Hierarchical Poisson Factorization

This is a Python package for hierarchical Poisson factorization, a form of probabilistic matrix factorization used for recommender systems with implicit count data, based on the paper Scalable Recommendation with Hierarchical Poisson Factorization (P. Gopalan, 2015).

Although the package was created with recommender systems in mind, it can also be used for other domains, e.g. as a faster alternative to LDA (Latent Ditichlet Allocation), where users become documents and items become words.

Supports parallelization, full-batch variational inference, mini-batch stochastic variational inference (alternating between epochs sampling batches of users and epochs sampling batches of items), and different stopping criteria for the coordinate-ascent procedure. The main computations are written in fast Cython code.

As a point of reference, fitting the model through full-batch updates to the MillionSong TasteProfile dataset (48M records from 1M users on 380K items) took around 45 minutes on a server from Google Cloud with Skylake CPU when using 24 cores.

For a similar package using also item/user side information see ctpfrec.

For a non-Bayesian version which can produce sparse factors see poismf.

---

Note: this package can also be used from within LensKit, which adds functionalities such as cross-validation and calculation of recommendation quality metrics.

Model description

The model consists in producing a non-negative low-rank matrix factorization of counts data (such as number of times each user played each song in some internet service) Y ~= UV', produced by a generative model as follows:

ksi_u ~ Gamma(a_prime, a_prime/b_prime)
Theta_uk ~ Gamma(a, ksi_u)

eta_i ~ Gamma(c_prime, c_prime/d_prime)
Beta_ik ~ Gamma(c, eta_i)

Y_ui ~ Poisson(Theta_u' Beta_i)

The parameters are fit using mean-field approximation (a form of Bayesian variational inference) with coordinate ascent (updating each parameter separately until convergence).

Installation

Note: requires a C compiler configured for Python. See this guide for instructions.

Package is available on PyPI, can be installed with:

pip install hpfrec

Or if that fails:

pip install --no-use-pep517 hpfrec

---

Note for macOS users: on macOS, the Python version of this package might compile without multi-threading capabilities. In order to enable multi-threading support, first install OpenMP:

brew install libomp

And then reinstall this package: pip install --upgrade --no-deps --force-reinstall hpfrec.

---

IMPORTANT: the setup script will try to add compilation flag -march=native. This instructs the compiler to tune the package for the CPU in which it is being installed (by e.g. using AVX instructions if available), but the result might not be usable in other computers. If building a binary wheel of this package or putting it into a docker image which will be used in different machines, this can be overriden either by (a) defining an environment variable DONT_SET_MARCH=1, or by (b) manually supplying compilation CFLAGS as an environment variable with something related to architecture. For maximum compatibility (but slowest speed), it's possible to do something like this:

export DONT_SET_MARCH=1
pip install hpfrec

or, for forcing a maximum-compatibility x86-64 binary:

export CFLAGS="-march=x86-64"
pip install hpfrec

---

Sample usage

import pandas as pd, numpy as np
from hpfrec import HPF

## Generating sample counts data
nusers = 10**2
nitems = 10**2
nobs   = 10**4

np.random.seed(1)
counts_df = pd.DataFrame({
	'UserId' : np.random.randint(nusers, size=nobs),
	'ItemId' : np.random.randint(nitems, size=nobs),
	'Count' :  (np.random.gamma(1,1, size=nobs) + 1).astype('int32')
	})
counts_df = counts_df.loc[~counts_df[['UserId', 'ItemId']].duplicated()].reset_index(drop=True)

## Initializing the model object
recommender = HPF()

## For stochastic variational inference, need to select batch size (number of users)
recommender = HPF(users_per_batch = 20)

## Full function call
recommender = HPF(
	k=30, a=0.3, a_prime=0.3, b_prime=1.0,
	c=0.3, c_prime=0.3, d_prime=1.0, ncores=-1,
	stop_crit='train-llk', check_every=10, stop_thr=1e-3,
	users_per_batch=None, items_per_batch=None, step_size=lambda x: 1/np.sqrt(x+2),
	maxiter=100, use_float=True, reindex=True, verbose=True,
	random_seed=None, allow_inconsistent_math=False, full_llk=False,
	alloc_full_phi=False, keep_data=True, save_folder=None,
	produce_dicts=True, keep_all_objs=True, sum_exp_trick=False
)

## Fitting the model to the data
recommender.fit(counts_df)

## Fitting the model while monitoring a validation set
recommender = HPF(stop_crit='val-llk')
recommender.fit(counts_df, val_set=counts_df.sample(10**2))
## Note: a real validation should NEVER be a subset of the training set

## Fitting the model to data in batches passed by the user
recommender = HPF(reindex=False, keep_data=False)
users_batch1 = np.unique(np.random.randint(10**2, size=20))
users_batch2 = np.unique(np.random.randint(10**2, size=20))
users_batch3 = np.unique(np.random.randint(10**2, size=20))
recommender.partial_fit(counts_df.loc[counts_df.UserId.isin(users_batch1)], nusers=10**2, nitems=10**2)
recommender.partial_fit(counts_df.loc[counts_df.UserId.isin(users_batch2)])
recommender.partial_fit(counts_df.loc[counts_df.UserId.isin(users_batch3)])

## Making predictions
# recommender.topN(user=10, n=10, exclude_seen=True) ## not available when using 'partial_fit'
recommender.topN(user=10, n=10, exclude_seen=False, items_pool=np.array([1,2,3,4]))
recommender.predict(user=10, item=11)
recommender.predict(user=[10,10,10], item=[1,2,3])
recommender.predict(user=[10,11,12], item=[4,5,6])

## Evaluating Poisson likelihood
recommender.eval_llk(counts_df, full_llk=True)

## Determining latent factors for a new user, given her item interactions
nobs_new = 20
np.random.seed(2)
counts_df_new = pd.DataFrame({
	'ItemId' : np.random.choice(np.arange(nitems), size=nobs_new, replace=False),
	'Count' : np.random.gamma(1,1, size=nobs_new).astype('int32')
	})
counts_df_new = counts_df_new.loc[counts_df_new.Count > 0].reset_index(drop=True)
recommender.predict_factors(counts_df_new)

## Adding a user without refitting the whole model
recommender.add_user(user_id=nusers+1, counts_df=counts_df_new)

## Updating data for an existing user without refitting the whole model
chosen_user = counts_df.UserId.values[10]
recommender.add_user(user_id=chosen_user, counts_df=counts_df_new, update_existing=True)

If passing reindex=True, all user and item IDs that you pass to .fit will be reindexed internally (they need to be hashable types like str, int or tuple), and you can use these same IDs to make predictions later. The IDs returned by predict and topN are these IDs passed to .fit too.

For a more detailed example, see the IPython notebook recommending songs with EchoNest MillionSong dataset illustrating its usage with the EchoNest TasteProfile dataset.

Documentation

Documentation is available at readthedocs: http://hpfrec.readthedocs.io

It is also internally documented through docstrings (e.g. you can try help(hpfrec.HPF)), help(hpfrec.HPF.fit), etc.

Serializing (pickling) the model

Don't use pickle to save an HPF object, as it will fail due to problems with lambda functions. Rather, use dill instead, which has the same syntax as pickle:

import dill
from hpfrec import HPF

h = HPF()
dill.dump(h, open("HPF_obj.dill", "wb"))
h = dill.load(open("HPF_obj.dill", "rb"))

Speeding up optimization procedure

For faster fitting and predictions, use SciPy and NumPy libraries compiled against MKL or OpenBLAS. These come by default with MKL in Anaconda installations.

The constructor for HPF allows some parameters to make it run faster (if you know what you're doing): these are allow_inconsistent_math=True, full_llk=False, stop_crit='diff-norm', reindex=False, verbose=False. See the documentation for more details.

Using stochastic variational inference, which fits the data in smaller batches containing all the user-item interactions only for subsets of users, might converge in fewer iterations (epochs), but the results tend be slightly worse.

References

• [1] Gopalan, Prem, Jake M. Hofman, and David M. Blei. "Scalable Recommendation with Hierarchical Poisson Factorization." UAI. 2015.
• [2] Gopalan, Prem, Jake M. Hofman, and David M. Blei. "Scalable recommendation with poisson factorization." arXiv preprint arXiv:1311.1704 (2013).
• [3] Hoffman, Matthew D., et al. "Stochastic variational inference." The Journal of Machine Learning Research 14.1 (2013): 1303-1347.