Tensor Flow Math
Example
#Addition
x = tf.add(5, 2)
sess = tf.Session()
print (sess.run(x))
#Subtraction
y = tf.subtract(10, 4)
sess = tf.Session()
print (sess.run(y))
#Multiplication
z = tf.multiply(2, 5)
sess = tf.Session()
print (sess.run(z))
#Converting Data
with tf.Session() as sess:
print (sess.run(tf.subtract(tf.cast(tf.constant(5.0), tf.int32), tf.constant(1))))
Output
7
6
10
4
Note:- tf.cast ,Casts a tensor to a new type (Convert one data to another data type, in this example 5.0 a float value is converted into int32 data type )
Tensor Flow Divide
import tensorflow as tf
x = tf.constant(10)
y = tf.constant(2)
z = tf.subtract(tf.divide(x,y), tf.cast(tf.constant(1),tf.float64))
with tf.Session() as sess:
output = sess.run(z)
print (output )
Output
4.0
Activation Functions
Sigmoid function (1 / (1 + exp(-x)))
# 1 / (1 + exp(-x)) sigmoid function expression
import numpy as np
def sigmoid_(a):
return 1/(1+np.exp(-a))
#calling function
a = [1,0,5,-6,7]
for i in a:
print (sigmoid_(i))
Output
0.7310585786300049 0.5 0.9933071490757153 0.0024726231566347743
0.9990889488055994
tanh (hyperbolic tangent function)
tanh(a) = (e^a - e^-a)/e^a + e^-a
def tanh_(a):
return np.tanh(a)
tanh_(.3)
a = [-4,0,2]
for i in a:
print(tanh_(i))
Output
-0.999329299739067 0.0
0.9640275800758169
ReLU (Rectified Linear Unit )
def relu_(a):
return np.maximum(0,a)
#relu_(.3)
a = [-4,-2,4,5]
for i in a:
print (relu_(i))
Ouput
0 0 4
5
Softmax Function
# Softmax
Scores = [12, 8,.3]
import numpy as np
def softmax(x):
return np.exp(x)/np.sum(np.exp(x), axis = 0)
print (softmax(Scores)) #Display Probability
print (sum(softmax(Scores))) # sum of all probabilities =1
Output
[9.82005792e-01 1.79860635e-02 8.14457845e-06]
1.0
How to Increase the efficiency of the Model
- The way to check the efficiency of any model is to check the loss function for thee model, such as how well the model is giving the correct result on the existing data.
- Updating model variables and re-calculating loss for better efficiency.
- Cycling until loss is very low.
Loss Function
- A loss function measures how far apart the current model is from the provided data
Example
# Loss Function
import tensorflow as tf
W = tf.Variable([.3], tf.float32)
b = tf.Variable([-.3], tf.float32)
x = tf.placeholder(tf.float32)
y = tf.placeholder(tf.float32)
linear_model = W*x + b
# sum(actual - preticted)^2
squared_delta = tf.square(linear_model - y)
loss = tf.reduce_sum(squared_delta)
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init)
print (sess.run(loss,{x:[1,2,3,4], y:[0,-1,-2,-3]}))
sess.close()
Output
23.66
Model Optimizer
- Optimizer modifies each variable according to the magnitude of the derivative of loss with respect to that variable.
- An optimization problem seeks to minimize a loss function.
Example
# Model Optimization
# Loss Function
W = tf.Variable([.5], tf.float32)
b = tf.Variable([.1], tf.float32)
x = tf.placeholder(tf.float32)
y = tf.placeholder(tf.float32)
linear_model = W*x + b
squared_delta = tf.square(linear_model - y)
loss = tf.reduce_sum(squared_delta)
optimizer = tf.train.GradientDescentOptimizer(0.01)
# 0.01 Learning rate
train = optimizer.minimize(loss)
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init)
for i in range(3):
sess.run(train, {x:[1,2,3,4],y:[0,-1,-2,-3]})
print (sess.run([W,b]))
Output
[array([-0.54620796], dtype=float32), array([-0.2057792], dtype=float32)]
Simplest TensorFlow Neural Network
Example
#import Data science libraries
import numpy as np
#import tensor flow
import tensorflow as tf
# Model parameters
W = tf.Variable([.9], tf.float32)
b = tf.Variable([.1], tf.float32)
# Model input and output
x = tf.placeholder(tf.float32)
linear_model = W * x + b
y = tf.placeholder(tf.float32)
# loss function
loss = tf.reduce_sum(tf.square(linear_model - y)) # sum of the squares
# optimizer
optimizer = tf.train.GradientDescentOptimizer(0.01)
train = optimizer.minimize(loss)
# training data
x_train = [1,2,3,4]
y_train = [0,-1,-2,-3]
# training loop
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init) # reset values to wrong
for i in range(10):
sess.run(train, {x:x_train, y:y_train})
# evaluate training accuracy
curr_W, curr_b, curr_loss = sess.run([W, b, loss], {x:x_train, y:y_train})
print("W: %s b: %s loss: %s"%(curr_W, curr_b, curr_loss))
Output
W: [-0.582103] b: [-0.22859187] loss: 1.0083919
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