LogLikelihood

class LogLikelihood

Bases: object

static categorical(predicted=None, observed=None, negative=True, **kwargs)

Compute the log likelihood of the predicted values given the observed values for categorical data.

Categorical(y|p) = p_y

Parameters:

predictedarray_like

The predicted values. It must have the same shape as observed. See Notes for more details.

observedarray_like

The observed values. It must have the same shape as predicted. See Notes for more details.

negativebool, optional

Flag indicating whether to return the negative log likelihood.

Returns:

float

The log likelihood or negative log likelihood.

Notes

predicted and observed must have the same shape. observed is a vector of integers starting from 0 (first possible response), where each integer corresponds to the observed value. If there are two choice options, then observed would have a shape of (n, 2) and predicted would have a shape of (n, 2). On each row of observed, the array would have a 1 in the column corresponding to the observed value and a 0 in the other column.

Examples

>>> import numpy as np
>>> observed = np.array([0, 1, 0, 1])
>>> predicted = np.array([[0.7, 0.3], [0.3, 0.7], [0.6, 0.4], [0.4, 0.6]])
>>> LogLikelihood.categorical(predicted, observed)
1.7350011354094463

static bernoulli(predicted=None, observed=None, negative=True, **kwargs)

Compute the log likelihood of the predicted values given the observed values for Bernoulli data.

Bernoulli(y|p) = p if y = 1 and 1 - p if y = 0

Parameters:

predictedarray_like

The predicted values. It must have the same shape as observed. See Notes for more details.

observedarray_like

The observed values. It must have the same shape as predicted. See Notes for more details.

negativebool, optional

Flag indicating whether to return the negative log likelihood.

Returns:

float

The summed log likelihood or negative log likelihood.

Notes

predicted and observed must have the same shape. observed is a binary variable, so it can only take the values 0 or 1. predicted must be a value between 0 and 1. Values are clipped to avoid log(0) and log(1). If we encounter any non-finite values, we set any log likelihood to the value of np.log(1e-100).

Examples

>>> import numpy as np
>>> observed = np.array([1, 0, 1, 0])
>>> predicted = np.array([0.7, 0.3, 0.6, 0.4])
>>> LogLikelihood.bernoulli(predicted, observed)
1.7350011354094463

static continuous(predicted, observed, negative=True, **kwargs)

Compute the log likelihood of the predicted values given the observed values for continuous data.

Parameters:

predictedarray_like

The predicted values.

observedarray_like

The observed values.

negativebool, optional

Flag indicating whether to return the negative log likelihood.

Returns:

float

The summed log likelihood or negative log likelihood.

Examples

>>> import numpy as np
>>> observed = np.array([1, 0, 1, 0])
>>> predicted = np.array([0.7, 0.3, 0.6, 0.4])
>>> LogLikelihood.continuous(predicted, observed)
1.7350011354094463

static multinomial(predicted, observed, negative=True, clip=1e-10, **kwargs)

Compute the log likelihood of the predicted values given the observed values for multinomial data.

Parameters:

predictedarray_like

The predicted values.

observedarray_like

The observed values.

negativebool, optional

Flag indicating whether to return the negative log likelihood.

Returns:

float

The summed log likelihood or negative summed log likelihood.

Examples

>>> # Sample data
>>> predicted = np.array([[0.2, 0.5, 0.3], [0.1, 0.7, 0.2]])
>>> observed = np.array([[2, 5, 3], [1, 7, 2]])

>>> # Calculate log likelihood
>>> ll_float = LogLikelihood.multinomial(predicted, observed)
>>> print("Log Likelihood (multinomial):", ll)
Log Likelihood (multinomial): 4.596597454123483

static product(predicted, observed, negative=True, clip=1e-10, **kwargs)

Compute the log likelihood of the predicted values given the observed values for continuous data, according to the following equation:

likelihood = sum(observed * log(predicted))

Parameters:

predictedarray_like

The predicted values.

observedarray_like

The observed values.

negativebool, optional

Flag indicating whether to return the negative log likelihood.

Returns:

float

The summed log likelihood or negative log likelihood.

Examples

>>> # Sample data
>>> predicted = np.array([[0.2, 0.5, 0.3], [0.1, 0.7, 0.2]])
>>> observed = np.array([[2, 5, 3], [1, 7, 2]])

>>> # Calculate log likelihood
>>> ll_float = LogLikelihood.product(predicted, observed)
>>> print("Log Likelihood :", ll_float)
Log Likelihood : 18.314715666079106