tfp.glm.ExponentialFamily

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Specifies a mean-value parameterized exponential family.

tfp.glm.ExponentialFamily(
    name=None
)

Subclasses implement exponential-family distribution properties (e.g., log_prob, variance) as a function of a real-value which is transformed via some link function to be interpreted as the distribution's mean. The distribution is parameterized by this mean, i.e., "mean-value parameterized."

Subclasses are typically used to specify a Generalized Linear Model (GLM). A GLM is a generalization of linear regression which enables efficient fitting of log-likelihood losses beyond just assuming Normal noise. See tfp.glm.fit for more details.

Subclasses must implement _as_distribution which does not need to be either "tape-safe" or "variable-safe." (tfp.glm families are however guaranteed to be both tape and variable safe.)

Subclasses may optionally implement _call and _log_prob which otherwise default to:

def _call(self, predicted_linear_response):
  with tf.GradientTape(watch_accessed_variables=False) as tape:
    tape.watch(predicted_linear_response)
    likelihood = self.as_distribution(predicted_linear_response)
    mean = likelihood.mean()
  variance = likelihood.variance()
  grad_mean = tape.gradient(mean, predicted_linear_response)
  return mean, variance, grad_mean

def _log_prob(self, response, predicted_linear_response):
  likelihood = self.as_distribution(predicted_linear_response)
  return likelihood.log_prob(response)

In context of tfp.glm.fit and tfp.glm.fit_sparse, these functions are used to find the best fitting weights for given model matrix ("X") and responses ("Y").

a = tf.Module()
b = tf.Module()
c = tf.Module()
a.b = b
b.c = c
list(a.submodules) == [b, c]
True
list(b.submodules) == [c]
True
list(c.submodules) == []
True

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)

log_prob

View source

log_prob(
    response, predicted_linear_response, name=None
)

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

with_name_scope

@classmethod
with_name_scope(
    method
)

Decorator to automatically enter the module name scope.

class MyModule(tf.Module):
  @tf.Module.with_name_scope
  def __call__(self, x):
    if not hasattr(self, 'w'):
      self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))
    return tf.matmul(x, self.w)

Using the above module would produce tf.Variables and tf.Tensors whose names included the module name:

mod = MyModule()
mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
mod.w
<tf.Variable &#x27;my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>

__call__

View source

__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.