This tutorial is organized as a series of examples that highlight some of Pebl’s various features. It is assumed that the reader is familiar with Bayesian networks and the python language and has read the Pebl Introduction.
Pebl includes a python library and a command line application that can be used with a configuration file. The pebl application is limited compared to the library but requires no programming. Each example in this tutorial will include a python script and a pebl configuration file that runs the same analysis (when possible).
Note
This tutorial uses Pebl 1.0
Bayesian networks have been used to model complex phenomena with non-linear, multimodal relationships between high-dimensional variables. When used to model gene regulatory networks, nodes usually represent the expression profile of genes while edges represent dependencies between them. The learned networks can be interpreted as causal models explaining the data and can hint at the underlying biological mechanisms and functions.
For this tutorial, we use the Cell Cycle data from Spellman, et. al [1] as an example dataset. This dataset contains 76 gene expression measurements of 6177 S. cerevisiae ORFs. The experiments include six time series using different cell cycle synchronization methods. In this example, we ignore the temporal aspect of the dataset and treat each measurement as an independent sample from the underlying biological phenomena. Spellman et al. identified 800 genes as cell cycle dependent and we use a small 12 gene subset of that (as show in Fig 8.11 of [2]).
pebl-tutorial-data1.txt contains the gene expression measurements for our 12 genes. Each row contains one sample (the gene expression data from one microarray assay) and each column contains the gene expression profile for a given gene over the 76 measurements. The first row containing the variable names (the gene associated with the measured ORF) is required for all pebl data files.
This is the simplest analysis in Pebl:
1 2 3 4 5 6 7 | >>> from pebl import data
>>> from pebl.learner import greedy
>>> dataset = data.fromfile("pebl-tutorial-data1.txt")
>>> dataset.discretize()
>>> learner = greedy.GreedyLearner(dataset)
>>> ex1result = learner.run()
>>> ex1result.tohtml("example1-result")
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The code above does the following:
- Imports the required modules (lines 1-2)
- Loads the dataset (line 3)
- Discretizes the continuous values in the dataset (line 4)
- Creates and runs a greedy learner with default parameters (lines 5-6)
- Creates a html report of the results (line 7)
The same analysis can be run with the following configuration file:
1 2 3 4 5 6 7 8 9 10 | [data]
filename = pebl-tutorial-data1.txt
discretize = 3
[learner]
type = greedy.GreedyLearner
[result]
format = html
outdir = example1-result
|
To use the configuration file above, save it as a text file (config1.txt) and run the pebl application:
$/usr/local/bin/pebl run config1.txt
Note
The location of the pebl application may be different based on your installation method
The result of this example is available here. Keep in mind that structure learning of Bayesian networks uses stochastic methods and the results from different runs will not be identical. Also, the results from this short run are not realistic or spectacular; they do, however, serve as a good demostration of the features of the html report.
The result is organized intro three tabs. The first tab shows the log scores for the top networks and some overall statistics. The second tab shows the top 10 networks found and the last tab shows consensus networks at different confidence thresholds. The consensus networks are built using estimated marginal posterior probabililty of each edge.
Pebl uses tab-delimited text files for its data. Each column represents a variable and each row represents a sample or observation. The data file can contain any number of comment rows that begin with a “#”. The first non-comment row is expected to be a header row that specifies the name and type of each variable. Pebl supports continuous, discrete and class variables. The three variable types have different header formats as shown below:
| Type | Header Format | Examples |
|---|---|---|
| continuous | <variable-name>[,continuous] | CLN2 CLN1,continuous |
| discrete | <variable-name>,discrete(<variable-arity>) | CLN2,discrete(2) CLN1,discrete(3) |
| class | <variable-name>,class(<class-labels>) | CLN2,class(low,high) phenotype,class(cancer,normal) |
Note
Although Pebl accepts continuous values in the data file, they must be discretized before use.
Each measured value can be annotated with two indicators. Append or prepend a ”!” to the value to indicate that the variable was intervened upon for that sample or observation. The intervention can be a gene knockdown, RNA silencing or any perturbation that directly affect the value for that variable. Missing values are indicated by using “X”. This can be the result of a scratch on a micrarray slide or, if all the rows for a variable include “X”, a variable that wasn’t measured.
Each sample (row) can have a name which should be in the first column. This is not used in learning a Bayesian network, but can be used to create subsets of the data based on the sample names.
pebl-tutorial-data2.txt is the discretized version of our data file with sample names and was created with the following script:
1 2 3 4 5 6 | >>> from pebl import data
>>> dataset = data.fromfile("pebl-tutorial-data1.txt")
>>> dataset.discretize(numbins=3)
>>> for i,s in enumerate(dataset.samples):
>>> s.name = "sample-%d" % i
>>> dataset.tofile("pebl-tutorial-data2.txt")
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In the first example, we used the default parameters for the greedy learner (1000 iterations) which is inadequate for a dataset of this size. In this example, we use custom stopping criteria:
1 2 3 4 5 6 7 8 9 | >>> from pebl import data, result
>>> from pebl.learner import greedy
>>> dataset = data.fromfile("pebl-tutorial-data2.txt")
>>> learner1 = greedy.GreedyLearner(dataset, max_iterations=1000000)
>>> learner2 = greedy.GreedyLearner(dataset, max_time=120) # in seconds
>>> result1 = learner1.run()
>>> result2 = learner2.run()
>>> merged_result = result.merge(result1, result2)
>>> merged_result.tohtml("example2-result")
|
The code above does the following:
- Imports the required modules (lines 1-2)
- Loads the discretized dataset (line 3)
- Creates and runs two greedy learners with specified stopping criteria (lines 4-7)
- Merges the two learner results and creates html report (lines 8-9)
A Pebl configuration file can be used to create multiple learners but they must be of the same type and use the same parameters (stopping criteria in this case). Thus, it is not possible to replicate the above code with a configuration file but it can be approximated:
1 2 3 4 5 6 7 8 9 10 11 12 13 | [data]
filename = pebl-tutorial-data2.txt
[learner]
type = greedy.GreedyLearner
numtasks = 2
[greedy]
max_iterations = 1000000
[result]
format = html
outdir = example2-result
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For large datasets, we might wish to do multiple learner runs and use different learners. The following example creates and runs 5 greedy and 5 simulated annealing learners:
1 2 3 4 5 6 7 | >>> from pebl import data, result
>>> from pebl.learner import greedy, simanneal
>>> dataset = data.fromfile("pebl-tutorial-data2.txt")
>>> learners = [ greedy.GreedyLearner(dataset, max_iterations=1000000) for i in range(5) ] + \
>>> [ simanneal.SimulatedAnnealingLearner(dataset) for i in range(5) ]
>>> merged_result = result.merge([learner.run() for learner in learners])
>>> merged_result.tohtml("example3-result")
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The code above is similar to the last example except that we create a list of 10 learners of two different types. The corresponding configuration file has the same caveat as in the previous example:
1 2 3 4 5 6 7 8 9 10 11 12 13 | [data]
filename = pebl-tutorial-data2.txt
[learner]
type = greedy.GreedyLearner
numtasks = 10
[greedy]
max_iterations = 1000000
[result]
format = html
outdir = example3-result
|
In the previous example, we run 10 learners serially. We can use Pebl’s taskcontroller package to run these learners in parallel:
1 2 3 4 5 6 7 8 9 10 | >>> from pebl import data, result
>>> from pebl.learner import greedy, simanneal
>>> from pebl.taskcontroller import multiprocess
>>> dataset = data.fromfile("pebl-tutorial-data2.txt")
>>> learners = [ greedy.GreedyLearner(dataset, max_iterations=1000000) for i in range(5) ] + \
>>> [ simanneal.SimulatedAnnealingLearner(dataset) for i in range(5) ]
>>> tc = multiprocess.MultiProcessController(poolsize=2)
>>> results = tc.run(learners)
>>> merged_result = result.merge(results)
>>> merged_result.tohtml("example4-result")
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In this example, we import the multiprocess module (line 3), create a multiprocess task controller with a pool size of two processes (line 7), run the learners using the task controller (line 8) and merge the results and create html report as before.
The corresponding configuration file (with the caveats mention in the previous example) would be:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | [data]
filename = pebl-tutorial-data1.txt
[learner]
type = greedy.GreedyLearner
numtasks = 10
[greedy]
max_iterations = 1000000
[taskcontroller]
type = multiprocess.MultiProcessController
[multiprocess]
poolsize = 2
[result]
format = html
outdir = example2-result
|
All task controllers can be used with the pebl application and configuration file and the only difference between their usage are the parameters they require. Thus, Pebl allows one to do preliminary analysis on their desktop with perhaps the multiprocess task controller and then do the full analysis using an XGrid or Amazon’s EC2 by simply changing one line of code or a few lines in a configuration file. The EC2 task controller is an especially attractive option for large analysis tasks because it allows one to rent the computing resources on an as-needed basis and without any cluster installation or configuration.
There is no principled way to determine the optimal stopping criteria or simulated annealing parameters for analyzing a given dataset. One common strategy is to construct consensus networks that show network features found with high confidence. Pebl’s html reports show such “model-averaged” networks in the third tab and the pebl.posterior module has methods for creating these programatically.
Another common strategy is to check for stability of results. You begin with some learning, save the results, do futher learning, merge the two results and see if the top networks and consensus networks have changed much. If they remain relatively stable, you can assume that you’ve reached a good solution. Keep in mind, however, that you can never guarantee that you’ve found the optimal network (or that there is a singular optimal network to be found) since structure learning of Bayesian network is a known NP-Hard problem.
In the examples above, we’ve been creating html reports of the results but these cannot be later merged. A better option is to save the result using the pebl.result.LearnerResult.tofile() method and then later read it with pebl.result.fromfile():
1 2 3 4 5 6 7 8 | >>> from pebl import data, result
>>> result1 = learner.run()
>>> result1.tofile("result1.pebl")
>>> result1.tohtml("result1")
>>> result2 = otherlearner.run()
>>> result1 = result.fromfile("result1.pebl")
>>> merged_result = result.merge(result1, result2)
>>> merged_result.tofile("results_sofar.pebl")
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A third strategy is to calculate a p-value for each scored network. This will be added to the tutorial shortly.
Pebl imposes few limits on the scale of problems it can handle other than the limits imposed by the hardware you use. The localscore_cache.maxsize configuration parameter can be used to control the size of the main cache used by pebl. With a value appropriate to your memory availability, pebl can be used for quite large datasets. We have successfully tested pebl with datasets of size (number variable, number samples) = (10000,10000) and (1000,100000) on a machine with 2GB memory.
While pebl can handle such large datasets without crashing, because structure learning is a known NP-Hard problem, using pebl with datasets containing more than a few hundred variables will likely give poor results due to poor coverage of the search space.
I will be adding examples for using prior knowledge and for calculating p-values using a bootstrapping approach.
This tutorial should have given you an overview of using Pebl. For further information about specific components, consult the API Reference, which contains detailed information about all parts of pebl. If you would like to add code to pebl, consult the Developer’s Guide. Feel free to contact me (Abhik Shah <abhikshah@gmail.com>) with any questions or comments.