pymalts2 0.0.2

Causal Inference Matching Package.

Introduction

PyMALTS is a learning-to-matching interpretable causal inference method. PyMALTS implements MALTS algorithm proposed by Harsh Parikh, Cynthia Rudin and Alexander Volfovsky in their 2019 paper titled "MALTS: Matching After Learning to Stretch"

Dependencies

PyMALTS is a Python3 library and it requires Numpy, Pandas, Scipy, Scikit-Learn, Matplotlib and Seaborn.

import pymalts
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
np.random.seed(0)
sns.set()

Reading Data

df = pd.read_csv('example/example_data.csv',index_col=0)
print(df.shape)
df.head()

(2500, 20)

	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	X12	X13	X14	X15	X16	X17	X18	outcome	treated
1355	1.881335	1.684164	0.532332	2.002254	1.435032	1.450196	1.974763	1.321659	0.709443	-1.141244	0.883130	0.956721	2.498229	2.251677	0.375271	-0.545129	3.334220	0.081259	-15.679894	0
1320	0.666476	1.263065	0.657558	0.498780	1.096135	1.002569	0.881916	0.740392	2.780857	-0.765889	1.230980	-1.214324	-0.040029	1.554477	4.235513	3.596213	0.959022	0.513409	-7.068587	0
1233	-0.193200	0.961823	1.652723	1.117316	0.590318	0.566765	0.775715	0.938379	-2.055124	1.942873	-0.606074	3.329552	-1.822938	3.240945	2.106121	0.857190	0.577264	-2.370578	-5.133200	0
706	1.378660	1.794625	0.701158	1.815518	1.129920	1.188477	0.845063	1.217270	5.847379	0.566517	-0.045607	0.736230	0.941677	0.835420	-0.560388	0.427255	2.239003	-0.632832	39.684984	1
438	0.434297	0.296656	0.545785	0.110366	0.151758	-0.257326	0.601965	0.499884	-0.973684	-0.552586	-0.778477	0.936956	0.831105	2.060040	3.153799	0.027665	0.376857	-1.221457	-2.954324	0

Using MALTS

Distance Metric Learning

Setting up the model for learning the distance metric.

1. Variable name for the outcome variable: 'outcome'.
2. Variable name for the treatment variable: 'treated'
3. Data is assigned to python variable df

m = pymalts.malts_mf( outcome='outcome', treatment='treated', data=df) # running MALTS with default setting

Matched Groups

Matched Group matrix (MG_matrix) is NxN matrix with each row corresponding to each query unit and each column corresponds to matched units. Cell (i,j) in the matrix corresponds to the weight of unit j in the matched group of unit i. The weight corresponds to the numbers of times a unit is included in a matched group across M-folds.

m.MG_matrix

	1355	1320	1233	706	438	184	1108	1612	816	131	...	1181	1698	916	59	2267	1520	1408	909	603	2285
1355	4.0	0.0	0.0	2.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	3.0	0.0	3.0
1320	0.0	4.0	0.0	0.0	0.0	0.0	0.0	1.0	4.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1233	0.0	0.0	4.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
706	0.0	0.0	0.0	4.0	0.0	0.0	0.0	1.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0
438	0.0	0.0	0.0	0.0	4.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
1520	0.0	0.0	0.0	0.0	2.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	4.0	0.0	0.0	0.0	0.0
1408	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	3.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	4.0	0.0	0.0	0.0
909	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	4.0	0.0	0.0
603	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	2.0	0.0	0.0	0.0	0.0	0.0	0.0	4.0	0.0
2285	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	4.0

2500 rows × 2500 columns

Visualizing matched group matrix as heatmap

fig = plt.figure(figsize=(10,10))
sns.heatmap(m.MG_matrix)

Accessing the matched group for an example unit with index equal to "1" and visualizing the weights as bar-chart

MG1 = m.MG_matrix.loc[1] #matched group for unit "1"
MG1[MG1>1].sort_values(ascending=False).plot(kind='bar',figsize=(20,5)) #Visualizing all the units matched to unit 1 more than once

ATE and CATE Estimates

m.CATE_df #each row is a cate estimate for a corresponding unit

	avg.CATE	std.CATE	outcome	treated
0	47.232061	21.808950	-15.313091	0.0
1	40.600643	21.958906	-16.963202	0.0
2	40.877320	22.204570	9.527929	1.0
3	37.768578	19.740320	-3.940218	0.0
4	39.920257	21.744433	-8.011915	0.0
...	...	...	...	...
2495	49.227788	21.581176	-14.529871	0.0
2496	42.352355	21.385861	19.570055	1.0
2497	43.737763	19.859275	-16.342666	0.0
2498	41.189297	20.346711	-9.165242	0.0
2499	45.427037	23.762884	-17.604829	0.0

2500 rows × 4 columns

Estimate Average Treatment Effect (ATE)

ATE = m.CATE_df['avg.CATE'].mean()
ATE

42.29673993471417

Visualizing ATE and probability density function of CATE (using KDE plot)

fig = plt.figure(figsize=(10,5))
sns.kdeplot(m.CATE_df['avg.CATE'],shade=True)
plt.axvline(ATE,c='black')
plt.text(ATE-4,0.04,'$\hat{ATE}$',rotation=90)

Text(38.29673993471417, 0.04, '$\\hat{ATE}$')

MALTS Arguments

1. outcome: Name of the outcome variable column in the data
2. treatment: Name of the treatment variable column in the data
3. data: Data in the pandas Dataframe format
4. discrete: List of column names which are discrete (dummified); Default=[]
5. C: Regularization constant; Default=1
6. k_tr: Size of matched group in training step; Default=15
7. k_est: Size of matched group in estimation step; Default=50
8. estimator: CATE estimator inside a matched group; Default='linear'; Options: 'linear','mean' or 'RF'
9. smooth_cate: Boolean to smoothen CATE estimates by fitting a regression model; Default=True
10. reweight: Reweight treated and control groups as per their respective sample sizes in training step; Default=False,
11. n_splits: Number of splits of the data for n_split-fold procedure; Default=5
12. n_repeats: Number of repeats of the whole procedure; Default=1
13. output_format: Output format of CATE dataframe; Default='brief'; Options: 'brief' or 'full'

Visualization

Looking Inside a Matched-Group

Plotting the X1 and X2 marginal of matched-group of unit "0"

MG0 = m.MG_matrix.loc[0] #fetching the matched group
matched_units_idx = MG0[MG0!=0].index #getting the indices of the matched units 
matched_units = df.loc[matched_units_idx] #fetching the data of matched units

sns.lmplot(x='X1', y='X2', hue='treated', data=matched_units,palette="Set1") #plotting the MG on (X1,X2)
plt.scatter(x=[df.loc[0,'X1']],y=[df.loc[0,'X2']],c='black',s=100) #plotting the unit-0 on (X1,X2)
plt.title('Matched Group for Unit-0') #setting title of the plot

Text(0.5, 1, 'Matched Group for Unit-0')

Plotting CATE versus covariate

Plotting CATE v.s. X1

data_w_cate = df.join(m.CATE_df, rsuffix='_').drop(columns=['outcome_','treated_']) #joining cate dataframe with data

sns.regplot( x='X1', y='avg.CATE', data=data_w_cate, scatter_kws={'alpha':0.5,'s':2}, line_kws={'color':'black'}, order=2 ) #fitting a degree 2 polynomial X1 on CATE