Neural Network Regression

What is a Regression Problems?

Example:

• How much will this house sell for?
• How many people will buy this app?
• How much will my health insurance be?
• How much should I save each week for fuel?

Regression Inputs and Outputs

Input --> Machine Learning Algorithms --> Outputs

• Input and Output Shapes

Architecture of a Regression Model

Hyper-Parameter	Typical Value
Input Layer Shape	Same shapes as number of features
Hidden Layer(s)	Problem specific, minimum=1, maximum=unlimited
Neurons per hidden layer	Problem specific, generally 10 to 100
Output layer shape	Same shape as desired

import tensorflow as tf

import numpy as np
import matplotlib.pyplot as plt

# Create Features
X = np.array([-7.0, -4.0, -1.0, 2.0, 5.0, 8.0, 11.0, 14.0])

# Create labels
y = np.array([3.0, 6.0, 9.0, 12.0, 15.0, 18.0, 21.0, 24.0])

# Visualize it
plt.scatter(X, y);

y == X + 10

array([ True,  True,  True,  True,  True,  True,  True,  True])

X = tf.constant(X)
y = tf.constant(y)

X, y

(<tf.Tensor: shape=(8,), dtype=float64, numpy=array([-7., -4., -1.,  2.,  5.,  8., 11., 14.])>,
 <tf.Tensor: shape=(8,), dtype=float64, numpy=array([ 3.,  6.,  9., 12., 15., 18., 21., 24.])>)

input_shape = X[0].shape
output_shape = y[0].shape

input_shape, output_shape

(TensorShape([]), TensorShape([]))

plt.scatter(X, y)

<matplotlib.collections.PathCollection at 0x2a90024ea60>

Step in modelling

1. Creating a Model - Define the input and output laysers, as well as the hidden layers of a deep learning model.

2. Compiling a model - Define the loss function (in other words, the function which tells our model how wrong it is) and the optimizer (tells our model how to improve the patterns its learning) and evaluation metrics (what we cna use to interpret the performance of our model).

3. Fitting a model - Letting the model try to find patterns between X & y (features and labels).

tf.random.set_seed(42)


# 1. Create a model using the Sequential API

model = tf.keras.Sequential(
    [
        tf.keras.layers.Dense(1),
    ]
)

# 2. Compile the model
model.compile(
    loss=tf.keras.losses.mae,  # Mean absolute error
    optimizer=tf.keras.optimizers.Adam(learning_rate=0.001),
    metrics=["mae"]
)

# 3. Fit the model
model.fit(X, y, epochs=50)

Epoch 1/50
1/1 [==============================] - 1s 788ms/step - loss: 11.5048 - mae: 11.5048
Epoch 2/50
1/1 [==============================] - 0s 4ms/step - loss: 11.5003 - mae: 11.5003
Epoch 3/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4958 - mae: 11.4958
Epoch 4/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4913 - mae: 11.4913
Epoch 5/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4868 - mae: 11.4868
Epoch 6/50
1/1 [==============================] - 0s 5ms/step - loss: 11.4823 - mae: 11.4823
Epoch 7/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4778 - mae: 11.4778
Epoch 8/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4733 - mae: 11.4733
Epoch 9/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4688 - mae: 11.4688
Epoch 10/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4643 - mae: 11.4643
Epoch 11/50
1/1 [==============================] - 0s 3ms/step - loss: 11.4598 - mae: 11.4598
Epoch 12/50
1/1 [==============================] - 0s 3ms/step - loss: 11.4553 - mae: 11.4553
Epoch 13/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4508 - mae: 11.4508
Epoch 14/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4463 - mae: 11.4463
Epoch 15/50
1/1 [==============================] - 0s 3ms/step - loss: 11.4418 - mae: 11.4418
Epoch 16/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4373 - mae: 11.4373
Epoch 17/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4328 - mae: 11.4328
Epoch 18/50
1/1 [==============================] - 0s 3ms/step - loss: 11.4283 - mae: 11.4283
Epoch 19/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4238 - mae: 11.4238
Epoch 20/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4193 - mae: 11.4193
Epoch 21/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4148 - mae: 11.4148
Epoch 22/50
1/1 [==============================] - 0s 5ms/step - loss: 11.4103 - mae: 11.4103
Epoch 23/50
1/1 [==============================] - 0s 4ms/step - loss: 11.4058 - mae: 11.4058
Epoch 24/50
1/1 [==============================] - 0s 3ms/step - loss: 11.4013 - mae: 11.4013
Epoch 25/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3968 - mae: 11.3968
Epoch 26/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3923 - mae: 11.3923
Epoch 27/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3878 - mae: 11.3878
Epoch 28/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3833 - mae: 11.3833
Epoch 29/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3788 - mae: 11.3788
Epoch 30/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3743 - mae: 11.3743
Epoch 31/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3698 - mae: 11.3698
Epoch 32/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3653 - mae: 11.3653
Epoch 33/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3608 - mae: 11.3608
Epoch 34/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3563 - mae: 11.3563
Epoch 35/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3518 - mae: 11.3518
Epoch 36/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3473 - mae: 11.3473
Epoch 37/50
1/1 [==============================] - 0s 5ms/step - loss: 11.3428 - mae: 11.3428
Epoch 38/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3383 - mae: 11.3383
Epoch 39/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3338 - mae: 11.3338
Epoch 40/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3293 - mae: 11.3293
Epoch 41/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3248 - mae: 11.3248
Epoch 42/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3203 - mae: 11.3203
Epoch 43/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3158 - mae: 11.3158
Epoch 44/50
1/1 [==============================] - 0s 4ms/step - loss: 11.3113 - mae: 11.3113
Epoch 45/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3068 - mae: 11.3068
Epoch 46/50
1/1 [==============================] - 0s 3ms/step - loss: 11.3023 - mae: 11.3023
Epoch 47/50
1/1 [==============================] - 0s 4ms/step - loss: 11.2978 - mae: 11.2978
Epoch 48/50
1/1 [==============================] - 0s 3ms/step - loss: 11.2933 - mae: 11.2933
Epoch 49/50
1/1 [==============================] - 0s 4ms/step - loss: 11.2888 - mae: 11.2888
Epoch 50/50
1/1 [==============================] - 0s 4ms/step - loss: 11.2843 - mae: 11.2843

<keras.callbacks.History at 0x2a96f12b3d0>

X, y

(<tf.Tensor: shape=(8,), dtype=float64, numpy=array([-7., -4., -1.,  2.,  5.,  8., 11., 14.])>,
 <tf.Tensor: shape=(8,), dtype=float64, numpy=array([ 3.,  6.,  9., 12., 15., 18., 21., 24.])>)

y_pred=model.predict([17.0])
y_pred

array([[10.591008]], dtype=float32)

for i in range(-10000, 1000):
    feature=np.array()
    print(feature)

[-10000  -9999]
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How to Improve the model

1. Creating a model:
   • Here we might add mor3e layers, increase the number of hidden units (all called neurons) within each of the hidden layers, change the activation function of each layer.
2. Compiling a model:
   • Here we might change the optimization function or perhaps the learning rate of the optimization f unction.
3. Fitting a model:
   • Here we might fit a model for more epochs (leave it training for longer) or on more data (give the model more example to learn from).

model_1 = tf.keras.Sequential(
    [
        tf.keras.layers.Dense(100, activation="relu"),
        tf.keras.layers.Dense(50, activation="relu"),
        tf.keras.layers.Dense(1)
    ]
)

# 2. Compile the model
model_1.compile(
    loss=tf.keras.losses.mae,
    optimizer=tf.keras.optimizers.Adam(learning_rate=0.001),
    metrics=["mae"]
)

# 3. Fit the model
model_1.fit(X, y, epochs=50, verbose=0)

<keras.callbacks.History at 0x2aaa2025fd0>

X, y

(<tf.Tensor: shape=(8,), dtype=float64, numpy=array([-7., -4., -1.,  2.,  5.,  8., 11., 14.])>,
 <tf.Tensor: shape=(8,), dtype=float64, numpy=array([ 3.,  6.,  9., 12., 15., 18., 21., 24.])>)

model_1.predict([12.0])

array([[18.989088]], dtype=float32)

Evaluating the model

In practice, a typical workflow you'll go through when building neural networks is:

Build a model --> Fit it --> Evaluate it --> Tweak a model --> Fit it --> Evaluate it --> Tweak a model --> Fit it --> Evaluate it.

In Evaluating we need to "Visualize the mode"