Collaborative Topic Poisson Factorization

Python implementation of the algorithm for probabilistic matrix factorization described in Content-based recommendations with poisson factorization (Gopalan, P.K., Charlin, L. and Blei, D., 2014).

This is a statistical model aimed at recommender systems with implicit data consisting of counts of user-item interactions (e.g. clicks by each user on different products) plus bag-of-words representations of the items. The model is fit using mean-field variational inference. Can also fit the model to side information on the users consisting of counts on different attributes (same format as the bag-of-words for items).

As it takes side information about items, it has the advantage of being able to recommend items without any ratings/clicks/plays/etc. If extending it with user side information, can also make cold-start recommendations, albeit speed is not great for that.

Supports parallelization, different stopping criteria for the optimziation procedure, and adding users/items without refitting the model entirely. The bottleneck computations are written in fast Cython code.

For a similar package for explicit feedback data see also cmfrec.

For Poisson factorization without side information see hpfrec and poismf.

Model description

The model consists in producing non-negative low-rank matrix factorizations of counts data (such as number of times each user played each song in some internet service) of user-item interactions and item-word counts, produced by a generative model specified as follows:

Item model:
B_vk ~ Gamma(a, b)
T_ik ~ Gamma(c, d)
W_iv ~ Poisson(T * B')

Interactions model:
N_uk ~ Gamma(e, f)
E_ik ~ Gamma(g, h)
R_ui ~ Poisson(N * (T + E)')

(Where W is the bag-of-words representation of the items, R is the user-item interactions matrix, u is the number of users, i is the number of items, v is the number of words, and k is the number of latent factors or topics)

For more details see the references section at the bottom.

When adding user information, the model becomes as follows:

Item model:
B_vk ~ Gamma(a, b)
T_ik ~ Gamma(c, d)
W_iv ~ Poisson(T * B')

User model:
K_ak ~ Gamma(e, f)
O_uk ~ Gamma(l, m)
Q_ua ~ Poisson(O * K')

Interactions model:
N_uk ~ Gamma(i, j)
E_ik ~ Gamma(g, h)
R_ui ~ Poisson((O + N) * (T + E)')

A huge drawback of this model compared to LDA is that, as the matrices are non-negative, items with more words will have larger values in their factors/topics, which will result in them having higher scores regardless of their popularity. This effect can be somewhat decreased by using only a limited number of words to represent each item (scaling upwards the ones that don't have enough words), by standardizing the bag-of-words to have all rows summing up to a certain number (this is hard to do when the counts are supposed to be integers, but the package can still work mostly fine with decimals that are at least >= 0.9, and has the option to standardize the inputs), or to a lesser extent by standardizing the resulting Theta shape matrix to have its rows sum to 1 (also supported in the package options).

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 ctpfrec

Or if that fails:

pip install --no-use-pep517 ctpfrec

---

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 ctpfrec.

---

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 ctpfrec

or, by specifying some compilation flag for architecture:

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

---

Sample usage

import numpy as np, pandas as pd
from ctpfrec import CTPF

## Generating a fake dataset
nusers = 10**2
nitems = 10**2
nwords = 5 * 10**2
nobs   = 10**4
nobs_bag_of_words = 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)

words_df = pd.DataFrame({
	'ItemId' : np.random.randint(nitems, size=nobs_bag_of_words),
	'WordId' : np.random.randint(nwords, size=nobs_bag_of_words),
	'Count'  : (np.random.gamma(1, 1, size=nobs_bag_of_words) + 1).astype('int32')
	})
words_df = words_df.loc[~words_df[['ItemId', 'WordId']].duplicated()].reset_index(drop=True)

## Fitting the model
## (Can also pass the inputs as COO matrices)
recommender = CTPF(k = 15, reindex=True)
recommender.fit(counts_df=counts_df, words_df=words_df)

## Making predictions
recommender.topN(user=10, n=10, exclude_seen=True)
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 log-likelihood
recommender.eval_llk(counts_df, full_llk=True)

## Adding new items without refitting
nitems_new = 10
nobs_bow_new = 2 * 10**3
np.random.seed(5)
words_df_new = pd.DataFrame({
	'ItemId' : np.random.uniform(low=nitems, high=nitems+nitems_new, size=nobs_bow_new),
	'WordId' : np.random.randint(nwords, size=nobs_bow_new),
	'Count' : np.random.gamma(1, 1, size=nobs_bow_new).astype('int32')
	})
words_df_new = words_df_new.loc[words_df_new.Count > 0]

recommender.add_items(words_df_new)

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 topN are these same IDs passed to .fit too.

For a more detailed example, see the IPython notebook recommending products with RetailRocket's event logs illustrating its usage with the RetailRocket dataset consisting of activity logs (view, add-to-basket, purchase) and item descriptions.

Documentation

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

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

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 CTPF 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.

Saving model with pickle

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

import dill
from ctpfrec import CTPF

c = CTPF()
dill.dump(c, open("CTPF_obj.dill", "wb"))
c = dill.load(open("CTPF_obj.dill", "rb"))

References

[1] Gopalan, Prem K., Laurent Charlin, and David Blei. "Content-based recommendations with poisson factorization." Advances in Neural Information Processing Systems. 2014.