causalexplain.estimators.notears package

Submodules

class LBFGSBScipy(params)

Bases: Optimizer

Wrap L-BFGS-B algorithm, using scipy routines.

Courtesy: Arthur Mensch’s gist https://gist.github.com/arthurmensch/c55ac413868550f89225a0b9212aa4cd

Methods

add_param_group(param_group)	Add a param group to the Optimizer s param_groups.
load_state_dict(state_dict)	Load the optimizer state.
register_load_state_dict_post_hook(hook[, ...])	Register a load_state_dict post-hook which will be called after load_state_dict() is called. It should have the following signature::.
register_load_state_dict_pre_hook(hook[, ...])	Register a load_state_dict pre-hook which will be called before load_state_dict() is called. It should have the following signature::.
register_state_dict_post_hook(hook[, prepend])	Register a state dict post-hook which will be called after state_dict() is called.
register_state_dict_pre_hook(hook[, prepend])	Register a state dict pre-hook which will be called before state_dict() is called.
register_step_post_hook(hook)	Register an optimizer step post hook which will be called after optimizer step.
register_step_pre_hook(hook)	Register an optimizer step pre hook which will be called before optimizer step.
state_dict()	Return the state of the optimizer as a dict.
step(closure)	Performs a single optimization step.
zero_grad([set_to_none])	Reset the gradients of all optimized torch.Tensor s.

OptimizerPostHook
OptimizerPreHook
profile_hook_step

__init__(params)

step(closure)

Performs a single optimization step.

Parameters:

closure (callable) – A closure that reevaluates the model and returns the loss.

main()

notears_linear(X, lambda1, loss_type, max_iter=100, h_tol=1e-08, rho_max=1e+16, w_threshold=0.3)

Solve min_W L(W; X) + lambda1 ‖W‖_1 s.t. h(W) = 0 using augmented Lagrangian.

Parameters:

• X (np.ndarray) – [n, d] sample matrix

• lambda1 (float) – l1 penalty parameter

• loss_type (str) – l2, logistic, poisson

• max_iter (int) – max num of dual ascent steps

• h_tol (float) – exit if |h(w_est)| <= htol

• rho_max (float) – exit if rho >= rho_max

• w_threshold (float) – drop edge if |weight| < threshold

Returns:

[d, d] estimated DAG

Return type:

W_est (np.ndarray)

class LocallyConnected(num_linear, input_features, output_features, bias=True)

Bases: Module

Local linear layer, i.e. Conv1dLocal() with filter size 1.

Parameters:

• num_linear – num of local linear layers, i.e.

• in_features – m1

• out_features – m2

• bias – whether to include bias or not

Shape:

• Input: [n, d, m1]

• Output: [n, d, m2]

weight

[d, m1, m2]

bias

[d, m2]

Methods

add_module(name, module)	Add a child module to the current module.
apply(fn)	Apply fn recursively to every submodule (as returned by .children()) as well as self.
bfloat16()	Casts all floating point parameters and buffers to bfloat16 datatype.
buffers([recurse])	Return an iterator over module buffers.
children()	Return an iterator over immediate children modules.
compile(*args, **kwargs)	Compile this Module's forward using torch.compile().
cpu()	Move all model parameters and buffers to the CPU.
cuda([device])	Move all model parameters and buffers to the GPU.
double()	Casts all floating point parameters and buffers to double datatype.
eval()	Set the module in evaluation mode.
extra_repr()	Return the extra representation of the module.
float()	Casts all floating point parameters and buffers to float datatype.
forward(input)	Define the computation performed at every call.
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_extra_state()	Return any extra state to include in the module's state_dict.
get_parameter(target)	Return the parameter given by target if it exists, otherwise throw an error.
get_submodule(target)	Return the submodule given by target if it exists, otherwise throw an error.
half()	Casts all floating point parameters and buffers to half datatype.
ipu([device])	Move all model parameters and buffers to the IPU.
load_state_dict(state_dict[, strict, assign])	Copy parameters and buffers from state_dict into this module and its descendants.
modules()	Return an iterator over all modules in the network.
mtia([device])	Move all model parameters and buffers to the MTIA.
named_buffers([prefix, recurse, ...])	Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
named_children()	Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
named_modules([memo, prefix, remove_duplicate])	Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
named_parameters([prefix, recurse, ...])	Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
parameters([recurse])	Return an iterator over module parameters.
register_backward_hook(hook)	Register a backward hook on the module.
register_buffer(name, tensor[, persistent])	Add a buffer to the module.
register_forward_hook(hook, *[, prepend, ...])	Register a forward hook on the module.
register_forward_pre_hook(hook, *[, ...])	Register a forward pre-hook on the module.
register_full_backward_hook(hook[, prepend])	Register a backward hook on the module.
register_full_backward_pre_hook(hook[, prepend])	Register a backward pre-hook on the module.
register_load_state_dict_post_hook(hook)	Register a post-hook to be run after module's load_state_dict() is called.
register_load_state_dict_pre_hook(hook)	Register a pre-hook to be run before module's load_state_dict() is called.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Add a parameter to the module.
register_state_dict_post_hook(hook)	Register a post-hook for the state_dict() method.
register_state_dict_pre_hook(hook)	Register a pre-hook for the state_dict() method.
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
set_extra_state(state)	Set extra state contained in the loaded state_dict.
set_submodule(target, module[, strict])	Set the submodule given by target if it exists, otherwise throw an error.
share_memory()	See torch.Tensor.share_memory_().
state_dict(*args[, destination, prefix, ...])	Return a dictionary containing references to the whole state of the module.
to(*args, **kwargs)	Move and/or cast the parameters and buffers.
to_empty(*, device[, recurse])	Move the parameters and buffers to the specified device without copying storage.
train([mode])	Set the module in training mode.
type(dst_type)	Casts all parameters and buffers to dst_type.
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

__call__
reset_parameters

__init__(num_linear, input_features, output_features, bias=True)

Initialize internal Module state, shared by both nn.Module and ScriptModule.

reset_parameters()

forward(input)

Define the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.

extra_repr()

Return the extra representation of the module.

To print customized extra information, you should re-implement this method in your own modules. Both single-line and multi-line strings are acceptable.

main()

least_squares_loss(W, data, cov, d, n)

least_squares_loss_grad(W, data, cov, d, n)

least_squares_loss_cov(W, data, cov, d, n)

least_squares_loss_cov_grad(W, data, cov, d, n)

run(variant, data, loss, loss_grad, **kwargs)

notears_standard(data, loss, loss_grad, c=0.25, r=10.0, e=1e-08, rnd_W_init=False, output_all_progress=False, verbose=False)

Runs NOTEARS algorithm.

Parameters:

• data (np.array) – n x d data matrix with n samples, d variables

• c (float) – minimum rate of progress, c in (0,1)

• r (float) – penalty growth rate, r > 1

• e (float) – optimation accuracy, e > 0 (acyclicity stopping criteria)

• loss (function) – loss function

• loss_grad (function) – gradient of the loss function

• rnd_W_init (bool) – initialize W to std. normal random matrix, rather than zero matrix

• output_all_progress (bool) – return all intermediate values of W, rather than

• value (just the final)

• verbose (bool) – print optimization information

Returns:

{ ‘h’: acyclicity of output,

’loss’: loss of output, ‘W’: resulting optimized adjacency matrix}

Return type:

dict

NOTEARS

3. Original code from xunzheng/notears

class NOTEARS(name, loss=<function least_squares_loss>, loss_grad=<function least_squares_loss_grad>, c=0.25, r=10.0, e=1e-08, rnd_W_init=False, verbose=False)

Bases: object

Methods

notears_standard(data[, return_all_progress])

Runs NOTEARS algorithm.

fit
fit_predict
predict

__init__(name, loss=<function least_squares_loss>, loss_grad=<function least_squares_loss_grad>, c=0.25, r=10.0, e=1e-08, rnd_W_init=False, verbose=False)

notears_standard(data, return_all_progress=False)

Runs NOTEARS algorithm.

Parameters:

• data (np.array) – n x d data matrix with n samples, d variables

• c (float) – minimum rate of progress, c in (0,1)

• r (float) – penalty growth rate, r > 1

• e (float) – optimation accuracy, e > 0 (acyclicity stopping criteria)

• loss (function) – loss function

• loss_grad (function) – gradient of the loss function

• rnd_W_init (bool) – initialize W to std. normal random matrix, rather than zero matrix

• output_all_progress (bool) – return all intermediate values of W, rather than

• value (just the final)

Returns:

{ ‘h’: acyclicity of output,

’loss’: loss of output, ‘W’: resulting optimized adjacency matrix}

Return type:

dict

fit(X, **kwargs)

predict(ref_graph=None, threshold=0.1)

fit_predict(train, test, ref_graph=None, threshold=0.1, **kwargs)

main(dataset_name, input_path='/Users/renero/phd/data/', output_path='/Users/renero/phd/output/', save=False)

class TraceExpm(*args, **kwargs)

Bases: Function

Attributes:

dirty_tensors

materialize_grads

metadata

needs_input_grad

next_functions

non_differentiable

requires_grad

saved_for_forward

saved_tensors

saved_variables

to_save

Methods

__call__(*args, **kwargs)	Call self as a function.
backward(ctx, grad_output)	Define a formula for differentiating the operation with backward mode automatic differentiation.
forward(ctx, input)	Define the forward of the custom autograd Function.
jvp(ctx, *grad_inputs)	Define a formula for differentiating the operation with forward mode automatic differentiation.
mark_dirty(*args)	Mark given tensors as modified in an in-place operation.
mark_non_differentiable(*args)	Mark outputs as non-differentiable.
save_for_backward(*tensors)	Save given tensors for a future call to backward().
save_for_forward(*tensors)	Save given tensors for a future call to jvp().
set_materialize_grads(value)	Set whether to materialize grad tensors.
setup_context(ctx, inputs, output)	There are two ways to define the forward pass of an autograd.Function.
vjp(ctx, *grad_outputs)	Define a formula for differentiating the operation with backward mode automatic differentiation.
vmap(info, in_dims, *args)	Define the behavior for this autograd.Function underneath torch.vmap().

apply
mark_shared_storage
maybe_clear_saved_tensors
name
register_hook
register_prehook

static forward(ctx, input)

Define the forward of the custom autograd Function.

This function is to be overridden by all subclasses. There are two ways to define forward:

Usage 1 (Combined forward and ctx):

@staticmethod
def forward(ctx: Any, *args: Any, **kwargs: Any) -> Any:
    pass

• It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

• See combining-forward-context for more details

Usage 2 (Separate forward and ctx):

@staticmethod
def forward(*args: Any, **kwargs: Any) -> Any:
    pass

@staticmethod
def setup_context(ctx: Any, inputs: Tuple[Any, ...], output: Any) -> None:
    pass

• The forward no longer accepts a ctx argument.

• Instead, you must also override the torch.autograd.Function.setup_context() staticmethod to handle setting up the ctx object. output is the output of the forward, inputs are a Tuple of inputs to the forward.

• See extending-autograd for more details

The context can be used to store arbitrary data that can be then retrieved during the backward pass. Tensors should not be stored directly on ctx (though this is not currently enforced for backward compatibility). Instead, tensors should be saved either with ctx.save_for_backward() if they are intended to be used in backward (equivalently, vjp) or ctx.save_for_forward() if they are intended to be used for in jvp.

static backward(ctx, grad_output)

Define a formula for differentiating the operation with backward mode automatic differentiation.

This function is to be overridden by all subclasses. (Defining this function is equivalent to defining the vjp function.)

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computed w.r.t. the output.

main()

set_random_seed(seed)

is_dag(W)

simulate_dag(d, s0, graph_type)

Simulate random DAG with some expected number of edges.

Parameters:

• d (int) – num of nodes

• s0 (int) – expected num of edges

• graph_type (str) – ER, SF, BP

Returns:

[d, d] binary adj matrix of DAG

Return type:

B (np.ndarray)

simulate_parameter(B, w_ranges=((-2.0, -0.5), (0.5, 2.0)))

Simulate SEM parameters for a DAG.

Parameters:

• B (np.ndarray) – [d, d] binary adj matrix of DAG

• w_ranges (tuple) – disjoint weight ranges

Returns:

[d, d] weighted adj matrix of DAG

Return type:

W (np.ndarray)

simulate_linear_sem(W, n, sem_type, noise_scale=None)

Simulate samples from linear SEM with specified type of noise.

For uniform, noise z ~ uniform(-a, a), where a = noise_scale.

Parameters:

• W (np.ndarray) – [d, d] weighted adj matrix of DAG

• n (int) – num of samples, n=inf mimics population risk

• sem_type (str) – gauss, exp, gumbel, uniform, logistic, poisson

• noise_scale (np.ndarray) – scale parameter of additive noise, default all ones

Returns:

[n, d] sample matrix, [d, d] if n=inf

Return type:

X (np.ndarray)

simulate_nonlinear_sem(B, n, sem_type, noise_scale=None)

Simulate samples from nonlinear SEM.

Parameters:

• B (np.ndarray) – [d, d] binary adj matrix of DAG

• n (int) – num of samples

• sem_type (str) – mlp, mim, gp, gp-add

• noise_scale (np.ndarray) – scale parameter of additive noise, default all ones

Returns:

[n, d] sample matrix

Return type:

X (np.ndarray)

count_accuracy(B_true, B_est)

Compute various accuracy metrics for B_est.

true positive = predicted association exists in condition in correct direction reverse = predicted association exists in condition in opposite direction false positive = predicted association does not exist in condition

Parameters:

• B_true (np.ndarray) – [d, d] ground truth graph, {0, 1}

• B_est (np.ndarray) – [d, d] estimate, {0, 1, -1}, -1 is undirected edge in CPDAG

Returns:

(reverse + false positive) / prediction positive tpr: (true positive) / condition positive fpr: (reverse + false positive) / condition negative shd: undirected extra + undirected missing + reverse nnz: prediction positive

Return type:

fdr

threshold_output(W, desired_edges=None, verbose=False)

generate_random_dag(num_nodes, num_edges, probabilistic=False, edge_coefficient_range=[0.5, 2.0])

simulate_from_dag_lg(tam, n_sample, mean=0, variance=1)

compare_graphs_undirected(true_graph, estimated_graph)

compare_graphs_precision(x)

compare_graphs_recall(x)

compare_graphs_specificity(x)

Module contents