Using the data from
SF Westinster election results
a neural network was trained with number of candidates in an election as input, and number of votes as output. Here is the python code:
import tensorflow as tf
x_train = [0.102, 0.005, 0.002, 0.012, 0.012, 0.014, 0.014, 0.014, 0.017, 0.018, 0.018, 0.017, 0.018, 0.018, 0.015]
y_train = [0.417211, 0.34181, 0.23362, 0.15231, 0.63415, 0.10270, 0.83389, 0.78291, 0.126921, 0.175933, 0.17453, 0.171942, 0.176232, 0.238915, 0.181853]
m = tf.Variable(0.)
c = tf.Variable(0.)
x = tf.placeholder(dtype = tf.float32)
y = tf.placeholder(dtype=tf.float32)
# using sigmoid function y = mx + c
model = tf.nn.sigmoid(tf.add(tf.multiply(x, m),c))
pred = tf.add(tf.multiply(x, m),c)
error = pred - y
loss = tf.reduce_mean(tf.square(error))
learn_rate = 0.005
num_epochs = 350
#using Gradient Descent with learning rate 0.005
train = tf.train.GradientDescentOptimizer(learn_rate).minimize(loss)
session = tf.Session()
init = tf.global_variables_initializer()
loss_trace = []
session.run(init)
#training model for 350 iterations
for epoch in range(num_epochs):
session.run([train], {x:x_train, y:y_train})
# lossval = session.run([loss], {x:x_train, y:y_train})
loss_trace.append(session.run([loss], {x:x_train, y:y_train}))
pred = tf.add(tf.multiply(x, m),c)
error = pred - y
error = session.run([error], {x:x_train, y:y_train})
prediction = session.run([pred],{x:x_train, y:y_train})
print('Iter: ', epoch, 'MSE in training: ', loss_trace[-1])
#final values of m and c
print('')
print('m =', session.run(m))
print('c =', session.run(c))
print('Final loss: ', loss_trace[-1])
print('Prediction :' , prediction)
print('Error: ', error)
import matplotlib.pyplot as plt
plt.xlabel('Number of epochs --------->')
plt.ylabel('Error (MSE) --------->')
plt.plot(loss_trace)
plt.show()
(virtualenvironment.) david@debian:~/pythonvirenv$ python3 sfseats.py
/home/david/pythonvirenv/virtualenvironment./lib/python3.5/site-packages/tensorflow/python/framework/dtypes.py:455: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
_np_qint8 = np.dtype([("qint8", np.int8, 1)])
/home/david/pythonvirenv/virtualenvironment./lib/python3.5/site-packages/tensorflow/python/framework/dtypes.py:456: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
_np_quint8 = np.dtype([("quint8", np.uint8, 1)])
/home/david/pythonvirenv/virtualenvironment./lib/python3.5/site-packages/tensorflow/python/framework/dtypes.py:457: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
_np_qint16 = np.dtype([("qint16", np.int16, 1)])
/home/david/pythonvirenv/virtualenvironment./lib/python3.5/site-packages/tensorflow/python/framework/dtypes.py:458: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
_np_quint16 = np.dtype([("quint16", np.uint16, 1)])
/home/david/pythonvirenv/virtualenvironment./lib/python3.5/site-packages/tensorflow/python/framework/dtypes.py:459: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
_np_qint32 = np.dtype([("qint32", np.int32, 1)])
/home/david/pythonvirenv/virtualenvironment./lib/python3.5/site-packages/tensorflow/python/framework/dtypes.py:462: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
np_resource = np.dtype([("resource", np.ubyte, 1)])
2021-01-23 19:45:45.073012: W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use SSE4.1 instructions, but these are available on your machine and could speed up CPU computations.
2021-01-23 19:45:45.073108: W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use SSE4.2 instructions, but these are available on your machine and could speed up CPU computations.
2021-01-23 19:45:45.073137: W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use AVX instructions, but these are available on your machine and could speed up CPU computations.
Iter: 0 MSE in training: [0.15254016]
Iter: 1 MSE in training: [0.15058766]
Iter: 2 MSE in training: [0.14867406]
Iter: 3 MSE in training: [0.14679854]
Iter: 4 MSE in training: [0.14496036]
Iter: 5 MSE in training: [0.14315876]
.
.
'
Iter: 345 MSE in training: [0.054557513]
Iter: 346 MSE in training: [0.054555614]
Iter: 347 MSE in training: [0.05455375]
Iter: 348 MSE in training: [0.054551926]
Iter: 349 MSE in training: [0.054550137]
m = 0.0074915974
c = 0.30681604
Final loss: [0.054550137]
Prediction : [array([0.30758017, 0.3068535 , 0.30683103, 0.30690596, 0.30690596,
0.30692092, 0.30692092, 0.30692092, 0.3069434 , 0.3069509 ,
0.3069509 , 0.3069434 , 0.3069509 , 0.3069509 , 0.30692843],
dtype=float32)]
Error: [array([-0.10963082, -0.03495649, 0.07321103, 0.15459596, -0.32724407,
0.20422092, -0.5269691 , -0.47598907, 0.18002239, 0.1310179 ,
0.1324209 , 0.13500139, 0.1307189 , 0.0680359 , 0.12507543],
dtype=float32)]
From y = mx + c
The votes for Westminster start to change when x is 0 for y = mx + c
When x is 0 on the sigmoid curve it is going from a negative value to a positive one indicating that the neural network has started to learn and has identified a pattern.
Where y is the number of votes
y = 0.0074915974x + 0.30681604
When x = 0
y = 0.0074915974*0 + 0.30681604
y = 0 + 0.30681604
y = 0.30681604
To scale up by a thousand as the input vectors were normalised to fall between 0 and 1 by dividing them by a thousand,
y = 306.81604
we get there must be 306 to 307 supporters or potential voters for the number of seats, or, the voting situation for Westminster to change in a general election.
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