Variational Inference for tree-structured Hidden-Markov Models

## Project description

This package implements a tree hidden Markov model for learning epigenetic states in multiple cell types. It’s similar to the bioinformatics tools ChromHMM and Segway, except that it allows the user to explicitly model the relationships between cell types or species. Please see our paper for further details!

For the development version, see our page on Github.

## Quickstart

# INSTALLATION
# If you're on Ubuntu
sudo apt-get install python-pip python-scipy python-matplotlib cython git

# OR if you're on a mac
ruby -e "$(curl -fsSL https://raw.github.com/mxcl/homebrew/go)" brew install python scipy matplotlib cython git # don't forget python prerequisite pysam sudo pip install -U pysam # grab and build the tree-hmm code # easiest way first: sudo pip install -U treehmm # OR using the latest development version git clone https://github.com/uci-cbcl/tree-hmm.git cd tree-hmm # building the package: # don't install-- just test: python setup.py build_ext --inplace export PYTHONPATH=$PYTHONPATH:pwd
export PATH=$PATH:pwd/bin # OR go ahead and install sudo pip install -e . # RUNNING # download some sample .bam files from our server and histogram them to binary .npy mkdir data && cd data tree-hmm convert --download_first \ --base_url "https://cbcl.ics.uci.edu/public_data/tree-hmm-sample-data/%s" \ --chromosomes chr19 \ --bam_template "wgEncodeBroadHistone{species}{mark}StdAlnRep{repnum}.REF_chr19.bam" \ --marks Ctcf H3k27me3 H3k36me3 H4k20me1 H3k4me1 H3k4me2 H3k4me3 H3k27ac H3k9ac \ --species H1hesc K562 Gm12878 Huvec Hsmm Nhlf Nhek Hmec # split chr19 into smaller pieces tree-hmm split observations.chr19.npy # do inference on the resulting chunks (creates infer_out directory) tree-hmm infer 5 --max_iter 3 --approx poc --run_local "observations.chr19.chunk*.npy" # convert the inferred states into BED format for viewing on the genome browser tree-hmm q_to_bed infer_out/mf/* # upload the BED files to UCSC, analyze, etc  ## Prerequisites • Scipy • Matplotlib (optional for plotting) • PySAM (optional for converting SAM files to 0/1 Numpy matrices) • Cython >= 0.15.1+ (required for converting .pyx => .c => .so) Platform-specific installation instructions are available in the quickstart. Please note we don’t support windows! ## Installing tree-hmm • The easiest way: sudo pip install treehmm  • For the latest development version: sudo pip install git+https://github.com/uci-cbcl/tree-hmm.git#egg=treehmm  • To be able to hack on the code yourself: git clone https://github.com/uci-cbcl/tree-hmm.git cd tree-hmm sudo pip install -e .  • Or alternatively, if you don’t have admin rights: git clone https://github.com/uci-cbcl/tree-hmm.git cd tree-hmm python setup.py build_ext --inplace export PYTHONPATH=pwd:$PYTHONPATH
export PATH=pwd/bin:\$PATH


## Running the commands

Use the tree-hmm command from the command line to perform the major commands, including:

• convert a set of BAM-formatted mapped reads to numpy matrices
• split a chromosome into several variable-length chunks, determined via a gaussian convolution of the raw read signal
• infer underlying chromatin states from a converted binary matrix
• q_to_bed convert the numpy probability matrices into BED files (maximum a posteriori state)

Each of these tasks has its own command-line help, accessible via:

tree-hmm convert --help
tree-hmm split --help
tree-hmm infer --help
tree-hmm q_to_bed --help


## Data Conversion

tree-hmm convert \
--marks Ctcf H3k4me2 \
--species H1hesc K562


We require at least one BAM input file for each species/mark combination. You can specify the naming convention your data follows via the --bam_template argument.

During this step, all of the BAM files will be scanned and histogrammed. Replicants are pooled together and the reads are binarized using a poisson background rate specific to each mark/species combination, i.e.,:

bgrate_{il} = \frac{\sum_{t=1}^T count_{itl}} {T}
markpresence_{il} = poisson.survival(count_{itl}, bg_rate_{il}) < max_pvalue


where max_pvalue can be specified by the user. This simply imposes a threshold value that’s specific to a species/mark combination and should account for sequencing depth differences and a variable number of replicates. Finally, the histograms are split by chromosome and, by default, written to observations.{chrom}.npy.

The ENCODE histone data available on UCSC can be downloaded by specifying the --download_first option, or you can specify other datasets by changing --base_url and --bam_template, just so long as the files are named systematically. See the quickstart above for an example using sample ENCODE data from hg19’s chr19.

The species and marks in use can be modified either by directly editing the treehmm/static.py file or by specifying --species and/or --marks in the convert step. Again, see the quickstart for an example.

This step creates a new file start_positions.pkl which contains information about the original coordinates and the species and marks used during the conversion. This file (or its twin created by the split step) is required by the final q_to_bed step.

Note: there is already preliminary support for missing marks/species already present which I can make more user-friendly if there is interest. There is also some work on allowing continuous observations (rather than the current binary-only observations). Raise an issue/feature request on Github if you’re interested.

## Splitting the data

Since the majority of the genome will not have any signal in any of the marks, it is very useful to split up the histone data and only perform inference on the regions with adequate signal. This step can also speed up inference as only a portion of the genome is used and each chunk is considered independent of all others.

We use a gaussian smoothing filter over the binarized data and cut out regions where there is no signal in any species or mark. A histogram of the resulting read lengths is drawn to help identify how much of the genome is retained for a given setting. The defaults retained about 50% of hg19 on the ENCODE data.

tree-hmm split \
observations.chr*.npy
start_positions.pkl \
--gauss_window_size 5 \
--min_size 25


Note: the --gauss_window_size and --min_size are in terms of bins. So if you want a smoothing window that acts over 10kb up and downstream (20kb total), and had specified a --window_size of 200bp in the convert phase, you’d specify a --gauss_window_size of 50.

This step creates a new file start_positions_split.pkl which retains information about the original read coordinates. This file (or its twin created by the convert step) is required during the final q_to_bed step.

## Inference

For inference, you must specify the number of hidden states to infer and one or more input files. There are also many parameters you can fine-tune with defaults as used in the paper.

Inference will try to submit jobs to an SGE cluster. If you don’t have such a cluster, make sure you specify the --run_local option. If you do, you should clean up the SGE_* files when inference is complete. Those files contain parameters and return values job submissions.

There are several inference engines implemented for comparison including:

mean field approximation (mf):
the simplest variational approximation, with every node optimized independently. Memory use is O(I * T * K), that is, it scales linearly with the number of species (I), the number of bins (T), and the number of states (K).
loopy belief propagation (loopy):
similar to mean field in that each node is optimized independently, but is has a non-monotonic energy trajectory. Works well in some applications, but not very well in ours. Memory use is O(I * T * K).
product of chains (poc):
the entire chain from each species is solved exactly, but different chains are optimized indepently. Memory use is O(I * T * K^2). This mode performed the best in our testing.
Exact inference using a cliqued HMM (clique):
the entire graph is solved exactly using a naive cliquing approach. Memory use is O(T * K^I). This mode EATS memory and is not recommended for K > 10.

There are also a few more “experimental” modes:

Independent chains (indep):
the entire chain from each species is solved exactly, but there are no connections between different chains (this is how ChromHMM handles joint inference). Memory use is O(I * T * K^2).
Exact inference using the Graphical Models Toolkit (gmtk):
exact inference using the Graphical Models Toolkit. If you have GMTK installed, this package provides an alternative to the clique mode. We found it to be a bit slower clique, but has much more reasonable memory usage. The easiest way to get GMTK might be to follow the documentation of segway, which requires it to run.

### Changing the phylogeny

The phyologeny connecting each species is specified in treehmm/static.py and is in the form of a python dictionary, each of whose keys are the child cell type and whose values are the parent cell type. For example, the default phylogeny used for the ENCODE data specifies that H1hesc is the parent of all other cell types:

phylogeny = {'H1hesc':'H1hesc',
'Huvec':'H1hesc',
'Hsmm':'H1hesc',
'Nhlf':'H1hesc',
'Gm12878':'H1hesc',
'K562':'H1hesc',
'Nhek':'H1hesc',
'Hmec':'H1hesc',
'Hepg2':'H1hesc'}


A few things to note:

• Cell types that specify themselves as their own parents (like H1hesc above) are considered root nodes (they have no parents) and use a different set of parameters than cell types with parents.
• While each cell type is allowed to have zero or as many children as you want, each cell type is only allowed to have a single parent. This is enforced already since dictionaries can’t have duplicate keys.
• Connecting the tree in a loop (s.t. there is no root node) violates a fundamental assumption in Bayesian networks (they are supposed to be directed, Acyclic Graphs). The code may run okay, but you will probably get incorrect results.
• You can have multiple roots in a graph (e.g., two independent trees or one tree and a single, unrelated cell type). This might help in learning a global set of parameters (more data), but shouldn’t affect the inference quality within each tree. Cell types without parents or children will behave exactly like standard hidden Markov models.
• We have preliminary code that uses a separate transition parameterization for each parent:child relationship. While this mode should increase accuracy and may reveal some unique trends along each branch of your phylogeny, keep in mind that the number of parameters is greatly increased and can lead to overfitting. You may want to reduce the number of states in use (K). If you’re interested in this mode, contact me/raise an issue on Github.
• Internal “hidden” nodes are possible using the --mark_avail parameter (which in turn is allowing some marks/species to be missing). This mode has some weird side-effects when run on heterogeneous mark combinations and wasn’t pursued further.

### Running on SGE vs. locally

By default, the inference stage in tree-hmm will try to submit jobs through the SGE grid. If it can’t do so, it will fall back to running the jobs locally. Here are a few tips to make things run faster:

• If you haven’t split your data into chunks using the split subcommand, you should set the --chunksize to 1. That way, each chromosome will be handled by a different job.
• For split data running on SGE, set the --chunksize fairly high (like 100, or even more if you have tens of thousands of chunks). This will start fewer SGE jobs that will each run longer and save you from being yelled at by your system administrators
• If you’re not using SGE, you should explicitly set --run_local since it will use a more efficient message passing algorithm (inter-process communication rather than writing parameters and results to disk).
• If you are using SGE, be sure to clean up the (many, many) SGE_* files which serve as temporary messages outputs while the job is running.

### Quick Example

To infer K=18 states, but only do five M-step iterations, up to 10 E-step iterations per M-step, use the product-of-chains approximation on the entire converted and split set of files, iterating until the change in free energy is < 1e-5 in either the E-step or the M-step and running in parallel locally rather than on an SGE grid:

tree-hmm infer \
18 \
--max_iter 5 \
--max_E_iter 10 \
--approx poc \
--epsilon 1e-5 \
--epsilon_e 1e-5 \
--run_local \
"observations.chr*.chunk*.npy"


After running this, you’ll find a new directory infer_out/mf/TIMESTAMP/.

In this directory, you’ll find several png formatted files showing the free energy trajectory across iterations, the parameters as they are learned (plotted at each iteration) as well as the Q distributions (marginal probabilities of each node being in a particular state) and the contributions of each job’s inferred state to each parameter (i.e., the transition matrices alpha, beta, gamma, and theta as well as the emission matrix e).

## Post-processing

To make any sense of the actual genomic segmentation, you’ll need to convert the marginal Q probabilities into BED-formatted files. If you used the split subcommand, you need to specify the start_positions_split.pkl file generated by that command:

tree-hmm q_to_bed infer_out/mf/TIMESTAMP/ start_positions_split.pkl


If you did not use the split, you may use the original pkl file:

tree-hmm q_to_bed infer_out/mf/TIMESTAMP/ start_positions.pkl


These commands will find and output the most likely state assignment in each bin for all species to a set of bed files treehmm_states.{species}.state{k}.bed.

Note that this is the maximum a posteriori (MAP) assignment, NOT the most likely joint configuration. ChromHMM also outputs the MAP, whereas Segway uses the most likely joint configuration or viterbi path. The gtmk inference mode can find the most likely joint configuration, but downstream tools are lacking at the moment. If you’re interested in this, please raise an issue on Github.

You can also get the full probability matrix (not just most likely state) by specifying --save_probs. This step relies on the start_positions.pkl file generated during the split phase. You may specify where that file is located via --start_positions. If you don’t want to split your data beyond by-chromosome, I can modify this step accordingly. Again, please raise an issue on Github if you’re interested.

Finally, you may want to check out pybedtools or Galaxy to do downstream analysis.