Note: This tutorial was generated from an IPython notebook that can be downloaded here.

Parallelization

Note

Some builds of NumPy (including the version included with Anaconda) will automatically parallelize some operations using something like the MKL linear algebra. This can cause problems when used with the parallelization methods described here so it can be good to turn that off (by setting the environment variable OMP_NUM_THREADS=1, for example).

import os
os.environ["OMP_NUM_THREADS"] = "1"

With emcee, it’s easy to make use of multiple CPUs to speed up slow sampling. There will always be some computational overhead introduced by parallelization so it will only be beneficial in the case where the model is expensive, but this is often true for real research problems. All parallelization techniques are accessed using the pool keyword argument in the EnsembleSampler class but, depending on your system and your model, there are a few pool options that you can choose from. In general, a pool is any Python object with a map method that can be used to apply a function to a list of numpy arrays. Below, we will discuss a few options.

This tutorial was executed with the following version of emcee:

import emcee
print(emcee.__version__)
/Users/dforeman/anaconda/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from float to np.floating is deprecated. In future, it will be treated as np.float64 == np.dtype(float).type.
  from ._conv import register_converters as _register_converters
3.0.0.dev0

In all of the following examples, we’ll test the code with the following convoluted model:

import time
import numpy as np

def log_prob(theta):
    t = time.time() + np.random.uniform(0.005, 0.008)
    while True:
        if time.time() >= t:
            break
    return -0.5*np.sum(theta**2)

This probability function will randomly sleep for a fraction of a second every time it is called. This is meant to emulate a more realistic situation where the model is computationally expensive to compute.

To start, let’s sample the usual (serial) way:

np.random.seed(42)
initial = np.random.randn(32, 5)
nwalkers, ndim = initial.shape
nsteps = 100

sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob)
start = time.time()
sampler.run_mcmc(initial, nsteps, progress=True)
end = time.time()
serial_time = end - start
print("Serial took {0:.1f} seconds".format(serial_time))
100%|██████████| 100/100 [00:21<00:00,  4.70it/s]
Serial took 21.3 seconds

Multiprocessing

The simplest method of parallelizing emcee is to use the multiprocessing module from the standard library. To parallelize the above sampling, you could update the code as follows:

from multiprocessing import Pool

with Pool() as pool:
    sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob, pool=pool)
    start = time.time()
    sampler.run_mcmc(initial, nsteps, progress=True)
    end = time.time()
    multi_time = end - start
    print("Multiprocessing took {0:.1f} seconds".format(multi_time))
    print("{0:.1f} times faster than serial".format(serial_time / multi_time))
100%|██████████| 100/100 [00:06<00:00, 16.05it/s]
Multiprocessing took 6.2 seconds
3.4 times faster than serial

I have 4 cores on the machine where this is being tested:

from multiprocessing import cpu_count
ncpu = cpu_count()
print("{0} CPUs".format(ncpu))
4 CPUs

We don’t quite get the factor of 4 runtime decrease that you might expect because there is some overhead in the parallelization, but we’re getting pretty close with this example and this will get even closer for more expensive models.

MPI

Multiprocessing can only be used for distributing calculations across processors on one machine. If you want to take advantage of a bigger cluster, you’ll need to use MPI. In that case, you need to execute the code using the mpiexec executable, so this demo is slightly more convoluted. For this example, we’ll write the code to a file called script.py and then execute it using MPI, but when you really use the MPI pool, you’ll probably just want to edit the script directly. To run this example, you’ll first need to install the schwimmbad library because emcee no longer includes its own MPIPool.

with open("script.py", "w") as f:
    f.write("""
import sys
import time
import emcee
import numpy as np
from schwimmbad import MPIPool

def log_prob(theta):
    t = time.time() + np.random.uniform(0.005, 0.008)
    while True:
        if time.time() >= t:
            break
    return -0.5*np.sum(theta**2)

with MPIPool() as pool:
    if not pool.is_master():
        pool.wait()
        sys.exit(0)

    np.random.seed(42)
    initial = np.random.randn(32, 5)
    nwalkers, ndim = initial.shape
    nsteps = 100

    sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob, pool=pool)
    start = time.time()
    sampler.run_mcmc(initial, nsteps)
    end = time.time()
    print(end - start)
""")

mpi_time = !mpiexec -n {ncpu} python script.py
mpi_time = float(mpi_time[0])
print("MPI took {0:.1f} seconds".format(mpi_time))
print("{0:.1f} times faster than serial".format(serial_time / mpi_time))
MPI took 8.3 seconds
2.6 times faster than serial

There is often more overhead introduced by MPI than multiprocessing so we get less of a gain this time. That being said, MPI is much more flexible and it can be used to scale to huge systems.

Pickling, data transfer & arguments

All parallel Python implementations work by spinning up multiple python processes with identical environments then and passing information between the processes using pickle. This means that the probability function must be picklable.

Some users might hit issues when they use args to pass data to their model. These args must be pickled and passed every time the model is called. This can be a problem if you have a large dataset, as you can see here:

def log_prob_data(theta, data):
    a = data[0]  # Use the data somehow...
    t = time.time() + np.random.uniform(0.005, 0.008)
    while True:
        if time.time() >= t:
            break
    return -0.5*np.sum(theta**2)

data = np.random.randn(5000, 200)

sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob_data, args=(data,))
start = time.time()
sampler.run_mcmc(initial, nsteps, progress=True)
end = time.time()
serial_data_time = end - start
print("Serial took {0:.1f} seconds".format(serial_data_time))
100%|██████████| 100/100 [00:21<00:00,  4.71it/s]
Serial took 21.3 seconds

We basically get no change in performance when we include the data argument here. Now let’s try including this naively using multiprocessing:

with Pool() as pool:
    sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob_data, pool=pool, args=(data,))
    start = time.time()
    sampler.run_mcmc(initial, nsteps, progress=True)
    end = time.time()
    multi_data_time = end - start
    print("Multiprocessing took {0:.1f} seconds".format(multi_data_time))
    print("{0:.1f} times faster(?) than serial".format(serial_data_time / multi_data_time))
100%|██████████| 100/100 [01:17<00:00,  1.32it/s]
Multiprocessing took 77.7 seconds
0.3 times faster(?) than serial

Brutal.

We can do better than that though. It’s a bit ugly, but if we just make data a global variable and use that variable within the model calculation, then we take no hit at all.

def log_prob_data_global(theta):
    a = data[0]  # Use the data somehow...
    t = time.time() + np.random.uniform(0.005, 0.008)
    while True:
        if time.time() >= t:
            break
    return -0.5*np.sum(theta**2)

with Pool() as pool:
    sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob_data_global, pool=pool)
    start = time.time()
    sampler.run_mcmc(initial, nsteps, progress=True)
    end = time.time()
    multi_data_global_time = end - start
    print("Multiprocessing took {0:.1f} seconds".format(multi_data_global_time))
    print("{0:.1f} times faster than serial".format(serial_data_time / multi_data_global_time))
100%|██████████| 100/100 [00:06<00:00, 16.46it/s]
Multiprocessing took 6.2 seconds
3.4 times faster than serial

That’s better! This works because, in the global variable case, the dataset is only pickled and passed between processes once (when the pool is created) instead of once for every model evaluation.