In [416]:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
from sqlalchemy import create_engine
engine = create_engine('postgresql://stuartlynn@localhost:5432/stuartlynn')
%matplotlib inline

Census segmentation Test¶

The Census produces summary tables of a large number of variables such as number of individuals in a given age bracket, rent range etc. While these are often sufficent for producing segments the joint probabilities for say vision problems by household income are not often avaliable.

Public use microdata however contain the individual responses of a number of individual at PUMA tract levels which allow any conditional probability distribution of any set of variables to be computed.

This document is a test to see if we can train a machine learning model to predict custom probability distributions for a given set of microdata variables and then map these to other census geometries

Data¶

To get a given breakdown of variables we use the Data Ferret tool provided by the census. This is not ideal for general use but it allows us to perform some easy tests.

From there we extract the variables $DEYE$, $DEAR$ and $age$ brackets

	DEYE	DEAR
1	Has Vision problem	Has Hearing problem
2	No Vision problem	No Hearing problem

The datafile pums_age_vision_hearing.csv extracted from Data Ferret has an entry per survey respondant with their age and their responses to the eye and ear questions

In [417]:

data = pd.read_csv("data/pums_age_vision_hearing.csv")
data.head()

Out[417]:

	AGEP	DEAR	DEYE	PUMA10
0	42	2	2	-9
1	42	2	2	-9
2	4	2	2	-9
3	3	2	2	-9
4	58	2	2	-9

In [418]:

fig = plt.figure( figsize= (20,10))
plt.subplot(121)
labels  = ['> 50 problem', '>50 no problem', '<50 problem', '<50 no problem']
ax = data.groupby([data['AGEP'] < 50, 'DEAR']).count()['AGEP'].plot(kind='bar')
ax.set_xticklabels(labels)
ax.set_title("EAR")
plt.subplot(122)
labels  = ['> 50 problem', '>50 no problem', '<50 problem', '<50 no problem']
ax = data.groupby([data['AGEP'] < 50, 'DEYE']).count()['AGEP'].plot(kind='bar')
ax.set_xticklabels(labels)
ax.set_title("EYE")

Out[418]:

<matplotlib.text.Text at 0x5b89c1190>

We are also going to read in the pumus summary table which contains the same columns as the other census geometries. This will give us the training data we need to train the model

In [419]:

pumas = pd.read_sql_query('select * from pumas_joined', engine)

Generate the target distribution¶

Our goal is going to be to calculate the joint distribution of a person having eye and ear problems per ceunsus geometry. To do this we group by PUMA and count up the various different variations

In [420]:

eye_ear = data[data['DEYE'] ==1][data['DEAR']==1].groupby("PUMA10").count()['AGEP']
eye_noear = data[data['DEYE']==1][data['DEAR']==2].groupby("PUMA10").count()['AGEP']
noeye_ear = data[data['DEYE']==2][data['DEAR']==1].groupby("PUMA10").count()['AGEP']
noeye_noear = data[data['DEYE']==2][data['DEAR']==2].groupby("PUMA10").count()['AGEP']

summary = pd.DataFrame({ "eye_ear": eye_ear, 
                         "eye_noear": eye_noear,
                         "noeye_ear": noeye_ear,
                         "noeye_no_ear":noeye_noear})
summary.head()

Out[420]:

	eye_ear	eye_noear	noeye_ear	noeye_no_ear
PUMA10
-9	52160	100221	203987	5817341
100	2221	3774	9436	188686
101	398	924	1786	53645
102	422	955	1920	57291
103	296	734	1266	44842

We can plot out some of the breakdown of our counts across a few PUMAS

In [421]:

summary.head().T.plot(kind='pie', subplots=True, figsize=(80,15))

Out[421]:

array([<matplotlib.axes._subplots.AxesSubplot object at 0x5d1353b50>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x6352e28d0>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x64f1c5650>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x64eb193d0>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x10f184050>], dtype=object)

Getting the model features¶

Next step is to generate the model features. We take the PUMAS dataset and discard id's, geometries etc.

In [422]:

a =pumas.set_index( pumas[ 'pumas_10'])
moe_cols  = [ f for f in a.columns if 'moe' in f ]
data  = a[a.columns.difference(['the_geom', 
                                'ogc_fid',
                                'wkb_geometry',
                                'cartodb_id', 
                                'geoid',
                                'pumas_10' ] + moe_cols)].join(summary)

data.head()

Out[422]:

	100_000_to_124_999_in_households	10_000_to_14_999_in_households	10_to_14_years_female_pop	10_to_14_years_male_pop	125_000_to_149_999_in_households	150_000_to_199_999_in_households	15_000_to_19_999_in_households	15_to_17_years_female_pop	15_to_17_years_male_pop	18_and_19_years_female_pop	...	total_pop	under_5_years_female_pop	under_5_years_male_pop	vacant_housing_units	walked_to_work	worked_at_home	eye_ear	eye_noear	noeye_ear	noeye_no_ear
pumas_10
109	2126	2678	1607	1616	1256	955	2659	1227	1347	4984	...	101906	2461	2876	6282	2506	3021	49	83	198	8091
110	9015	1579	7441	7776	7193	10286	1557	4496	4541	2301	...	205918	6491	6486	3516	2026	5853	54	120	258	9374
111	3986	1151	2645	2622	3676	4024	1634	2109	2044	799	...	105432	1874	2217	11680	832	5464	29	42	91	2477
803	3036	2648	3765	4242	1582	1486	2309	2214	2288	2438	...	122624	4044	4452	6364	1055	1132	148	313	571	16515
804	2288	3077	2764	2781	1321	1702	3308	1363	1618	1550	...	100406	2889	3030	4949	2231	2226	104	194	311	10604

5 rows × 98 columns

We next normalize the various target counts to get a probability matrix across the different variables we are interested in

In [423]:

target= data[summary.columns].apply(lambda x: x/data[summary.columns].sum(axis=1), axis=0)
features = data[data.columns.difference(summary.columns)]
print ' target : ', np.shape(target.as_matrix()), " features", np.shape(features.as_matrix())
target.head()

 target :  (982, 4)  features (982, 94)

Out[423]:

	eye_ear	eye_noear	noeye_ear	noeye_no_ear
pumas_10
109	0.005819	0.009856	0.023513	0.960812
110	0.005507	0.012237	0.026310	0.955945
111	0.010989	0.015915	0.034483	0.938613
803	0.008434	0.017838	0.032541	0.941187
804	0.009275	0.017301	0.027736	0.945688

For the machine learning algorithm to work well we need to make sure that both our features are distributed about 0 and are all scaled to roughtly the same range. to do this we first normalize any columns that are fractional counts by their universe root and then we subtract the mean and divide by the standard deviation.

$$ \frac{x- \bar{x}}{ \sigma(x)}$$

In [424]:

def scale_features(features):
    housing_brackets  = [ f for f in features if 'in_households' in f and 'gini' not in f]
    housing_features = features[housing_brackets].apply(lambda x: x/features[housing_brackets].sum(axis=1))
    other_housing = [a for a in  features.columns if 'housing' in a and 'moe' not in a ]
    other_housing_features = features[other_housing].apply(lambda x: x/ features[other_housing].sum(axis=1), axis=0)
    pop_brackets  = [ f for f in features if 'pop' in f and 'not_a_us_citizen_pop' not in f]

    ignore = ['rn','not_a_us_citizen_pop','not_a_us_citizen_pop_moe','total_pop'] + [ r for r in features.columns if 'moe' in r]

    scaled_features = features[pop_brackets].apply(lambda x: x/features['total_pop'])
    scaled_features = scaled_features.join(housing_features).join(other_housing_features)
    normed_features = scaled_features.join(features[features.columns.difference(ignore+housing_brackets+pop_brackets+other_housing)])
    normed_features = normed_features[normed_features.columns.difference(['total_pop'])]

    return normed_features

def norm_features(features,means,stds):             
    normed_features = features.apply(lambda x: (x-np.mean(x))/np.std(x), axis=0) 
    return normed_features

In [425]:

scaled_features  = scale_features(features)
means = scaled_features.apply(lambda x: np.mean(x), axis=0)
stds  = scaled_features.apply(lambda x: np.std(x), axis=0)
normed_features = norm_features(scaled_features,means,stds)

normed_features.head()
normed_features[['median_age_female', 
                 'median_age',
                 'percent_household_income_spent_on_rent',
                 '10_to_14_years_female_pop']].hist( figsize=(20,10))

Out[425]:

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x168d860d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x168e96f90>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x168ecc890>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1694b59d0>]], dtype=object)

In [426]:

scaled_features.to_csv("/Users/stuartlynn/scaled_pumas.csv")

In [427]:

target_means = target.apply(lambda x: np.mean(x), axis=0 ) 
target_std   = target.apply(lambda x: np.std(x), axis =0)
target_max   = target.apply(lambda x: np.min(x), axis=0)
target_min   = target.apply(lambda x: np.max(x), axis=0)
normed_target = target.apply(lambda x: (x-np.min(x))/(np.max(x)-np.min(x)), axis=0 )
normed_target.hist(figsize=(20,10))

Out[427]:

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x168d303d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x16c210c90>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x16c29e190>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x16c711390>]], dtype=object)

Training the model¶

Now we have the data in good condition we try to train our model. We split the data in to training and test data.

In [428]:

from keras.models import Sequential
from keras.layers.core import Dense, Activation, Dropout
from sklearn.cross_validation  import train_test_split 
x_train, x_test, y_train, y_test  = train_test_split(normed_features.as_matrix(), 
                                                     normed_target.as_matrix(), 
                                                     test_size=0.30, 
                                                     random_state=42)

In [429]:

def invert_target(t):
    return t*target_std + target_means

Our model is going to be a multiple layer neural network with $tanh$ activation between layers and a linear activation for the final output. We define the loss by the mean squared error and use a stochastic gradient descent method to train the network.

The input dimension is the number of features we are useing and as we are predicting the probability of 4 classes our output layer is a vector or 4 values

In [430]:

model = Sequential()
model.add(Dense(output_dim=70, input_dim=np.shape(x_train)[1]))
model.add(Dropout(0.2))
model.add(Activation('tanh'))
# model.add(Dense(20))
# model.add(Dropout(0.2))
# model.add(Activation('tanh'))

model.add(Dense(output_dim=4))
model.add(Activation('tanh'))

model.compile(loss='mean_squared_error', optimizer='sgd')

With the model compiled we can fit it to our training set

In [431]:

history = model.fit(x_train, y_train, 
                    verbose=0, 
                    nb_epoch=3000, 
                    batch_size=600, 
                    show_accuracy=True, 
                    validation_data=(x_test, y_test) )

In [432]:

def plot_model_perfromance(history):
    fig   = plt.figure(figsize=(20,10))
    plt.subplot(121)
    plt.title('Loss')
    plt.xlabel('epoch')
    plt.ylabel('loss')
    
    train = plt.plot(history.epoch, history.history['loss'], 'g-', label='train')
    val   = plt.plot(history.epoch, history.history['val_loss'], 'r-', label='validation')
    plt.legend( loc='upper left' )
    plt.subplot(122)
    plt.title('Accuracy')
    plt.xlabel('epoch')
    plt.ylabel('accuracy')
    plt.plot(history.epoch, history.history['acc'], 'g-', label='train')
    plt.plot(history.epoch, history.history['val_acc'], 'r-',label='validation')
    plt.legend( loc='upper left' )


plot_model_perfromance(history)

In [433]:

score = model.evaluate(x_test, y_test, batch_size=2000)
print 'error %f, error in units of sd %f, accuracy %f ' %(score, score/np.std(y_test), 1-score)

295/295 [==============================] - 0s
error 0.009941, error in units of sd 0.045114, accuracy 0.990059

With the model trained we can predict our test set results and comapre with the actual data

In [434]:

result = model.predict_proba(x_test, batch_size=16)
result

295/295 [==============================] - 0s

Out[434]:

array([[ 0.25860682,  0.33563152,  0.2973173 ,  0.65109867],
       [ 0.20303848,  0.14913028,  0.35877565,  0.76830971],
       [ 0.20047362,  0.17980911,  0.33872399,  0.79012567],
       ..., 
       [ 0.17843936,  0.20258643,  0.28450835,  0.75755018],
       [ 0.1778084 ,  0.31786487,  0.32266736,  0.67827946],
       [ 0.19241875,  0.32983372,  0.0998479 ,  0.78881645]])

In [435]:

bins = 20
range = [0,1]
alpha = 0.7
fig = plt.figure(figsize=(20,10))
plt.subplot(141)
labels = target.columns

plt.xlabel('Probability')

plt.title("Both vision and hearing disability")
truth      = [r[0] for r in y_test]
prediction = [r[0] for r in result]
range  = [np.min(truth + prediction), np.max(truth + prediction)]
plt.hist(truth, color='red', bins=bins ,alpha =alpha, range=range )
plt.hist(prediction, color='blue', bins=bins, alpha =alpha, range=range )
plt.subplot(142)

plt.title("Vision disability only")
plt.xlabel('Probability')
truth      = [r[1] for r in y_test]
prediction = [r[1] for r in result]
range  = [np.min(truth + prediction), np.max(truth + prediction)]
plt.hist([r[1] for r in y_test], color='red', bins=bins,  alpha =alpha, range=range )
plt.hist([r[1] for r in result], color='blue',bins=bins,  alpha =alpha, range=range )
plt.subplot(143)
plt.title("Hearing disability only")
plt.xlabel('Probability')

truth      = [r[2] for r in y_test]
prediction = [r[2] for r in result]
range  = [np.min(truth + prediction), np.max(truth + prediction)]
plt.hist([r[2] for r in y_test], color='red',bins=bins, alpha =alpha, range=range)
plt.hist([r[2] for r in result], color='blue',bins=bins,  alpha =alpha,range=range )
plt.subplot(144)
plt.title("No disability")
plt.xlabel('Probability')

truth      = [r[3] for r in y_test]
prediction = [r[3] for r in result]
range  = [np.min(truth + prediction), np.max(truth + prediction)]
plt.hist([r[3] for r in y_test], color='red', bins=bins,  alpha =alpha,range=range )
plt.hist([r[3] for r in result], color='blue' ,bins=bins, alpha =alpha,range=range)

Out[435]:

(array([  0.,   1.,   0.,   1.,   0.,   1.,   4.,   8.,  12.,  12.,  16.,
         17.,  28.,  41.,  35.,  50.,  34.,  27.,   8.,   0.]),
 array([ 0.0864582,  0.1304984,  0.1745386,  0.2185788,  0.262619 ,
         0.3066592,  0.3506994,  0.3947396,  0.4387798,  0.48282  ,
         0.5268602,  0.5709004,  0.6149406,  0.6589808,  0.703021 ,
         0.7470612,  0.7911014,  0.8351416,  0.8791818,  0.923222 ,
         0.9672622]),
 <a list of 20 Patch objects>)

In [436]:

fig = plt.figure(figsize=(20,10))

plt.title('Errors')

def invert(x,xmin,xmax):
    return x*(xmax-xmin) + xmin

plt.subplot(231)
plt.title("Both vision and hearing disability")
plt.xlabel('Truth')
plt.ylabel('Predction')

truth      = [invert(r[0],target_min[0], target_max[0]) for r in y_test]
prediction = [invert(r[0],target_min[0], target_max[0]) for r in result]
plt.scatter(truth , prediction)
plt.plot( [np.min(truth), np.max(truth)], [np.min(truth),np.max(truth)], 'r' )

plt.subplot(232)
plt.title("Vision and hearing disability")
plt.xlabel('Truth')
plt.ylabel('Predction')
truth      = [invert(r[1],target_min[1], target_max[1]) for r in y_test]
prediction = [invert(r[1],target_min[1], target_max[1]) for r in result]
plt.scatter(truth , prediction)
plt.plot( [np.min(truth), np.max(truth)], [np.min(truth),np.max(truth)], 'r' )

plt.subplot(233)
plt.title("Hearing disability only")
plt.xlabel('Truth')
plt.ylabel('Predction')
truth      = [invert(r[2],target_min[2], target_max[2]) for r in y_test]
prediction = [invert(r[2],target_min[2], target_max[2]) for r in result]
plt.scatter(truth , prediction)
plt.plot( [np.min(truth), np.max(truth)], [np.min(truth),np.max(truth)], 'r' )

plt.subplot(234)
plt.title("No disability")
plt.xlabel('Truth')
plt.ylabel('Predction')

truth      = [invert(r[3],target_min[3], target_max[3]) for r in y_test]
prediction = [invert(r[3],target_min[3], target_max[3]) for r in result]
plt.scatter(truth , prediction)
plt.plot( [np.min(truth), np.max(truth)], [np.min(truth),np.max(truth)], 'r' )

Out[436]:

[<matplotlib.lines.Line2D at 0x171f97050>]

Predicting the output for census blocks¶

In [437]:

feature_list = ','.join(normed_features.columns)
reader  = pd.read_sql_query('select * from census_tacts_human' % locals(),
                               engine,
                               chunksize=10000)
results = []
geoms   = []


for chunk in reader:
    data  = chunk[normed_features.columns | ['total_pop', 'geoid']]   
    data  = data.convert_objects(convert_numeric=True)
    data.index = data['geoid']
    new_features = data[data.columns.difference(['geoid'])]

    scaled_data = scale_features(new_features)
    normed_data = norm_features(scaled_data, means,stds )
    prediction = model.predict_proba(normed_data.as_matrix(), batch_size=16)
    results.append(pd.DataFrame(prediction,
                                columns=['eye_ear','eye_noear','noeye_ear', 'noeye_noear'],
                                index= chunk['geoid'] ))
    

10000/10000 [==============================] - 0s     
10000/10000 [==============================] - 0s     
10000/10000 [==============================] - 0s     
10000/10000 [==============================] - 1s     
10000/10000 [==============================] - 0s     
10000/10000 [==============================] - 1s     
10000/10000 [==============================] - 0s     
4001/4001 [==============================] - 0s

/Users/stuartlynn/anaconda/lib/python2.7/site-packages/IPython/kernel/__main__.py:11: FutureWarning: convert_objects is deprecated.  Use the data-type specific converters pd.to_datetime, pd.to_timedelta and pd.to_numeric.

In [438]:

result = pd.concat(results)
result['eye_ear']= invert(result['eye_ear'], target_min[0], target_max[0]) 
result['eye_noear'] = invert(result['eye_noear'], target_min[1], target_max[1])
result['noeye_ear'] = invert(result['noeye_ear'], target_min[2], target_max[2])
result['noeye_noear'] = invert(result['noeye_noear'],target_min[3], target_max[3])

In [439]:

geom_lookup = pd.read_sql_query('select geoid, the_geom, total_pop from census_tacts_human', engine)
geom_lookup.index= geom_lookup['geoid']

In [440]:

result.join(geom_lookup).to_csv("eye_ear_result.csv")

In [441]:

pumas.index = pumas['pumas_10']
target_with_geom = target.join(pumas[['pumas_10','total_pop','geoid']], )
target_with_geom.to_csv("pumas_eye_ear.csv")

Results¶

In [442]:

from IPython.display import IFrame

Origional data on pumas¶

In [443]:

IFrame('https://team.cartodb.com/u/stuartlynn/viz/e02906b6-e0a8-11e5-b257-0e787de82d45/embed_map',
      width=800, height=700)

Out[443]:

In [444]:

IFrame('https://team.cartodb.com/u/stuartlynn/viz/355e76f6-e0aa-11e5-bf37-0e5db1731f59/embed_map',
      width=800, height=700)

Out[444]:

In [ ]: