01-Recommender-System


01 - Recommender System

  • "Given the values I do have, predict my missing values"
  • This is a kind of imputation / recommender system
  • Straight-forward matrix decomposition methods can help here

In [302]:
import numpy as np
import pandas as pd
from scipy.sparse.linalg import svds
from sklearn.metrics import mean_squared_error
import matplotlib.pyplot as plt

In [2]:
from jlab import load_test_data

In [110]:
X_train = pd.read_csv('MLchallenge2_training.csv')
X_test = load_test_data('test_in.csv')
X = (pd.concat([X_test, X_train], axis=0)
     .reset_index(drop=True)
     .fillna(0.0))
X_true = pd.read_csv('test_prediction.csv', names=['x', 'y', 'px', 'py', 'pz'],
                     header=None)

In [111]:
X.head()


Out[111]:
x y z px py pz x1 y1 z1 px1 ... z23 px23 py23 pz23 x24 y24 z24 px24 py24 pz24
0 0.877 1.322 65.0 -0.244 -0.053 2.414 -10.669 0.330 176.944 -0.254 ... 0.00 0.000 0.000 0.000 0.0 0.0 0.000 0.0 0.0 0.0
1 0.786 -2.483 65.0 0.103 0.432 2.593 7.366 15.502 176.944 0.206 ... 0.00 0.000 0.000 0.000 0.0 0.0 0.000 0.0 0.0 0.0
2 -13.134 -26.531 65.0 0.064 -0.021 0.953 -7.586 -30.687 176.944 0.027 ... 0.00 0.000 0.000 0.000 0.0 0.0 0.000 0.0 0.0 0.0
3 18.454 2.805 65.0 -0.019 0.069 1.833 18.043 6.797 176.944 0.013 ... 0.00 0.000 0.000 0.000 0.0 0.0 0.000 0.0 0.0 0.0
4 15.552 -19.196 65.0 -0.010 -0.011 2.366 15.068 -19.750 176.944 -0.014 ... 341.28 -0.014 -0.002 2.351 0.0 0.0 343.405 0.0 0.0 0.0

5 rows × 150 columns


In [112]:
X_true.head()


Out[112]:
x y px py pz
0 -23.123945 3.142886 -0.235592 0.091612 2.413377
1 19.633486 32.319292 0.314376 0.316425 2.592952
2 -8.308506 -39.299613 -0.020097 -0.051232 0.948906
3 19.918838 10.664617 0.038102 0.047740 1.864014
4 13.649239 -20.616935 -0.015548 0.001471 2.323953

In [97]:
U, sigma, Vt = svds(X, k=30)
sigma = np.diag(sigma)

In [98]:
X_pred = pd.DataFrame(np.dot(np.dot(U, sigma), Vt), columns=X.columns, index=X.index)
X_pred.head()


Out[98]:
x y z px py pz x1 y1 z1 px1 ... z23 px23 py23 pz23 x24 y24 z24 px24 py24 pz24
0 1.139458 1.841577 65.000348 -0.132866 -0.152526 2.278765 -10.308074 0.077691 176.945038 -0.140774 ... -0.001327 -0.020493 -0.114052 0.212795 -0.317946 0.195674 -0.005499 -0.020159 -0.113749 0.212069
1 1.538296 -3.277263 65.000407 -0.142155 0.290338 2.350373 6.721598 15.147325 176.945195 -0.041034 ... -0.005960 -0.140109 0.100994 0.363288 0.135978 0.424870 -0.004066 -0.140975 0.100855 0.362115
2 -13.669357 -25.403695 64.999143 0.235995 0.027828 1.139225 -7.365034 -31.750689 176.941817 0.189261 ... -0.004733 0.290119 0.160645 -0.763249 0.596819 3.866317 0.006622 0.293293 0.166603 -0.759302
3 18.292252 2.048436 64.999907 -0.122082 0.101017 1.869429 18.183965 7.240228 176.943918 -0.092881 ... -0.006987 -0.185933 0.090368 -0.093341 1.670177 0.903375 0.008946 -0.176907 0.092282 -0.100364
4 15.657900 -19.322310 65.000323 -0.012487 0.010699 2.273879 14.897386 -19.569022 176.945024 -0.021853 ... 341.263763 -0.022465 0.067983 2.253718 6.673950 -10.270620 343.400090 -0.025013 0.081539 2.256946

5 rows × 150 columns

Hooray, we did it

  • Now we need to figure out how well it actually did

In [303]:
def get_test_detector_plane(row):
    # Find location of nans, get the first one
    # Then divide by 6 (6 values per detector plane)
    plane = np.where(np.isnan(row.values))[0][0]/6
    return int(plane)

In [304]:
def get_vals_at_plane(row, plane):
    cols = [i + str(int(plane)) for i in ['x','y','px','py','pz']]
    return row[cols].values

In [305]:
def get_vals_at_eval_plane(X_test, X_pred):
    X = X_pred.copy()
    X['eval_plane'] = X_test.apply(get_test_detector_plane, axis=1)
    retvals = X.loc[X_test.index.values].apply(lambda x: get_vals_at_plane(x, x['eval_plane']), axis=1)
    return retvals

In [306]:
eval_planes = X_test.apply(get_test_detector_plane, axis=1)

In [309]:
get_vals_at_plane(X_test.loc[15], 7)


Out[309]:
array([24.406, 30.898,  0.139,  0.107,  2.34 ])

Make a recommender class, a la sklearn

  • Should have fit, predict methods

In [311]:
import logging
from jlab import COLS
from sklearn.preprocessing import StandardScaler

class DetectorRecommender(object):
    
    def __init__(self, k=20):
        
        self.logger = logging.getLogger(__name__)
        self.k = k
        self.planes = 27
        self.kinematics = ["x", "y", "px", "py", "pz"]
        self.cols = COLS
        self.X_train = pd.DataFrame(columns=self.cols)
        self.X_test = pd.DataFrame(columns=self.cols)
        self.scaler = StandardScaler()
        
    def fit(self, df):
        """SVD isn't really 'trained', but... """
        
        self.X_train = df.copy(deep=True)
        
    def predict(self, df):
        
        # Make a copy, index it from 0 to N
        self.logger.debug("Making a copy")
        self.X_test = df.copy(deep=True).reset_index(drop=True)
        
        # For each track, figure out which detector plane we'll evaluate
        self.logger.debug("Determining evaluation planes")
        eval_planes = self.X_test.apply(self.get_eval_detector_plane, axis=1)
        
        # Combine with the training set, shuffle it, and fill missing values
        self.logger.debug("Combining train and test sets for SVD")
        X = (pd.concat([self.X_test, self.X_train], axis=0)
             .reset_index(drop=True)
             .sample(replace=False, frac=1.0))
        
        # Fill with the mean values of each column
        self.logger.debug("Filling with mean values")
        X = X.fillna(X.mean())
        
        # Normalize the values
        self.logger.debug("Applying standardscaler")
        X_norm_values = self.scaler.fit_transform(X)
        X_norm = pd.DataFrame(X_norm_values, columns=X.columns, index=X.index)
        
        # Single-value Decomposition
        self.logger.debug("Making predictions")
        X_pred_norm = self.fit_predict_svds(X_norm)
        
        # Extract our test tracks
        X_pred_norm = X_pred_norm.loc[self.X_test.index, :].sort_index()
        
        # Un-normalize them
        X_pred_values = self.scaler.inverse_transform(X_pred_norm)
        X_pred = pd.DataFrame(X_pred_values, columns=X_pred_norm.columns,
                              index=X_pred_norm.index)
        self.logger.debug("De-normalized. Extracting pred values.")
        
        # Extract just the non-z kinematic values for the eval planes
        det_eval_values = self.extract_values_at_eval_planes(X_pred, eval_planes)
        
        return det_eval_values
    

    def fit_predict_svds(self, X):
        U, sigma, Vt = svds(X, k=self.k)
        sigma = np.diag(sigma)
        X_pred = pd.DataFrame(np.dot(np.dot(U, sigma), Vt),
                              columns=X.columns, index=X.index)
        return X_pred
        
    def extract_values_at_eval_planes(self, pred, planes):
        X = pred.copy(deep=True)
        X['eval_plane'] = planes
        retvals = X.apply(lambda x: self.get_vals_at_plane(x, x['eval_plane']), axis=1)
        retvals_df = pd.DataFrame(retvals.values.tolist(), columns=self.kinematics)
        return retvals_df
    
    def get_vals_at_plane(self, row, plane):
        cols = [i + str(int(plane)) for i in self.kinematics]
        return row[cols].values
    
    def get_eval_detector_plane(self, row):
        # Find location of nans, get the first one
        # Then divide by 6 (6 values per detector plane)
        plane = np.where(np.isnan(row.values))[0][0]/6
        return int(plane)

In [284]:
logging.basicConfig(level=logging.DEBUG,
                    format='%(asctime)s - %(name)-12s - %(levelname)-8s - %(message)s')

In [285]:
predictor = DetectorRecommender()

In [286]:
predictor.fit(X_train)

In [287]:
X_pred = predictor.predict(X_test)


2019-10-29 07:24:55,659 __main__     DEBUG    Making a copy
2019-10-29 07:24:55,667 __main__     DEBUG    Determining evaluation planes
2019-10-29 07:24:55,770 __main__     DEBUG    Combining train and test sets for SVD
2019-10-29 07:24:56,855 __main__     DEBUG    Filling with mean values
2019-10-29 07:24:57,086 __main__     DEBUG    Applying standardscaler
2019-10-29 07:24:57,899 __main__     DEBUG    Making predictions
2019-10-29 07:24:59,484 __main__     DEBUG    De-normalized. Extracting pred values.

In [288]:
X_pred.head()


Out[288]:
x y px py pz
0 -10.402730 0.495083 -0.101857 0.040509 2.136227
1 9.098936 15.436974 0.151903 0.137151 2.225860
2 -4.508659 -18.078571 0.009943 0.003992 1.521642
3 10.067680 4.905410 0.003623 0.020500 1.921455
4 12.463507 -17.100075 -0.009114 0.004804 2.296975

In [290]:
mean_squared_error(X_true, X_pred)


Out[290]:
37.71380513026001

Tune the one hyperparameter we have


In [294]:
for k in range(5,15):
    predictor = DetectorRecommender(k=k)
    predictor.fit(X_train)
    X_pred = predictor.predict(X_test)
    print(k, mean_squared_error(X_true, X_pred))


2019-10-29 08:40:56,810 __main__     DEBUG    Making a copy
2019-10-29 08:40:56,824 __main__     DEBUG    Determining evaluation planes
2019-10-29 08:40:56,949 __main__     DEBUG    Combining train and test sets for SVD
2019-10-29 08:40:58,033 __main__     DEBUG    Filling with mean values
2019-10-29 08:40:58,278 __main__     DEBUG    Applying standardscaler
2019-10-29 08:40:59,122 __main__     DEBUG    Making predictions
2019-10-29 08:40:59,872 __main__     DEBUG    De-normalized. Extracting pred values.
---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
//anaconda3/lib/python3.7/importlib/_bootstrap.py in _find_and_load(name, import_)

//anaconda3/lib/python3.7/importlib/_bootstrap.py in _find_and_load_unlocked(name, import_)

//anaconda3/lib/python3.7/importlib/_bootstrap.py in _call_with_frames_removed(f, *args, **kwds)

ModuleNotFoundError: No module named 'pandas._libs.pandas'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-294-acb4781ec768> in <module>
      3     predictor = DetectorRecommender(k=k)
      4     predictor.fit(X_train)
----> 5     X_pred = predictor.predict(X_test)
      6     print(k, mean_squared_error(X_true, X_pred))

<ipython-input-283-ed69ee6e949e> in predict(self, df)
     60 
     61         # Extract just the non-z kinematic values for the eval planes
---> 62         det_eval_values = self.extract_values_at_eval_planes(X_pred, eval_planes)
     63 
     64         return det_eval_values

<ipython-input-283-ed69ee6e949e> in extract_values_at_eval_planes(self, pred, planes)
     74         X = pred.copy(deep=True)
     75         X['eval_plane'] = planes
---> 76         retvals = X.apply(lambda x: self.get_vals_at_plane(x, x['eval_plane']), axis=1)
     77         retvals_df = pd.DataFrame(retvals.values.tolist(), columns=self.kinematics)
     78         return retvals_df

//anaconda3/lib/python3.7/site-packages/pandas/core/frame.py in apply(self, func, axis, broadcast, raw, reduce, result_type, args, **kwds)
   6485                          args=args,
   6486                          kwds=kwds)
-> 6487         return op.get_result()
   6488 
   6489     def applymap(self, func):

//anaconda3/lib/python3.7/site-packages/pandas/core/apply.py in get_result(self)
    149             return self.apply_raw()
    150 
--> 151         return self.apply_standard()
    152 
    153     def apply_empty_result(self):

//anaconda3/lib/python3.7/site-packages/pandas/core/apply.py in apply_standard(self)
    255 
    256         # compute the result using the series generator
--> 257         self.apply_series_generator()
    258 
    259         # wrap results

//anaconda3/lib/python3.7/site-packages/pandas/core/apply.py in apply_series_generator(self)
    284             try:
    285                 for i, v in enumerate(series_gen):
--> 286                     results[i] = self.f(v)
    287                     keys.append(v.name)
    288             except Exception as e:

<ipython-input-283-ed69ee6e949e> in <lambda>(x)
     74         X = pred.copy(deep=True)
     75         X['eval_plane'] = planes
---> 76         retvals = X.apply(lambda x: self.get_vals_at_plane(x, x['eval_plane']), axis=1)
     77         retvals_df = pd.DataFrame(retvals.values.tolist(), columns=self.kinematics)
     78         return retvals_df

<ipython-input-283-ed69ee6e949e> in get_vals_at_plane(self, row, plane)
     80     def get_vals_at_plane(self, row, plane):
     81         cols = [i + str(int(plane)) for i in self.kinematics]
---> 82         return row[cols].values
     83 
     84     def get_eval_detector_plane(self, row):

//anaconda3/lib/python3.7/site-packages/pandas/core/series.py in __getitem__(self, key)
    909             key = check_bool_indexer(self.index, key)
    910 
--> 911         return self._get_with(key)
    912 
    913     def _get_with(self, key):

//anaconda3/lib/python3.7/site-packages/pandas/core/series.py in _get_with(self, key)
    949             # handle the dup indexing case (GH 4246)
    950             if isinstance(key, (list, tuple)):
--> 951                 return self.loc[key]
    952 
    953             return self.reindex(key)

//anaconda3/lib/python3.7/site-packages/pandas/core/indexing.py in __getitem__(self, key)
   1498 
   1499             maybe_callable = com.apply_if_callable(key, self.obj)
-> 1500             return self._getitem_axis(maybe_callable, axis=axis)
   1501 
   1502     def _is_scalar_access(self, key):

//anaconda3/lib/python3.7/site-packages/pandas/core/indexing.py in _getitem_axis(self, key, axis)
   1900                     raise ValueError('Cannot index with multidimensional key')
   1901 
-> 1902                 return self._getitem_iterable(key, axis=axis)
   1903 
   1904             # nested tuple slicing

//anaconda3/lib/python3.7/site-packages/pandas/core/indexing.py in _getitem_iterable(self, key, axis)
   1203             # A collection of keys
   1204             keyarr, indexer = self._get_listlike_indexer(key, axis,
-> 1205                                                          raise_missing=False)
   1206             return self.obj._reindex_with_indexers({axis: [keyarr, indexer]},
   1207                                                    copy=True, allow_dups=True)

//anaconda3/lib/python3.7/site-packages/pandas/core/indexing.py in _get_listlike_indexer(self, key, axis, raise_missing)
   1152             if len(ax) or not len(key):
   1153                 key = self._convert_for_reindex(key, axis)
-> 1154             indexer = ax.get_indexer_for(key)
   1155             keyarr = ax.reindex(keyarr)[0]
   1156         else:

//anaconda3/lib/python3.7/site-packages/pandas/core/indexes/base.py in get_indexer_for(self, target, **kwargs)
   4453         """
   4454         if self.is_unique:
-> 4455             return self.get_indexer(target, **kwargs)
   4456         indexer, _ = self.get_indexer_non_unique(target, **kwargs)
   4457         return indexer

//anaconda3/lib/python3.7/site-packages/pandas/core/indexes/base.py in get_indexer(self, target, method, limit, tolerance)
   2716     def get_indexer(self, target, method=None, limit=None, tolerance=None):
   2717         method = missing.clean_reindex_fill_method(method)
-> 2718         target = ensure_index(target)
   2719         if tolerance is not None:
   2720             tolerance = self._convert_tolerance(tolerance, target)

//anaconda3/lib/python3.7/site-packages/pandas/core/indexes/base.py in ensure_index(index_like, copy)
   5362             index_like = list(index_like)
   5363 
-> 5364         converted, all_arrays = lib.clean_index_list(index_like)
   5365 
   5366         if len(converted) > 0 and all_arrays:

pandas/_libs/lib.pyx in pandas._libs.lib.clean_index_list()

pandas/_libs/lib.pyx in pandas._libs.lib.infer_dtype()

//anaconda3/lib/python3.7/importlib/_bootstrap.py in _find_and_load(name, import_)

KeyboardInterrupt: 
  • Optimal performance at k=7

In [300]:
predictor = DetectorRecommender(k=7)
predictor.fit(X_train)
X_pred = predictor.predict(X_test)
print(mean_squared_error(X_true, X_pred))


2019-10-29 08:47:32,386 __main__     DEBUG    Making a copy
2019-10-29 08:47:32,391 __main__     DEBUG    Determining evaluation planes
2019-10-29 08:47:32,498 __main__     DEBUG    Combining train and test sets for SVD
2019-10-29 08:47:33,901 __main__     DEBUG    Filling with mean values
2019-10-29 08:47:34,069 __main__     DEBUG    Applying standardscaler
2019-10-29 08:47:35,066 __main__     DEBUG    Making predictions
2019-10-29 08:47:35,796 __main__     DEBUG    De-normalized. Extracting pred values.
20.43716499928241

Surprise!

Try out this well-supported recommender package


In [314]:
!pip install scikit-surprise


Collecting scikit-surprise
  Using cached https://files.pythonhosted.org/packages/f5/da/b5700d96495fb4f092be497f02492768a3d96a3f4fa2ae7dea46d4081cfa/scikit-surprise-1.1.0.tar.gz
Requirement already satisfied: joblib>=0.11 in /anaconda3/lib/python3.7/site-packages (from scikit-surprise) (0.13.2)
Requirement already satisfied: numpy>=1.11.2 in /anaconda3/lib/python3.7/site-packages (from scikit-surprise) (1.16.4)
Requirement already satisfied: scipy>=1.0.0 in /anaconda3/lib/python3.7/site-packages (from scikit-surprise) (1.3.0)
Requirement already satisfied: six>=1.10.0 in /anaconda3/lib/python3.7/site-packages (from scikit-surprise) (1.12.0)
Building wheels for collected packages: scikit-surprise
  Building wheel for scikit-surprise (setup.py) ... done
  Stored in directory: /Users/dannowitz/Library/Caches/pip/wheels/cc/fa/8c/16c93fccce688ae1bde7d979ff102f7bee980d9cfeb8641bcf
Successfully built scikit-surprise
Installing collected packages: scikit-surprise
Successfully installed scikit-surprise-1.1.0

In [298]:
import surprise


---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
<ipython-input-298-7ee1a83cf20e> in <module>
----> 1 import surprise

ModuleNotFoundError: No module named 'surprise'

In [ ]:
X.melt()

In [169]:
X.index.name = "track_id"

In [170]:
X.head().reset_index().melt(id_vars=['track_id'])


Out[170]:
track_id variable value
0 0 x 0.877
1 1 x 0.786
2 2 x -13.134
3 3 x 18.454
4 4 x 15.552
5 0 y 1.322
6 1 y -2.483
7 2 y -26.531
8 3 y 2.805
9 4 y -19.196
10 0 z 65.000
11 1 z 65.000
12 2 z 65.000
13 3 z 65.000
14 4 z 65.000
15 0 px -0.244
16 1 px 0.103
17 2 px 0.064
18 3 px -0.019
19 4 px -0.010
20 0 py -0.053
21 1 py 0.432
22 2 py -0.021
23 3 py 0.069
24 4 py -0.011
25 0 pz 2.414
26 1 pz 2.593
27 2 pz 0.953
28 3 pz 1.833
29 4 pz 2.366
... ... ... ...
720 0 x24 0.000
721 1 x24 0.000
722 2 x24 0.000
723 3 x24 0.000
724 4 x24 0.000
725 0 y24 0.000
726 1 y24 0.000
727 2 y24 0.000
728 3 y24 0.000
729 4 y24 0.000
730 0 z24 0.000
731 1 z24 0.000
732 2 z24 0.000
733 3 z24 0.000
734 4 z24 343.405
735 0 px24 0.000
736 1 px24 0.000
737 2 px24 0.000
738 3 px24 0.000
739 4 px24 0.000
740 0 py24 0.000
741 1 py24 0.000
742 2 py24 0.000
743 3 py24 0.000
744 4 py24 0.000
745 0 pz24 0.000
746 1 pz24 0.000
747 2 pz24 0.000
748 3 pz24 0.000
749 4 pz24 0.000

750 rows × 3 columns


In [164]:
X.sample(replace=False, frac=1.0)


Out[164]:
x y z px py pz x1 y1 z1 px1 ... z23 px23 py23 pz23 x24 y24 z24 px24 py24 pz24
52641 -17.403500 -21.669100 65.0 0.018850 -0.070221 2.808130 -17.098200 -24.305200 176.944 -0.004557 ... 341.280 -0.018001 -0.067943 2.800710 -18.208300 -28.138900 343.405 -0.017034 -0.068414 2.800680
153188 -2.030520 7.950830 65.0 0.140483 0.195651 2.262990 6.209280 16.391700 176.944 0.191073 ... 341.280 0.224867 0.054636 2.249030 22.275300 23.367100 343.405 0.224612 0.054472 2.249040
26736 3.743760 -20.476100 65.0 -0.016751 -0.022347 0.948275 0.072519 -22.697500 176.944 -0.041323 ... 341.280 -0.020188 0.031900 0.936075 -6.918930 -20.234000 343.405 -0.018757 0.031732 0.936098
113795 -8.214490 12.470600 65.0 -0.127324 -0.017557 2.029990 -15.177600 12.624900 176.944 -0.126454 ... 341.280 -0.105276 0.072318 2.020760 -24.585400 17.047300 343.405 -0.105614 0.071741 2.020650
72875 5.645860 -16.347100 65.0 0.062687 -0.018573 0.946145 11.775000 -20.705000 176.944 0.038080 ... 341.280 -0.015396 -0.050101 0.934989 12.384100 -31.306800 343.405 -0.014956 -0.049401 0.935021
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204601 rows × 150 columns


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