myfm 0.4.0
Yet another Bayesian factorization machines.

# myFM
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myFM is an implementation of Bayesian [Factorization Machines](https://ieeexplore.ieee.org/abstract/document/5694074/) based on Gibbs sampling, which I believe is a wheel worth reinventing.

Currently this supports most options for libFM MCMC engine, such as

- Grouping of input variables (`-meta` option of [libFM](https://github.com/srendle/libfm))
- Relation Data format (See the paper ["Scaling Factorization Machines to relational data"](https://dl.acm.org/citation.cfm?id=2488340))

There are also functionalities not present in libFM:

- The gibbs sampler for Ordered probit regression [5] implementing Metropolis-within-Gibbs scheme of [6].
- Variational inference for regression and binary classification.

Tutorial and reference doc is provided at https://myfm.readthedocs.io/en/latest/.

# Installation

The package is pip-installable.

```
pip install myfm
```

There are binaries for major operating systems.

If you are working with less popular OS/architecture, pip will attempt to build myFM from the source (you need a decent C++ compiler!). In that case, in addition to installing python dependencies (`numpy`, `scipy`, `pandas`, ...), the above command will automatically download eigen (ver 3.4.0) to its build directory and use it during the build.

# Examples

## A Toy example

This example is taken from [pyfm](https://github.com/coreylynch/pyFM) with some modification.

```python
import myfm
from sklearn.feature_extraction import DictVectorizer
import numpy as np
train = [
	{"user": "1", "item": "5", "age": 19},
	{"user": "2", "item": "43", "age": 33},
	{"user": "3", "item": "20", "age": 55},
	{"user": "4", "item": "10", "age": 20},
]
v = DictVectorizer()
X = v.fit_transform(train)
print(X.toarray())
# print
# [[ 19.   0.   0.   0.   1.   1.   0.   0.   0.]
#  [ 33.   0.   0.   1.   0.   0.   1.   0.   0.]
#  [ 55.   0.   1.   0.   0.   0.   0.   1.   0.]
#  [ 20.   1.   0.   0.   0.   0.   0.   0.   1.]]
y = np.asarray([0, 1, 1, 0])
fm = myfm.MyFMClassifier(rank=4)
fm.fit(X,y)
fm.predict(v.transform({"user": "1", "item": "10", "age": 24}))
```

## A Movielens-100k Example

This example will require `pandas` and `scikit-learn`. `movielens100k_loader` is present in `examples/movielens100k_loader.py`.

You will be able to obtain a result comparable to SOTA algorithms like GC-MC. See `examples/ml-100k.ipynb` for the detailed version.

```python
import numpy as np
from sklearn.preprocessing import OneHotEncoder
from sklearn import metrics

import myfm
from myfm.utils.benchmark_data import MovieLens100kDataManager

data_manager = MovieLens100kDataManager()
df_train, df_test = data_manager.load_rating_predefined_split(
    fold=3
)  # Note the dependence on the fold

def test_myfm(df_train, df_test, rank=8, grouping=None, n_iter=100, samples=95):
    explanation_columns = ["user_id", "movie_id"]
    ohe = OneHotEncoder(handle_unknown="ignore")
    X_train = ohe.fit_transform(df_train[explanation_columns])
    X_test = ohe.transform(df_test[explanation_columns])
    y_train = df_train.rating.values
    y_test = df_test.rating.values
    fm = myfm.MyFMRegressor(rank=rank, random_seed=114514)

    if grouping:
        # specify how columns of X_train are grouped
        group_shapes = [len(category) for category in ohe.categories_]
        assert sum(group_shapes) == X_train.shape[1]
    else:
        group_shapes = None

    fm.fit(
        X_train,
        y_train,
        group_shapes=group_shapes,
        n_iter=n_iter,
        n_kept_samples=samples,
    )
    prediction = fm.predict(X_test)
    rmse = ((y_test - prediction) ** 2).mean() ** 0.5
    mae = np.abs(y_test - prediction).mean()
    print("rmse={rmse}, mae={mae}".format(rmse=rmse, mae=mae))
    return fm


# basic regression
test_myfm(df_train, df_test, rank=8)
# rmse=0.90321, mae=0.71164

# with grouping
fm = test_myfm(df_train, df_test, rank=8, grouping=True)
# rmse=0.89594, mae=0.70481
```

## Examples for Relational Data format

Below is a toy movielens-like example that utilizes relational data format proposed in [3].

This example, however, is too simplistic to exhibit the computational advantage of this data format. For an example with drastically reduced computational complexity, see `examples/ml-100k-extended.ipynb`;

```python
import pandas as pd
import numpy as np
from myfm import MyFMRegressor, RelationBlock
from sklearn.preprocessing import OneHotEncoder

users = pd.DataFrame([
    {'user_id': 1, 'age': '20s', 'married': False},
    {'user_id': 2, 'age': '30s', 'married': False},
    {'user_id': 3, 'age': '40s', 'married': True}
]).set_index('user_id')

movies = pd.DataFrame([
    {'movie_id': 1, 'comedy': True, 'action': False },
    {'movie_id': 2, 'comedy': False, 'action': True },
    {'movie_id': 3, 'comedy': True, 'action': True}
]).set_index('movie_id')

ratings = pd.DataFrame([
    {'user_id': 1, 'movie_id': 1, 'rating': 2},
    {'user_id': 1, 'movie_id': 2, 'rating': 5},
    {'user_id': 2, 'movie_id': 2, 'rating': 4},
    {'user_id': 2, 'movie_id': 3, 'rating': 3},
    {'user_id': 3, 'movie_id': 3, 'rating': 3},
])

user_ids, user_indices = np.unique(ratings.user_id, return_inverse=True)
movie_ids, movie_indices = np.unique(ratings.movie_id, return_inverse=True)

user_ohe = OneHotEncoder(handle_unknown='ignore').fit(users.reset_index()) # include user id as feature
movie_ohe = OneHotEncoder(handle_unknown='ignore').fit(movies.reset_index())

X_user = user_ohe.transform(
    users.reindex(user_ids).reset_index()
)
X_movie = movie_ohe.transform(
    movies.reindex(movie_ids).reset_index()
)

block_user = RelationBlock(user_indices, X_user)
block_movie = RelationBlock(movie_indices, X_movie)

fm = MyFMRegressor(rank=2).fit(None, ratings.rating.values, X_rel=[block_user, block_movie])

prediction_df = pd.DataFrame([
    dict(user_id=user_id,movie_id=movie_id,
         user_index=user_index, movie_index=movie_index)
    for user_index, user_id in enumerate(user_ids)
    for movie_index, movie_id in enumerate(movie_ids)
])
predicted_rating = fm.predict(None, [
    RelationBlock(prediction_df.user_index, X_user),
    RelationBlock(prediction_df.movie_index, X_movie)
])

prediction_df['prediction']  = predicted_rating

print(
    prediction_df.merge(ratings.rename(columns={'rating':'ground_truth'}), how='left')
)
```

# References

1. Rendle, Steffen. "Factorization machines." 2010 IEEE International Conference on Data Mining. IEEE, 2010.
1. Rendle, Steffen. "Factorization machines with libfm." ACM Transactions on Intelligent Systems and Technology (TIST) 3.3 (2012): 57.
1. Rendle, Steffen. "Scaling factorization machines to relational data." Proceedings of the VLDB Endowment. Vol. 6. No. 5. VLDB Endowment, 2013.
1. Bayer, Immanuel. "fastfm: A library for factorization machines." arXiv preprint arXiv:1505.00641 (2015).
1. Albert, James H., and Siddhartha Chib. "Bayesian analysis of binary and polychotomous response data." Journal of the American statistical Association 88.422 (1993): 669-679.
1. Albert, James H., and Siddhartha Chib. "Sequential ordinal modeling with applications to survival data." Biometrics 57.3 (2001): 829-836.