Introduction

Author:	Thomas Wiecki, Imri Sofer
Contact:	[email protected], [email protected]
Web site:	http://github.com/hddm-dev/kabuki
Copyright:	This document has been placed in the public domain.
License:	Simplified BSD (see LICENSE)
Version:	0.6.5

Purpose

Kabuki is a Python library intended to make hierarchical PyMC models reusable, portable and more flexible. Once a model has been formulated in kabuki it is trivial to apply it to new datasets in various ways. Currently, it is geared towards hierarchical Bayesian models that are common in the cognitive sciences but it might be easily adapted to other domains.

In essence, kabuki allows easy creation of model-factories. After specifiyng the model structure, models tailored to new data sets and new configurations can be instantiated easily.

To see it in action, check out HDDM which uses kabuki for the heavy lifting. Especially the How-to should give a comprehensive overview of kabuki's features.

Features

• Easy model specification: It is quite trivial to convert an existing PyMC model to kabuki.
• Models are classes: The resulting kabuki model is one class with methods for setting the nodes to their MAP, sampling from the posterior, saving and loading models, plotting output statistics etc.
• Easy interface: New model variations can be constructed and estimated automatically either.
• Statistical analysis: Automatically create nicely formatted summary output statistics, posterior plots and run posterior predictive checks.
• Data generation: By providing a function to generate data from your model given paramters you can create new, simulated data sets with multiple groups and multiple conditions (e.g. for testing parameter recovery).
• Batteries included: Over time we will add more standard models to kabuki such as a model to perform Bayesian ANOVA or regression analysis.

Motivation

Hierarchical Bayesian models are gaining popularity in many scientific disciplines such as cognitive and health sciences, but also economics. While quite a few useful models have been developed (e.g. hierarchical Bayesian regression, hierarchical estimation of drift-diffusion parameters) in the literature, often with reference implementations in WinBUGS (and sometimes PyMC), applying them to new data sets requires changing the model code to your specific needs.

If you build your model in kabuki, using it on a new data set with different conditions and different structure will come for free. All a user has to do is instantiate the model class and kabuki will automatically create a new PyMC model tailored to the data in a user-specified way.

Usage

Since kabuki builds on top of PyMC you have to know the basic model creation process there. Check out the PyMC documentation first if you are not familiar.

To create your own model you have to inherit from the kabuki.Hierarchical base class which provides all of the functionality. Instead of directly instantiating PyMC nodes you have to wrap them in a kabuki.Knode object. This provides the information of how to create PyMC nodes once the model is instantiated.

Example model

Here is a very simple example model where we assume that multiple subjects provided normal distributed data and we want to infer the mean of each subject but also assume that subject means themselves are distributed according to a normal group distribution for which we want to estimate the mean and variance:

from kabuki import Hierarchical, Knode
import pymc

class MyModel(Hierarchical):
    # We have to overload the create_knodes() method. It is
    # expected to return a list of knodes.
    def create_knodes(self):

        mu_g = Knode(pymc.Uniform, 'mu_g', lower=-5, upper=5, depends=self.depends['mu'])

        mu_subj = Knode(pymc.Normal, 'mu_subj', mu=mu_g, tau=1, depends=('subj_idx',), subj=True)

        like = Knode(pymc.Normal, 'like', mu=mu_subj, tau=1, col_name='data', observed=True)

        return [mu_g, mu_subj, like]

OK, what's going on here?

Creation of group mu node

The first line of create_knodes() creates the group mean knode.

• The first argument is the pymc distribution of the parameter.
• The second argument is the name you want to give to this knode 'lower' and 'upper' in this case are keyword arguments that get passed to PyMC during node creation.
• The depends keyword argument means that seperate PyMC nodes can be created for user-supplied conditions (this will become clear later).
• self.depends is a user-supplied dictionary that maps a parameter name to a column in the data specifying the different conditions. Kabuki will then create different group mean nodes depending on the conditions found in this data column.

Creation of subject node

In the second line we create the subject knode with mu being distributed according to the parent distribution we just created. Linking the hierarchical structure works in the same way as with PyMC nodes, however, note that here we pass in our newly create Knode to mu.

Note moreover that while we say that this node depends on the data column 'subj_idx' (this column is supposed to have all the subject indices), we don't have to specify again that this child node also depends on the user-specified column. Kabuki knows that since the parent (mu_group) depends on a user-defined column name, the child (mu_subj) also has to depend on the same conditions in the data.

The subj keyword specifies that this is a subject knode (this is required for internal purposes).

Creation of observed node

Finally, we have to create the likelihood or observed node. The only difference to before is the observed=True keyword and col_name which specifies on which data column the likelihood depends on. As we will see later, kabuki will parcel the data column appropriately so that each subject observed node is linked to the data belonging to that subject (and that condition).

Running the example model

After we specified our model in this way we can construct new models very easily. Say we had an experiment where we tested each subject on two conditions, 'low' and 'high', and we suspect that this will result in different means of their normal distributed responses.

An example data file in csv might looks this:

subj_idx, data, condition
1,        0.3,  'low'
1,        -0.25,'low'
1,        1.3,  'high'
1,        0.5.1.dev,  'high'
[...]
24,       0.8,  'low'
24,       0.1,  'high'

Here is how you would create a model tailored around this data set, set the parameters to their MAP, sample and print some output statistics:

data = kabuki.load_csv('data.csv')
# create the model. depends_on tells it that the parameter
# 'mu' (this links to depends=self.depends['mu'] we specified above
# when we created the group knode) depends on the data column
# 'condition'
model = MyModel(data, depends_on={'mu': 'condition})

model.map()
model.sample(5000, burn=1000)

# Print the stats to the console
model.print_stats()
# Plot posterior distributions
model.plot_posteriors()
# Plot the posterior predictive on top of the subject data
model.plot_posterior_predictive()

Conclusion

The resulting model will have 2 group-mean distributions ('mu_low' and 'mu_high', one for each condition), 2 subject-mean distributions per subject (so 48 in total, assuming we had 24 subjects, which are linked to their appropriate group-mean) and 2 likelihoods (i.e. observeds) per subject which are linked to the appropriate subject's data.

As you can see, kabuki takes care of creating multiple nodes where appropriate (i.e. for different conditions), provides meaningful names and parcels the data so that the likelihoods are linked correctly.

There are many more features for more complex models and advanced diagnostics (like posterior predictive checks).