Non-linear regression in Seaborn Python

Question

I have the following dataframe that I wish to perform some regression on. I am using Seaborn but can't quite seem to find a non-linear function that fits. Below is my code and it's output, and below that is the dataframe I am using, df. Note I have truncated the axis in this plot.

I would like to fit either a Poisson or Gaussian distribution style of function.

import pandas 
import seaborn


graph = seaborn.lmplot('$R$', 'Equilibrium Value', data = df, fit_reg=True, order=2, ci=None)
graph.set(xlim = (-0.25,10))

However this produces the following figure.

df

     R          Equilibrium Value
0   5.102041    7.849315e-03
1   4.081633    2.593005e-02
2   0.000000    9.990000e-01
3   30.612245   4.197446e-14
4   14.285714   6.730133e-07
5   12.244898   5.268202e-06
6   15.306122   2.403316e-07
7   39.795918   3.292955e-18
8   19.387755   3.875505e-09
9   45.918367   5.731842e-21
10  1.020408    9.936863e-01
11  50.000000   8.102142e-23
12  2.040816    7.647420e-01
13  48.979592   2.353931e-22
14  43.877551   4.787156e-20
15  34.693878   6.357120e-16
16  27.551020   9.610208e-13
17  29.591837   1.193193e-13
18  31.632653   1.474959e-14
19  3.061224    1.200807e-01
20  23.469388   6.153965e-11
21  33.673469   1.815181e-15
22  42.857143   1.381050e-19
23  25.510204   7.706746e-12
24  13.265306   1.883431e-06
25  9.183673    1.154141e-04
26  41.836735   3.979575e-19
27  36.734694   7.770915e-17
28  18.367347   1.089037e-08
29  44.897959   1.657448e-20
30  16.326531   8.575577e-08
31  28.571429   3.388120e-13
32  40.816327   1.145412e-18
33  11.224490   1.473268e-05
34  24.489796   2.178927e-11
35  21.428571   4.893541e-10
36  32.653061   5.177167e-15
37  8.163265    3.241799e-04
38  22.448980   1.736254e-10
39  46.938776   1.979881e-21
40  47.959184   6.830820e-22
41  26.530612   2.722925e-12
42  38.775510   9.456077e-18
43  6.122449    2.632851e-03
44  37.755102   2.712309e-17
45  10.204082   4.121137e-05
46  35.714286   2.223883e-16
47  20.408163   1.377819e-09
48  17.346939   3.057373e-08
49  7.142857    9.167507e-04

EDIT

Attached are two graphs produced from both this and another data set when increasing the order parameter beyond 20.

Order = 3

@BenT I have tried multiple values of the order parameter :/ — AngusTheMan
Does it not modify the shape of your curve? It uses np.polyfit which should reduce the cost function with the higher order functions. Can you post what that does to your graph? — BenT
@BenT Hmm actually you are right, it does look better now that I am pushing the value quite high (25 + ). It is a bit jumpy however, not a continuous curve. — AngusTheMan
Im surprised it doesn't look better with just a 3rd order function. It would be expected to have such a complicated curve with a 25th order polynomial function fitted to the line. If you want to compare the curve to gaussian you may just want to plot an actual gaussian curve instead of trying to fit one. You could also just make this a line plot which would clearly show that the data points look gaussian. — BenT

ImportanceOfBeingErnest ImportanceOfBeingErnest · Accepted Answer · 2017-09-30T11:38:28

I have problems understanding why a lmplot is needed here. Usually you want to perform a fit by taking a model function and fit it to the data. Assume you want a gaussian function

model = lambda x, A, x0, sigma, offset:  offset+A*np.exp(-((x-x0)/sigma)**2)

you can fit it to your data with scipy.optimize.curve_fit:

popt, pcov = curve_fit(model, df["R"].values, 
                              df["EquilibriumValue"].values, p0=[1,0,2,0])

Complete code:

import pandas as pd
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

df = ... # your dataframe

# plot data
plt.scatter(df["R"].values,df["EquilibriumValue"].values, label="data")

# Fitting
model = lambda x, A, x0, sigma, offset:  offset+A*np.exp(-((x-x0)/sigma)**2)
popt, pcov = curve_fit(model, df["R"].values, 
                              df["EquilibriumValue"].values, p0=[1,0,2,0])
#plot fit
x = np.linspace(df["R"].values.min(),df["R"].values.max(),250)
plt.plot(x,model(x,*popt), label="fit")

# Fitting
model2 = lambda x, sigma:  model(x,1,0,sigma,0)
popt2, pcov2 = curve_fit(model2, df["R"].values, 
                              df["EquilibriumValue"].values, p0=[2])
#plot fit2
x2 = np.linspace(df["R"].values.min(),df["R"].values.max(),250)
plt.plot(x2,model2(x2,*popt2), label="fit2")

plt.xlim(None,10)
plt.legend()
plt.show()

Non-linear regression in Seaborn Python

1 Answers