Predictive distribution#

The predictive distribution is the component of the probabilistic model responsible for the computation of predictive statistics. We support a classification predictive for classification and a regression predictive for regression. Please find their references below.

class fortuna.output_calib_model.predictive.classification.ClassificationPredictive(output_calib_manager, prob_output_layer)[source]#

Abstract predictive distribution. It characterizes the distribution of the target variable given the calibrated outputs. It can be see as \(p(y|\omega)\), where \(y\) is a target variable and \(\omega\) a calibrated output.

entropy(outputs, calibrated=True, **kwargs)#

Estimate the entropy of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (jnp.ndarray) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated mean for each output.

Return type:

jnp.ndarray

log_prob(outputs, targets, calibrated=True, **kwargs)#

Evaluate the log-probability density function (a.k.a. log-pdf) given the outputs and target data.

Parameters:

  • outputs (Array) – Calibrated outputs.

  • targets (Array) – Target data points.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

An evaluation of the log-pdf for each data point.

Return type:

jnp.ndarray

mean(outputs, calibrated=True, **kwargs)[source]#

Estimate the mean of the one-hot encoded target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (Array) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated mean for each output.

Return type:

jnp.ndarray

mode(outputs, calibrated=True, **kwargs)[source]#

Estimate the mode of the one-hot encoded target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (Array) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated mode for each output.

Return type:

jnp.ndarray

property rng: RandomNumberGenerator#

Invoke the random number generator object.

Return type:

The random number generator object.

sample(n_samples, outputs, rng=None, calibrated=True, **kwargs)#

Sample target variables for each outputs.

Parameters:

  • n_samples (int) – The number of target samples to draw for each of the outputs.

  • outputs (Array) – Calibrated outputs.

  • rng (Optional[PRNGKeyArray]) – A random number generator. If not passed, this will be taken from the attributes of this class.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

Samples of the target variable for each output.

Return type:

jnp.ndarray

std(outputs, variances=None, calibrated=True)[source]#

Estimate the standard deviation of the one-hot encoded target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (jnp.ndarray) – Model outputs.

  • variances (Optional[jnp.ndarray]) – Variance for each output.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated standard deviation for each output.

Return type:

jnp.ndarray

variance(outputs, calibrated=True, **kwargs)[source]#

Estimate the variance of the one-hot encoded target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (jnp.ndarray) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated variance for each output.

Return type:

jnp.ndarray

class fortuna.output_calib_model.predictive.regression.RegressionPredictive(output_calib_manager, prob_output_layer)[source]#

Abstract predictive distribution. It characterizes the distribution of the target variable given the calibrated outputs. It can be see as \(p(y|\omega)\), where \(y\) is a target variable and \(\omega\) a calibrated output.

credible_interval(outputs, n_samples=30, error=0.05, interval_type='two-tailed', rng=None, calibrated=True)[source]#

Estimate a credible interval of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (Array) – Model outputs.

  • n_samples (int) – Number of target samples to draw for each output.

  • error (float) – The interval error. This must be a number between 0 and 1, extremes included. For example, error=0.05 corresponds to a 95% level of credibility.

  • interval_type (str) – The interval type. We support “two-tailed” (default), “right-tailed” and “left-tailed”.

  • rng (Optional[PRNGKeyArray]) – A random number generator. If not passed, this will be taken from the attributes of this class.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated credible interval for each output.

Return type:

jnp.ndarray

entropy(outputs, calibrated=True, **kwargs)#

Estimate the entropy of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (jnp.ndarray) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated mean for each output.

Return type:

jnp.ndarray

log_prob(outputs, targets, calibrated=True, **kwargs)#

Evaluate the log-probability density function (a.k.a. log-pdf) given the outputs and target data.

Parameters:

  • outputs (Array) – Calibrated outputs.

  • targets (Array) – Target data points.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

An evaluation of the log-pdf for each data point.

Return type:

jnp.ndarray

mean(outputs, calibrated=True, **kwargs)#

Estimate the mean of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (Array) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated mean for each output.

Return type:

jnp.ndarray

mode(outputs, calibrated=True, **kwargs)#

Estimate the mode of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (Array) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated mode for each output.

Return type:

jnp.ndarray

quantile(q, outputs, n_samples=30, rng=None, calibrated=True)[source]#

Estimate the quantile of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • q (Union[float, Array, List]) – Quantile(s) to estimate.

  • outputs (jnp.ndarray) – Model outputs.

  • n_samples (Optional[int]) – Number of target samples to draw when computing quantiles.

  • rng (Optional[PRNGKeyArray]) – A random number generator.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated quantiles for each output.

Return type:

jnp.ndarray

property rng: RandomNumberGenerator#

Invoke the random number generator object.

Return type:

The random number generator object.

sample(n_samples, outputs, rng=None, calibrated=True, **kwargs)#

Sample target variables for each outputs.

Parameters:

  • n_samples (int) – The number of target samples to draw for each of the outputs.

  • outputs (Array) – Calibrated outputs.

  • rng (Optional[PRNGKeyArray]) – A random number generator. If not passed, this will be taken from the attributes of this class.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

Samples of the target variable for each output.

Return type:

jnp.ndarray

std(outputs, variances=None, calibrated=True)#

Estimate the standard deviation of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (jnp.ndarray) – Model outputs.

  • variances (Optional[jnp.ndarray]) – Variance for each output.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated standard deviation for each output.

Return type:

jnp.ndarray

variance(outputs, calibrated=True, **kwargs)#

Estimate the variance of the target variable given the output, with respect to the predictive distribution.

Parameters:

  • outputs (jnp.ndarray) – Model outputs.

  • calibrated (bool) – Whether the outputs should be calibrated when computing this method. If calibrated is set to True, the model must have been calibrated beforehand.

Returns:

The estimated variance for each output.

Return type:

jnp.ndarray