pygsti.tools.likelihoodfns.two_delta_logl

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pygsti.tools.likelihoodfns.two_delta_logl#

two_delta_logl(model, dataset, circuits=None, min_prob_clip=1e-06, prob_clip_interval=(-1000000.0, 1000000.0), radius=0.0001, poisson_picture=True, op_label_aliases=None, dof_calc_method=None, wildcard=None, mdc_store=None, comm=None)#

Twice the difference between the maximum and actual log-likelihood.

Optionally also can return the Nsigma (# std deviations from mean) and p-value relative to expected chi^2 distribution (when dof_calc_method is not None).

This function’s arguments are supersets of logl(), and logl_max(). This is a convenience function, equivalent to 2*(logl_max(…) - logl(…)), whose value is what is often called the log-likelihood-ratio between the “maximal model” (that which trivially fits the data exactly) and the model given by model.

Parameters:

  • model (Model) – Model of parameterized gates

  • dataset (DataSet) – Probability data

  • circuits (list of (tuples or Circuits), optional) – Each element specifies a circuit to include in the log-likelihood sum. Default value of None implies all the circuits in dataset should be used.

  • min_prob_clip (float, optional) – The minimum probability treated normally in the evaluation of the log-likelihood. A penalty function replaces the true log-likelihood for probabilities that lie below this threshold so that the log-likelihood never becomes undefined (which improves optimizer performance).

  • prob_clip_interval (2-tuple or None, optional) – (min,max) values used to clip the probabilities predicted by models during MLEGST’s search for an optimal model (if not None). if None, no clipping is performed.

  • radius (float, optional) – Specifies the severity of rounding used to “patch” the zero-frequency terms of the log-likelihood.

  • poisson_picture (boolean, optional) – Whether the log-likelihood-in-the-Poisson-picture terms should be included in the computed log-likelihood values.

  • op_label_aliases (dictionary, optional) – Dictionary whose keys are operation label “aliases” and whose values are tuples corresponding to what that operation label should be expanded into before querying the dataset. Defaults to the empty dictionary (no aliases defined) e.g. op_label_aliases[‘Gx^3’] = (‘Gx’,’Gx’,’Gx’)

  • dof_calc_method ({None, "all", "modeltest"}) – How model’s number of degrees of freedom (parameters) are obtained when computing the number of standard deviations and p-value relative to a chi2_k distribution, where k is additional degrees of freedom possessed by the maximal model. If None, then Nsigma and pvalue are not returned (see below).

  • wildcard (WildcardBudget) – A wildcard budget to apply to this log-likelihood computation. This increases the returned log-likelihood value by adjusting (by a maximal amount measured in TVD, given by the budget) the probabilities produced by model to optimially match the data (within the bugetary constraints) evaluating the log-likelihood.

  • mdc_store (ModelDatasetCircuitsStore, optional) – An object that bundles cached quantities along with a given model, dataset, and circuit list. If given, model and dataset and circuits should be set to None.

  • comm (mpi4py.MPI.Comm, optional) – When not None, an MPI communicator for distributing the computation across multiple processors.

Returns:

  • twoDeltaLogL (float) – 2*(loglikelihood(maximal_model,data) - loglikelihood(model,data))

  • Nsigma, pvalue (float) – Only returned when dof_calc_method is not None.

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