Error measures

Error measures are callable objects that return some scalar representing the error between a model and an experiment.

Example:

error = pints.SumOfSquaresError(problem)
x = [1,2,3]
fx = error(x)

class pints.ErrorMeasure

Abstract base class for objects that calculate some scalar measure of goodness-of-fit (for a model and a data set), such that a smaller value means a better fit.

ErrorMeasures are callable objects: If e is an instance of an ErrorMeasure class you can calculate the error by calling e(x) where x is a point in parameter space. In PINTS, all parameters must be continuous and real.

All subclasses of ErrorMeasure should provide an implementation of __call__() and n_parameters().

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

Evaluates this error measure, and returns the result plus the partial derivatives of the result with respect to the parameters.

The returned data has the shape (e, e') where e is a scalar value and e' is a sequence of length n_parameters.

This is an optional method that is not always implemented.

n_parameters()

Returns the dimension of the parameter space this measure is defined over.

class pints.MeanSquaredError(problem, weights=None)

Calculates the mean square error:

\[f = \sum _i^n \frac{(y_i - x_i)^2}{n},\]

where \(y\) is the data, \(x\) the model output and \(n\) is the total number of data points.

Extends ProblemErrorMeasure.

Parameters:

• problem – A pints.SingleOutputProblem or pints.MultiOutputProblem.

• weights – An optional sequence of (float) weights, exactly one per problem output. If given, the error in each individual output will be multiplied by the corresponding weight. If no weights are specified all outputs will be weighted equally.

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

See ErrorMeasure.evaluateS1().

n_parameters()

See ErrorMeasure.n_parameters().

problem()

Returns the problem this error measure was defined on.

class pints.NormalisedRootMeanSquaredError(problem)

Calculates a normalised root mean squared error:

\[f = \frac{1}{C}\sqrt{\frac{\sum _i^n (y_i - x_i) ^ 2}{n}},\]

where \(C\) is the normalising constant, \(y\) is the data, \(x\) the model output and \(n\) is the total number of data points. The normalising constant is given by

\[C = \sqrt{\frac{\sum _i^n y_i^2}{n}}.\]

This error measure is similar to the (unnormalised) RootMeanSquaredError.

Extends ProblemErrorMeasure.

Parameters:

problem – A pints.SingleOutputProblem.

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

Evaluates this error measure, and returns the result plus the partial derivatives of the result with respect to the parameters.

The returned data has the shape (e, e') where e is a scalar value and e' is a sequence of length n_parameters.

This is an optional method that is not always implemented.

n_parameters()

See ErrorMeasure.n_parameters().

problem()

Returns the problem this error measure was defined on.

class pints.ProbabilityBasedError(log_pdf)

Changes the sign of a LogPDF to use it as an error. Minimising this error will maximise the probability.

Extends ErrorMeasure.

Parameters:

log_pdf (pints.LogPDF) – The LogPDF to base this error on.

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

See ErrorMeasure.evaluateS1().

This method only works if the underlying LogPDF implements the optional method LogPDF.evaluateS1()!

n_parameters()

See ErrorMeasure.n_parameters().

class pints.ProblemErrorMeasure(problem)

Abstract base class for ErrorMeasures defined for single or multi-output problems.

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

Evaluates this error measure, and returns the result plus the partial derivatives of the result with respect to the parameters.

The returned data has the shape (e, e') where e is a scalar value and e' is a sequence of length n_parameters.

This is an optional method that is not always implemented.

n_parameters()

See ErrorMeasure.n_parameters().

problem()

Returns the problem this error measure was defined on.

class pints.RootMeanSquaredError(problem)

Calculates a normalised root mean squared error:

\[f = \sqrt{\frac{\sum _i^n (y_i - x_i) ^ 2}{n}},\]

where \(y\) is the data, \(x\) the model output and \(n\) is the total number of data points.

Extends ProblemErrorMeasure.

Parameters:

problem – A pints.SingleOutputProblem.

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

Evaluates this error measure, and returns the result plus the partial derivatives of the result with respect to the parameters.

The returned data has the shape (e, e') where e is a scalar value and e' is a sequence of length n_parameters.

This is an optional method that is not always implemented.

n_parameters()

See ErrorMeasure.n_parameters().

problem()

Returns the problem this error measure was defined on.

class pints.SumOfErrors(error_measures, weights=None)

Calculates a sum of ErrorMeasure objects, all defined on the same parameter space

\[f = \sum _i f_i,\]

where \(f_i\) are the individual error meaures.

Extends ErrorMeasure.

Parameters:

• error_measures – A sequence of error measures.

• weights – An optional sequence of (float) weights, exactly one per error measure. If given, each individual error will be multiplied by the corresponding weight. If no weights are given all sums will be weighted equally.

Examples

errors = [
    pints.MeanSquaredError(problem1),
    pints.MeanSquaredError(problem2),
]

# Equally weighted
e1 = pints.SumOfErrors(errors)

# Differrent weights:
weights = [
    1.0,
    2.7,
]
e2 = pints.SumOfErrors(errors, weights)

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

See ErrorMeasure.evaluateS1().

This method only works if all the underlying :class:`ErrorMeasure` objects implement the optional method :meth:`ErrorMeasure.evaluateS1()`!

n_parameters()

See ErrorMeasure.n_parameters().

class pints.SumOfSquaresError(problem, weights=None)

Calculates the sum of squares error:

\[f = \sum _i^n (y_i - x_i) ^ 2,\]

where \(y\) is the data, \(x\) the model output and \(n\) is the total number of data points.

Extends ErrorMeasure.

Parameters:

• problem – A pints.SingleOutputProblem or pints.MultiOutputProblem.

• weights – An optional sequence of (float) weights, exactly one per problem output. If given, the error in each individual output will be multiplied by the corresponding weight. If no weights are specified all outputs will be weighted equally.

__call__(x)

Evaluates this error measure for parameters x.

evaluateS1(x)

See ErrorMeasure.evaluateS1().

n_parameters()

See ErrorMeasure.n_parameters().

problem()

Returns the problem this error measure was defined on.