Multiple superset models

The PEtab Select model space table is designed to express large model spaces based on a single superset model, concisely. However, model selection problem can also involve multiple superset models that are structurally different. For example, one superset may be a linear model, and the other superset may be an ordinary differential equation (ODE) model. To express this concisely, we suggest using two model space tables; one per superset.

We illustrate this with two of the other examples in this documentation, specifically:

• Example: ODE with timeseries data: an ODE model with parameters k1 through k3, and

• Model selection with non-SBML models and unsupported calibration tools: a polynomial model with parameters k1 through k5.

Example file layout

The PEtab Select problem YAML file and the two model space files are kept in a top directory. The PEtab problems for each superset model are kept in separate directories.

model_selection_problem/
├── petab_select_problem.yaml
├── model_space_polynomial.tsv
├── model_space_ode_timeseries.tsv
├── polynomial_petab_files/
│   └── ...
└── ode_timeseries_petab_files/
    └── ...

The PEtab Select problem YAML

The PEtab Select problem YAML lists both model space files.

format_version: 1.0.0
criterion: AIC
method: brute_force
model_space_files:
- model_space_polynomial.tsv
- model_space_ode_timeseries.tsv

The model space tables

The model space can be defined in a single model space table; however, this can lead to sparse tables. Hence, we suggest splitting the table into one per superset.

model_space_polynomial.tsv:

model_subspace_id	model_subspace_petab_yaml	k0	k1	k2	k3	k4	k5
polynomial	polynomial_petab_files/problem.yaml	0;estimate	0;estimate	0;estimate	0;estimate	0;estimate	0;estimate

model_space_ode_timeseries.tsv:

model_subspace_id	model_subspace_petab_yaml	k1	k2	k3
ode_timeseries	ode_timeseries_petab_files/petab_problem.yaml	0;estimate	0;estimate	0;estimate

Together, these two model spaces define \(2^6 + 2^3 = 72\) candidate models.

Notes

• Method The stepwise methods (forward, backward) move between models will not visit model subspaces with a different model_subspace_petab_yaml than the initial model. Hence, multiple stepwise searches initialized in the model subspaces associated with each superset model are required to explore the full space. brute_force will search all models regardless.

• Criteria The information criteria (AIC etc.) require that models are compared on the same dataset. Hence, the PEtab problems inside polynomial_petab_files/ and ode_timeseries_petab_files/ should use the same data.