tfp.glm.CustomExponentialFamily

Class CustomExponentialFamily

Inherits From: ExponentialFamily

Constucts GLM from arbitrary distribution and inverse link function.

__init__

__init__(
    distribution_fn,
    linear_model_to_mean_fn,
    is_canonical=False,
    name=None
)

Creates the CustomExponentialFamily.

Args:

  • distribution_fn: Python callable which returns a tf.distribution.Distribution-like instance from a single input representing the distribution's required mean, i.e., mean = linear_model_to_mean_fn(matmul(model_matrix, weights)).
  • linear_model_to_mean_fn: Python callable which returns the distribution's required mean as computed from the predicted linear response, matmul(model_matrix, weights).
  • is_canonical: Python bool indicating that taken together, distribution_fn and linear_model_to_mean_fn imply that the distribution's variance is equivalent to d/dr linear_model_to_mean_fn(r).
  • name: Python str used as TF namescope for ops created by member functions. Default value: None (i.e., the subclass name).

Properties

distribution_fn

is_canonical

Returns True when variance(r) == grad_mean(r) for all r.

linear_model_to_mean_fn

name

Returns TF namescope prefixed to ops created by member functions.

Methods

__call__

__call__(
    predicted_linear_response,
    name=None
)

Computes mean(r), var(mean), d/dr mean(r) for linear response, r.

Here mean and var are the mean and variance of the sufficient statistic, which may not be the same as the mean and variance of the random variable itself. If the distribution's density has the form

p_Y(y) = h(y) Exp[dot(theta, T(y)) - A]

where theta and A are constants and h and T are known functions, then mean and var are the mean and variance of T(Y). In practice, often T(Y) := Y and in that case the distinction doesn't matter.

Args:

  • predicted_linear_response: float-like Tensor corresponding to tf.matmul(model_matrix, weights).
  • name: Python str used as TF namescope for ops created by member functions. Default value: None (i.e., 'call').

Returns:

  • mean: Tensor with shape and dtype of predicted_linear_response representing the distribution prescribed mean, given the prescribed linear-response to mean mapping.
  • variance: Tensor with shape and dtype of predicted_linear_response representing the distribution prescribed variance, given the prescribed linear-response to mean mapping.
  • grad_mean: Tensor with shape and dtype of predicted_linear_response representing the gradient of the mean with respect to the linear-response and given the prescribed linear-response to mean mapping.

log_prob

log_prob(
    response,
    predicted_linear_response,
    name=None
)

Computes D(param=mean(r)).log_prob(response) for linear response, r.

Args:

  • response: float-like Tensor representing observed ("actual") responses.
  • predicted_linear_response: float-like Tensor corresponding to tf.matmul(model_matrix, weights).
  • name: Python str used as TF namescope for ops created by member functions. Default value: None (i.e., 'log_prob').

Returns:

  • log_prob: Tensor with shape and dtype of predicted_linear_response representing the distribution prescribed log-probability of the observed responses.