Baseline model and assessment

In [34]:
import pandas as pd
import numpy as np
%matplotlib inline

import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline
from sklearn.grid_search import GridSearchCV
from sklearn.metrics import r2_score
from sklearn.metrics import mean_squared_error
In [35]:
df = pd.read_feather('../data/basemodel_cumsum.feather')

model = LinearRegression(fit_intercept = True)
x = df[['popularity']]
y = df[['log_all_streams_cumsum']]

def PolynomialRegression(degree=2, **kwargs):
    return make_pipeline(PolynomialFeatures(degree), LinearRegression(**kwargs))

param_grid = {'polynomialfeatures__degree': np.arange(3), 'linearregression__normalize': [True, False]}

grid = GridSearchCV(PolynomialRegression(), param_grid, cv = 5, error_score=mean_squared_error)

Baseline model (2018-05-21 22:12)

In [36]:
def fitAndEvaluate(x,y,grid):
    grid.fit(x,y)
    model = grid.best_estimator_
    print(f'Best model: {model}')
    y_pred = model.predict(x)

    plt.subplot(1,2,1)
    plt.scatter(y_pred, y_pred - y)
    plt.hlines(y = 0, xmin = min(y_pred), xmax = max(y_pred))
    plt.title('Residual Errors')
    
    plt.subplot(1,2,2)
    plt.scatter(x,y)
    lim = plt.axis()
    plt.scatter(x,y_pred, c = 'red')
    plt.title('Prediction versus actual')

    rmse = np.sqrt(np.sum((y_pred - y)**2))[0]
    print(f'RMSE: {rmse}')
    print(f'Rsq: {r2_score(y,y_pred)}')
    

fitAndEvaluate(x,y,grid)

Best model: Pipeline(memory=None,
     steps=[('polynomialfeatures', PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)), ('linearregression', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True))])
RMSE: 5.691645826227121
Rsq: 0.5953026658448666

Baseline with outlier removed (2018-05-22 22:15)

  • Evaluate outlier at 0 popularity. It seems to skew the results. It looks like linear would be a good fit here actually
In [37]:
df.sort_values('popularity').head()
Out[37]:
track_id popularity all_streams_cumsum log_all_streams_cumsum
6 0A488iaPeDAUP5q7Jm3paF 0 791514 13.581703
41 1ekNZULmcBHp3WRNKft7ou 8 68719 11.137781
11 0DPXH5sPDVwjsqfgvmi1yt 26 139665 11.847002
37 1cinSNWNJeGVxMgUSNCHRT 27 137729 11.833043
1 00mc2RHScEYMEFlc7FRGaK 28 93919 11.450188

Popularity 0 outlier

There is an outlier that has massive impact on the curve with 0 popularity, ,this could be some corner case but also some data error. Look into this explicitly.

  • 0A488iaPeDAUP5q7Jm3paF

UPDATE this was caused by an erratic jump to 0 and back

In [38]:
df = pd.read_feather('../data/basemodel_cumsum_outlier_removed.feather')
In [39]:
x = df[['popularity']]
y = df[['log_all_streams_cumsum']]
In [40]:
fitAndEvaluate(x,y,grid)

Best model: Pipeline(memory=None,
     steps=[('polynomialfeatures', PolynomialFeatures(degree=1, include_bias=True, interaction_only=False)), ('linearregression', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True))])
RMSE: 5.600131028898197
Rsq: 0.6082121300639243
In [ ]: