tfp.substrates.numpy.glm.GammaExp

Gamma(concentration=1, rate=1 / mean) where mean = exp(X @ w)).

Inherits From: ExponentialFamily

tfp.substrates.numpy.glm.GammaExp(
    concentration=1.0, name=None
)

name Python str used as TF namescope for ops created by member functions. Default value: None (i.e., the subclass name).

name

trainable_variables

variables

Methods

as_distribution

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as_distribution(
    predicted_linear_response, name=None
)

Builds a mean parameterized TFP Distribution from linear response.

Example:

model = tfp.glm.Bernoulli()
r = tfp.glm.compute_predicted_linear_response(x, w)
yhat = model.as_distribution(r)

Args
predicted_linear_response response-shaped Tensor representing linear predictions based on new model_coefficients, i.e., tfp.glm.compute_predicted_linear_response( model_matrix, model_coefficients, offset).
name Python str used as TF namescope for ops created by member functions. Default value: None (i.e., 'log_prob').

Returns
model tfp.distributions.Distribution-like object with mean parameterized by predicted_linear_response.

log_prob

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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.linalg.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.

__call__

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__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.linalg.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.