manual_grad(params)	Compute the Jacobian of __call__() with respect to trainable parameters using a closed-form analytic expression.
map_theta_to_dv(theta)	An interface compatible with torch_openreml.REML that maps parameters to the matrix Jacobian.
map_theta_to_v(theta)	An interface compatible with torch_openreml.REML that maps parameters to a matrix.
reset_intermediates()	Clear the intermediate computation cache.
set_intermediates(params, intermediates)	Cache intermediate computation results keyed by parameter hash.
set_no_grad([index, param_name])	Set the indices of parameters to exclude from gradient computation.
to_param_dict(params)	Convert a flat parameter tensor to a parameter dictionary.
trans_grad(params)	Compute the element-wise derivative of the parameter transforms.
trans_params(params)	Apply parameter transforms to a flat parameter tensor.

Attributes

no_grad_index	Indices of parameters excluded from gradient computation.
num_params	Total number of parameters.
param_names	Ordered parameter names.
repr_dict	Key-value pairs used to build the string representation.
shape	Output matrix shape.
trans	Parameter transforms.

__call__(params)

Construct the matrix from a flat parameter tensor.

Must be implemented by subclasses. Implementations should convert params via from_param_dict() or to_param_dict(), then call check_params() to validate and trans_params() to apply transforms before any computation.

Parameters:

params (torch.Tensor or dict) – Flat 1D parameter tensor or parameter dictionary.

Returns:

Constructed matrix of shape shape.

Return type:

torch.Tensor

manual_grad(params)

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

Parameters:

params (torch.Tensor or dict) – Flat 1D parameter tensor or parameter dictionary.

Returns:

(grad, grad_names), where grad is a 3D tensor of shape (num_params - len(no_grad_index), *shape) and grad_names is a list of the corresponding parameter names. Returns (None, []) if all parameters are excluded from gradient computation.

Return type:

tuple