Identity Flow¶

Implements a simple indentity bijector.

\[f(x) = y\]

Amount of parameters: \(0\)

Inverse Log Det Jacobian (ILDJ):

\[\log(\det(\mathbf{J}^{-1})) = 0\]

class cde.density_estimator.normalizing_flows.IdentityFlow(params, n_dims, name='IdentityFlow')[source]¶

Implements the identity bijector y = x

dtype¶: dtype of `Tensor`s transformable by this distribution.

event_ndims¶: Returns then number of event dimensions this bijector operates on.

forward(x, name='forward')¶

Returns the forward Bijector evaluation, i.e., X = g(Y).

Parameters

x – Tensor. The input to the “forward” evaluation.
name – The name to give this op.

Returns

Tensor.

Raises

TypeError – if self.dtype is specified and x.dtype is not self.dtype.
NotImplementedError – if _forward is not implemented.

forward_event_shape(input_shape)¶

Shape of a single sample from a single batch as a TensorShape.

Same meaning as forward_event_shape_tensor. May be only partially defined.

Parameters

input_shape – TensorShape indicating event-portion shape passed into forward function.

Returns

TensorShape indicating event-portion shape: after applying forward. Possibly unknown.

Return type

forward_event_shape_tensor

forward_event_shape_tensor(input_shape, name='forward_event_shape_tensor')¶

Shape of a single sample from a single batch as an int32 1D Tensor.

Parameters

input_shape – Tensor, int32 vector indicating event-portion shape passed into forward function.
name – name to give to the op

Returns

Tensor, int32 vector indicating: event-portion shape after applying forward.

Return type

forward_event_shape_tensor

forward_log_det_jacobian(x, name='forward_log_det_jacobian')¶

Returns both the forward_log_det_jacobian.

Parameters

x – Tensor. The input to the “forward” Jacobian evaluation.
name – The name to give this op.

Returns

Tensor, if this bijector is injective.: If not injective this is not implemented.

Raises

TypeError – if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError – if neither _forward_log_det_jacobian nor {_inverse, _inverse_log_det_jacobian} are implemented, or this is a non-injective bijector.

static get_param_size(n_dims)[source]¶

Parameters: n_dims – The dimension of the distribution to be transformed by the flow. For this flow it’s irrelevant
Returns: (int) The dimension of the parameter space for the flow. This flow doesn’t have parameters, hence it’s always 0

graph_parents¶: Returns this Bijector’s graph_parents as a Python list.

inverse(y, name='inverse')¶

Returns the inverse Bijector evaluation, i.e., X = g^{-1}(Y).

Parameters

y – Tensor. The input to the “inverse” evaluation.
name – The name to give this op.

Returns

Tensor, if this bijector is injective.: If not injective, returns the k-tuple containing the unique k points (x1, …, xk) such that g(xi) = y.

Raises

TypeError – if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError – if _inverse is not implemented.

inverse_event_shape(output_shape)¶

Shape of a single sample from a single batch as a TensorShape.

Same meaning as inverse_event_shape_tensor. May be only partially defined.

Parameters

output_shape – TensorShape indicating event-portion shape passed into inverse function.

Returns

TensorShape indicating event-portion shape: after applying inverse. Possibly unknown.

Return type

inverse_event_shape_tensor

inverse_event_shape_tensor(output_shape, name='inverse_event_shape_tensor')¶

Shape of a single sample from a single batch as an int32 1D Tensor.

Parameters

output_shape – Tensor, int32 vector indicating event-portion shape passed into inverse function.
name – name to give to the op

Returns

Tensor, int32 vector indicating: event-portion shape after applying inverse.

Return type

inverse_event_shape_tensor

inverse_log_det_jacobian(y, name='inverse_log_det_jacobian')¶

Returns the (log o det o Jacobian o inverse)(y).

Mathematically, returns: log(det(dX/dY))(Y). (Recall that: X=g^{-1}(Y).)

Note that forward_log_det_jacobian is the negative of this function, evaluated at g^{-1}(y).

Parameters

y – Tensor. The input to the “inverse” Jacobian evaluation.
name – The name to give this op.

Returns

Tensor, if this bijector is injective.: If not injective, returns the tuple of local log det Jacobians, log(det(Dg_i^{-1}(y))), where g_i is the restriction of g to the ith partition Di.

Raises

TypeError – if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError – if _inverse_log_det_jacobian is not implemented.

is_constant_jacobian¶

Returns true iff the Jacobian is not a function of x.

Note: Jacobian is either constant for both forward and inverse or neither.

Returns: Python bool.
Return type: is_constant_jacobian

name¶: Returns the string name of this Bijector.

validate_args¶: Returns True if Tensor arguments will be validated.