[ML] The Basics: Training Your First Model

The problem we will solve is to convert from Celsius to Fahrenheit, where the approximate formula is:

𝑓=𝑐×1.8+32

We will give TensorFlow some sample Celsius values (0, 8, 15, 22, 38) and their corresponding Fahrenheit values (32, 46, 59, 72, 100). Then, we will train a model that figures out the above formula through the training process.

 

Import dependencies

from __future__ import absolute_import, division, print_function, unicode_literals
import tensorflow as tf
tf.logging.set_verbosity(tf.logging.ERROR)

import numpy as np

 

Set up training data

Supervised Machine Learning is all about figuring out an algorithm given a set of inputs and outputs. Since the task in this Codelab is to create a model that can give the temperature in Fahrenheit when given the degrees in Celsius, we create two lists celsius_q and fahrenheit_a that we can use to train our model.

celsius_q    = np.array([-40, -10,  0,  8, 15, 22,  38],  dtype=float)
fahrenheit_a = np.array([-40,  14, 32, 46, 59, 72, 100],  dtype=float)

for i,c in enumerate(celsius_q):
  print("{} degrees Celsius = {} degrees Fahrenheit".format(c, fahrenheit_a[i]))

/**
-40.0 degrees Celsius = -40.0 degrees Fahrenheit
-10.0 degrees Celsius = 14.0 degrees Fahrenheit
0.0 degrees Celsius = 32.0 degrees Fahrenheit
8.0 degrees Celsius = 46.0 degrees Fahrenheit
15.0 degrees Celsius = 59.0 degrees Fahrenheit
22.0 degrees Celsius = 72.0 degrees Fahrenheit
38.0 degrees Celsius = 100.0 degrees Fahrenheit
*/

 

Some Machine Learning terminology

• Feature — The input(s) to our model. In this case, a single value — the degrees in Celsius.

• Labels — The output our model predicts. In this case, a single value — the degrees in Fahrenheit.

• Example — A pair of inputs/outputs used during training. In our case a pair of values from celsius_q and fahrenheit_a at a specific index, such as (22,72).

 

Create the model

We will use simplest possible model we can, a Dense network. Since the problem is straightforward, this network will require only a single layer, with a single neuron.

Build a layer

We'll call the layer l0 and create it by instantiating tf.keras.layers.Dense with the following configuration:

• input_shape=[1] — This specifies that the input to this layer is a single value. That is, the shape is a one-dimensional array with one member. Since this is the first (and only) layer, that input shape is the input shape of the entire model. The single value is a floating point number, representing degrees Celsius.

• units=1 — This specifies the number of neurons in the layer. The number of neurons defines how many internal variables the layer has to try to learn how to solve the problem (more later). Since this is the final layer, it is also the size of the model's output — a single float value representing degrees Fahrenheit. (In a multi-layered network, the size and shape of the layer would need to match the input_shape of the next layer.)

l0 = tf.keras.layers.Dense(units=1, input_shape=[1])  

Assemble layers into the model

Once layers are defined, they need to be assembled into a model. The Sequential model definition takes a list of layers as argument, specifying the calculation order from the input to the output.

This model has just a single layer, l0.

model = tf.keras.Sequential([l0])

 

Compile the model, with loss and optimizer functions

Before training, the model has to be compiled. When compiled for training, the model is given:

• Loss function — A way of measuring how far off predictions are from the desired outcome. (The measured difference is called the "loss".)

• Optimizer function — A way of adjusting internal values in order to reduce the loss.

model.compile(loss='mean_squared_error',
              optimizer=tf.keras.optimizers.Adam(0.1))

The loss function (mean squared error) and the optimizer (Adam) used here are standard for simple models like this one, but many others are available. It is not important to know how these specific functions work at this point.

One part of the Optimizer you may need to think about when building your own models is the learning rate (0.1 in the code above). This is the step size taken when adjusting values in the model. If the value is too small, it will take too many iterations to train the model. Too large, and accuracy goes down. Finding a good value often involves some trial and error, but the range is usually within 0.001 (default), and 0.1

 

Train the model

Train the model by calling the fit method.

During training, the model takes in Celsius values, performs a calculation using the current internal variables (called "weights") and outputs values which are meant to be the Fahrenheit equivalent. Since the weights are initially set randomly, the output will not be close to the correct value. The difference between the actual output and the desired output is calculated using the loss function, and the optimizer function directs how the weights should be adjusted.

This cycle of calculate, compare, adjust is controlled by the fit method. The first argument is the inputs, the second argument is the desired outputs. The epochsargument specifies how many times this cycle should be run, and the verbose argument controls how much output the method produces.

history = model.fit(celsius_q, fahrenheit_a, epochs=500, verbose=False)
print("Finished training the model")

 

Display training statistics

The fit method returns a history object. We can use this object to plot how the loss of our model goes down after each training epoch. A high loss means that the Fahrenheit degrees the model predicts is far from the corresponding value in fahrenheit_a.

We'll use Matplotlib to visualize this (you could use another tool). As you can see, our model improves very quickly at first, and then has a steady, slow improvement until it is very near "perfect" towards the end.

import matplotlib.pyplot as plt
plt.xlabel('Epoch Number')
plt.ylabel("Loss Magnitude")
plt.plot(history.history['loss'])

 

Use the model to predict values

Now you have a model that has been trained to learn the relationship between celsius_q and fahrenheit_a. You can use the predict method to have it calculate the Fahrenheit degrees for a previously unknown Celsius degrees.

So, for example, if the Celsius value is 100, what do you think the Fahrenheit result will be? Take a guess before you run this code.

print(model.predict([100.0]))

## [[211.303]]

The correct answer is 100×1.8+32=212, so our model is doing really well.

To review

• We created a model with a Dense layer
• We trained it with 3500 examples (7 pairs, over 500 epochs).

Our model tuned the variables (weights) in the Dense layer until it was able to return the correct Fahrenheit value for any Celsius value. (Remember, 100 Celsius was not part of our training data.)

 

Looking at the layer weights

Finally, let's print the internal variables of the Dense layer.

print("These are the layer variables: {}".format(l0.get_weights()))

# These are the layer variables: [array([[1.8252475]], dtype=float32), array([28.778244], dtype=float32)]

The first variable is close to ~1.8 and the second to ~32. These values (1.8 and 32) are the actual variables in the real conversion formula.

 

A little experiment

Just for fun, what if we created more Dense layers with different units, which therefore also has more variables?

l0 = tf.keras.layers.Dense(units=4, input_shape=[1])  
l1 = tf.keras.layers.Dense(units=4)  
l2 = tf.keras.layers.Dense(units=1)  
model = tf.keras.Sequential([l0, l1, l2])
model.compile(loss='mean_squared_error', optimizer=tf.keras.optimizers.Adam(0.1))
model.fit(celsius_q, fahrenheit_a, epochs=500, verbose=False)
print("Finished training the model")
print(model.predict([100.0]))
print("Model predicts that 100 degrees Celsius is: {} degrees Fahrenheit".format(model.predict([100.0])))
print("These are the l0 variables: {}".format(l0.get_weights()))
print("These are the l1 variables: {}".format(l1.get_weights()))
print("These are the l2 variables: {}".format(l2.get_weights()))



###
Finished training the model
[[211.74745]]
Model predicts that 100 degrees Celsius is: [[211.74745]] degrees Fahrenheit
These are the l0 variables: [array([[ 0.7958135 , -0.16632499,  0.11443137, -0.280223  ]],
      dtype=float32), array([ 4.1227775, -3.92107  , -2.5417457, -2.2459867], dtype=float32)]
These are the l1 variables: [array([[-1.3943726 ,  1.0559316 , -0.5147954 , -0.33001336],
       [ 0.03978904, -0.4641624 , -1.4814638 , -0.43406987],
       [ 0.31194925, -1.185125  ,  0.4769898 ,  0.3058445 ],
       [-0.11030926,  0.20886262, -1.6987535 , -0.16482909]],
      dtype=float32), array([-3.245772 ,  4.2540045,  2.5424657, -1.3285651], dtype=float32)]
These are the l2 variables: [array([[-0.6510125 ],
       [ 1.1381707 ],
       [ 0.8112351 ],
       [ 0.06158872]], dtype=float32), array([3.7988825], dtype=float32)]
###

As you can see, this model is also able to predict the corresponding Fahrenheit value really well. But when you look at the variables (weights) in the l0 and l1layers, they are nothing even close to ~1.8 and ~32. The added complexity hides the "simple" form of the conversion equation.

Stay tuned for the upcoming video on how Dense layers work for the explanation.

 

Recap

 

The training process (happening in model.fit(...)) is really about tuning the internal variables of the networks to the best possible values, so that they can map the input to the output. This is achieved through an optimization process called Gradient Descent, which uses Numeric Analysis to find the best possible values to the internal variables of the model.

To do machine learning, you don't really need to understand these details. But for the curious: gradient descent iteratively adjusts parameters, nudging them in the correct direction a bit at a time until they reach the best values. In this case “best values” means that nudging them any more would make the model perform worse. The function that measures how good or bad the model is during each iteration is called the “loss function”, and the goal of each nudge is to “minimize the loss function.”

The training process starts with a forward pass, where the input data is fed to the neural network (see Fig.1). Then the model applies its internal math on the input and internal variables to predict an answer ("Model Predicts a Value" in Fig. 1).

In our example, the input was the degrees in Celsius, and the model predicted the corresponding degrees in Fahrenheit.

 

Once a value is predicted, the difference between that predicted value and the correct value is calculated. This difference is called the loss, and it's a measure of how well the model performed the mapping task. The value of the loss is calculated using a loss function, which we specified with the loss parameter when calling model.compile().

After the loss is calculated, the internal variables (weights and biases) of all the layers of the neural network are adjusted, so as to minimize this loss — that is, to make the output value closer to the correct value (see Fig. 2).

 

 This optimization process is called Gradient Descent. The specific algorithm used to calculate the new value of each internal variable is specified by the optimizer parameter when calling model.compile(...). In this example we used the Adam optimizer.

 

By now you should know what the following terms are:

• Feature: The input(s) to our model
• Examples: An input/output pair used for training
• Labels: The output of the model
• Layer: A collection of nodes connected together within a neural network.
• Model: The representation of your neural network
• Dense and Fully Connected (FC): Each node in one layer is connected to each node in the previous layer.
• Weights and biases: The internal variables of model
• Loss: The discrepancy between the desired output and the actual output
• MSE: Mean squared error, a type of loss function that counts a small number of large discrepancies as worse than a large number of small ones.
• Gradient Descent: An algorithm that changes the internal variables a bit at a time to gradually reduce the loss function.
• Optimizer: A specific implementation of the gradient descent algorithm. (There are many algorithms for this. In this course we will only use the “Adam” Optimizer, which stands for ADAptive with Momentum. It is considered the best-practice optimizer.)
• Learning rate: The “step size” for loss improvement during gradient descent.
• Batch: The set of examples used during training of the neural network
• Epoch: A full pass over the entire training dataset
• Forward pass: The computation of output values from input
• Backward pass (backpropagation): The calculation of internal variable adjustments according to the optimizer algorithm, starting from the output layer and working back through each layer to the input.

 

Learning note from Udacity