How to smooth and plot x vs weighted average of y, weighted by x?

Question

I have a dataframe with a column of weights and one of values. I'd need:

• to discretise weights and, for each interval of weights, plot the weighted average of values , then
• to extend the same logic to another variable: discretise z, and for each interval, plot the weighted average of values, weighted by weights

Is there an easy way to achieve this?I have found a way, but it seems a bit cumbersome:

• I discretise the dataframe with pandas.cut()
• do a groupby and calculate the weighted average
• plot the mean of each bin vs the weighted average
• I have also tried to smooth the curve with a spline, but it doesn't do much

Basically I'm looking for a better way to produce a more smoothed curve.

My output looks like this:

and my code, with some random data, is:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.interpolate import make_interp_spline, BSpline

n=int(1e3)
df=pd.DataFrame()
np.random.seed(10)
df['w']=np.arange(0,n)
df['v']=np.random.randn(n)
df['ranges']=pd.cut(df.w, bins=50)
df['one']=1.
def func(x, df):
    # func() gets called within a lambda function; x is the row, df is the entire table
    b1= x['one'].sum()
    b2 = x['w'].mean()
    b3 = x['v'].mean()       
    b4=( x['w'] * x['v']).sum() / x['w'].sum() if x['w'].sum() >0 else np.nan

    cols=['# items','avg w','avg v','weighted avg v']
    return pd.Series( [b1, b2, b3, b4], index=cols )

summary = df.groupby('ranges').apply(lambda x: func(x,df))

sns.set(style='darkgrid')

fig,ax=plt.subplots(2)
sns.lineplot(summary['avg w'], summary['weighted avg v'], ax=ax[0])
ax[0].set_title('line plot')

xnew = np.linspace(summary['avg w'].min(), summary['avg w'].max(),100)
spl = make_interp_spline(summary['avg w'], summary['weighted avg v'], k=5) #BSpline object
power_smooth = spl(xnew)
sns.lineplot(xnew, power_smooth, ax=ax[1])
ax[1].set_title('not-so-interpolated plot')

Answer 1

The first part of your question is rather easy to do.

I'm not sure what you mean with the second part. Do you want a (simplified) reproduction of your code or a new approach that better fits your need?

Anyway i had to look at your code to understand what you mean by weighting the values. I think people would normally expect something different from the term (just as a warning).

Here's the simplified version of your approach:

df['prod_v_w'] = df['v']*df['w']
weighted_avg_v = df.groupby(pd.cut(df.w, bins=50))[['prod_v_w','w']].sum()\
                   .eval('prod_v_w/w')
print(np.allclose(weighted_avg_v, summary['weighted avg v']))
Out[18]: True

Answer 2

I think you're using few values for the interpolation, by changing xnew = np.linspace(summary['avg w'].min(), summary['avg w'].max(),100) to xnew = np.linspace(summary['avg w'].min(), summary['avg w'].max(),500) I get the following:

And changint the spline degree to k=2 i get the following:

I think a good starting point for the interpolation could be n/2 and k=2 as it presents less data deformation. Hope it helps.

Answer 3

If I'm understanding correctly, you're trying to recreate a rolling average.

This is already a capability of Pandas dataframes, using the rolling function:

dataframe.rolling(n).mean()

where n is the number of adjacent points used in the 'window' or 'bin' for the average, so you can tweak it for different degrees of smoothness.

You can find examples here:

• https://www.datacamp.com/community/tutorials/time-series-analysis-tutorial

• https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.rolling.html

Answer 4

I think this is a solution to what you are seeking. It uses rolling window as others have suggested. a little bit more work was needed to get it working properly.

df["w*v"] = df["w"] * df["v"]

def rolling_smooth(df,N):
    df_roll = df.rolling(N).agg({"w":["sum","mean"],"v":["mean"],"w*v":["sum"]})
    df_roll.columns = [' '.join(col).strip() for col in df_roll.columns.values]
    df_roll['weighted avg v'] = np.nan
    cond = df_roll['w sum'] > 0
    df_roll.loc[cond,'weighted avg v'] = df_roll.loc[cond,'w*v sum'] / df_roll.loc[cond,'w sum']
    return df_roll

df_roll_100 = rolling_smooth(df,100)
df_roll_200 = rolling_smooth(df,200)

plt.plot(summary['avg w'], summary['weighted avg v'],label='original')
plt.plot(df_roll_100["w mean"],df_roll_100["weighted avg v"],label='rolling N=100')
plt.plot(df_roll_200["w mean"],df_roll_200["weighted avg v"],label='rolling N=200')
plt.legend()