# 01. Neural Network Regression with TensorFlow¶

There are many definitions for a regression problem but in our case, we're going to simplify it to be: predicting a number.

For example, you might want to:

- Predict the selling price of houses given information about them (such as number of rooms, size, number of bathrooms).
- Predict the coordinates of a bounding box of an item in an image.
- Predict the cost of medical insurance for an individual given their demographics (age, sex, gender, race).

In this notebook, we're going to set the foundations for how you can take a sample of inputs (this is your data), build a neural network to discover patterns in those inputs and then make a prediction (in the form of a number) based on those inputs.

## What we're going to cover¶

Specifically, we're going to go through doing the following with TensorFlow:

- Architecture of a regression model
- Input shapes and output shapes
`X`

: features/data (inputs)`y`

: labels (outputs)

- Creating custom data to view and fit
- Steps in modelling
- Creating a model
- Compiling a model
- Defining a loss function
- Setting up an optimizer
- Creating evaluation metrics

- Fitting a model (getting it to find patterns in our data)

- Evaluating a model
- Visualizng the model ("visualize, visualize, visualize")
- Looking at training curves
- Compare predictions to ground truth (using our evaluation metrics)

- Saving a model (so we can use it later)
- Loading a model

Don't worry if none of these make sense now, we're going to go through each.

## How you can use this notebook¶

You can read through the descriptions and the code (it should all run), but there's a better option.

Write all of the code yourself.

Yes. I'm serious. Create a new notebook, and rewrite each line by yourself. Investigate it, see if you can break it, why does it break?

You don't have to write the text descriptions but writing the code yourself is a great way to get hands-on experience.

Don't worry if you make mistakes, we all do. The way to get better and make less mistakes is to **write more code**.

## Typical architecture of a regresison neural network¶

The word *typical* is on purpose.

Why?

Because there are many different ways (actually, there's almost an infinite number of ways) to write neural networks.

But the following is a generic setup for ingesting a collection of numbers, finding patterns in them and then outputting some kind of target number.

Yes, the previous sentence is vague but we'll see this in action shortly.

Hyperparameter |
Typical value |
---|---|

Input layer shape | Same shape as number of features (e.g. 3 for # bedrooms, # bathrooms, # car spaces in housing price prediction) |

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 prediction shape (e.g. 1 for house price) |

Hidden activation | Usually ReLU (rectified linear unit) |

Output activation | None, ReLU, logistic/tanh |

Loss function | MSE (mean square error) or MAE (mean absolute error)/Huber (combination of MAE/MSE) if outliers |

Optimizer | SGD (stochastic gradient descent), Adam |

*Table 1: Typical architecture of a regression network. Source: Adapted from page 293 of Hands-On Machine Learning with Scikit-Learn, Keras & TensorFlow Book by Aurélien Géron*

Again, if you're new to neural networks and deep learning in general, much of the above table won't make sense. But don't worry, we'll be getting hands-on with all of it soon.

🔑

Note:Ahyperparameterin machine learning is something a data analyst or developer can set themselves, where as aparameterusually describes something a model learns on its own (a value not explicitly set by an analyst).

Okay, enough talk, let's get started writing code.

To use TensorFlow, we'll import it as the common alias `tf`

(short for TensorFlow).

```
import tensorflow as tf
print(tf.__version__) # check the version (should be 2.x+)
import datetime
print(f"Notebook last run (end-to-end): {datetime.datetime.now()}")
```

2.12.0 Notebook last run (end-to-end): 2023-05-07 23:10:01.302908

## Creating data to view and fit¶

Since we're working on a **regression problem** (predicting a number) let's create some linear data (a straight line) to model.

```
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);
```

Before we do any modelling, can you calculate the pattern between `X`

and `y`

?

For example, say I asked you, based on this data what the `y`

value would be if `X`

was 17.0?

Or how about if `X`

was -10.0?

This kind of pattern discovery is the essence of what we'll be building neural networks to do for us.

## Regression input shapes and output shapes¶

One of the most important concepts when working with neural networks are the input and output shapes.

The **input shape** is the shape of your data that goes into the model.

The **output shape** is the shape of your data you want to come out of your model.

These will differ depending on the problem you're working on.

Neural networks accept numbers and output numbers. These numbers are typically represented as tensors (or arrays).

Before, we created data using NumPy arrays, but we could do the same with tensors.

```
# Example input and output shapes of a regression model
house_info = tf.constant(["bedroom", "bathroom", "garage"])
house_price = tf.constant([939700])
house_info, house_price
```

(<tf.Tensor: shape=(3,), dtype=string, numpy=array([b'bedroom', b'bathroom', b'garage'], dtype=object)>, <tf.Tensor: shape=(1,), dtype=int32, numpy=array([939700], dtype=int32)>)

```
house_info.shape
```

TensorShape([3])

```
import numpy as np
import matplotlib.pyplot as plt
# Create features (using tensors)
X = tf.constant([-7.0, -4.0, -1.0, 2.0, 5.0, 8.0, 11.0, 14.0])
# Create labels (using tensors)
y = tf.constant([3.0, 6.0, 9.0, 12.0, 15.0, 18.0, 21.0, 24.0])
# Visualize it
plt.scatter(X, y);
```

Our goal here will be to use `X`

to predict `y`

.

So our **input** will be `X`

and our **output** will be `y`

.

Knowing this, what do you think our input and output shapes will be?

Let's take a look.

```
# Take a single example of X
input_shape = X[0].shape
# Take a single example of y
output_shape = y[0].shape
input_shape, output_shape # these are both scalars (no shape)
```

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

Huh?

From this it seems our inputs and outputs have no shape?

How could that be?

It's because no matter what kind of data we pass to our model, it's always going to take as input and return as output some kind of tensor.

But in our case because of our dataset (only 2 small lists of numbers), we're looking at a special kind of tensor, more specifically a rank 0 tensor or a scalar.

```
# Let's take a look at the single examples invidually
X[0], y[0]
```

(<tf.Tensor: shape=(), dtype=float32, numpy=-7.0>, <tf.Tensor: shape=(), dtype=float32, numpy=3.0>)

In our case, we're trying to build a model to predict the pattern between `X[0]`

equalling `-7.0`

and `y[0]`

equalling `3.0`

.

So now we get our answer, we're trying to use 1 `X`

value to predict 1 `y`

value.

You might be thinking, "this seems pretty complicated for just predicting a straight line...".

And you'd be right.

But the concepts we're covering here, the concepts of input and output shapes to a model are fundamental.

In fact, they're probably two of the things you'll spend the most time on when you work with neural networks: **making sure your input and outputs are in the correct shape**.

If it doesn't make sense now, we'll see plenty more examples later on (soon you'll notice the input and output shapes can be almost anything you can imagine).

*If you were working on building a machine learning algorithm for predicting housing prices, your inputs may be number of bedrooms, number of bathrooms and number of garages, giving you an input shape of 3 (3 different features). And since you're trying to predict the price of the house, your output shape would be 1.*

## Steps in modelling with TensorFlow¶

Now we know what data we have as well as the input and output shapes, let's see how we'd build a neural network to model it.

In TensorFlow, there are typically 3 fundamental steps to creating and training a model.

**Creating a model**- piece together the layers of a neural network yourself (using the Functional or Sequential API) or import a previously built model (known as transfer learning).**Compiling a model**- defining how a models performance should be measured (loss/metrics) as well as defining how it should improve (optimizer).**Fitting a model**- letting the model try to find patterns in the data (how does`X`

get to`y`

).

Let's see these in action using the Keras Sequential API to build a model for our regression data. And then we'll step through each.

Note:If you're using TensorFlow 2.7.0+, the`fit()`

function no longer upscales input data to go from`(batch_size, )`

to`(batch_size, 1)`

. To fix this, you'll need to expand the dimension of input data using`tf.expand_dims(input_data, axis=-1)`

.In our case, this means instead of using

`model.fit(X, y, epochs=5)`

, use`model.fit(tf.expand_dims(X, axis=-1), y, epochs=5)`

.

```
# Set random seed
tf.random.set_seed(42)
# Create a model using the Sequential API
model = tf.keras.Sequential([
tf.keras.layers.Dense(1)
])
# Compile the model
model.compile(loss=tf.keras.losses.mae, # mae is short for mean absolute error
optimizer=tf.keras.optimizers.SGD(), # SGD is short for stochastic gradient descent
metrics=["mae"])
# Fit the model
# model.fit(X, y, epochs=5) # this will break with TensorFlow 2.7.0+
model.fit(tf.expand_dims(X, axis=-1), y, epochs=5)
```

Epoch 1/5 1/1 [==============================] - 6s 6s/step - loss: 19.2976 - mae: 19.2976 Epoch 2/5 1/1 [==============================] - 0s 18ms/step - loss: 19.0164 - mae: 19.0164 Epoch 3/5 1/1 [==============================] - 0s 12ms/step - loss: 18.7351 - mae: 18.7351 Epoch 4/5 1/1 [==============================] - 0s 13ms/step - loss: 18.4539 - mae: 18.4539 Epoch 5/5 1/1 [==============================] - 0s 13ms/step - loss: 18.1726 - mae: 18.1726

<keras.callbacks.History at 0x7f00663d2680>

Boom!

We've just trained a model to figure out the patterns between `X`

and `y`

.

How do you think it went?

```
# Check out X and y
X, y
```

(<tf.Tensor: shape=(8,), dtype=float32, numpy=array([-7., -4., -1., 2., 5., 8., 11., 14.], dtype=float32)>, <tf.Tensor: shape=(8,), dtype=float32, numpy=array([ 3., 6., 9., 12., 15., 18., 21., 24.], dtype=float32)>)

What do you think the outcome should be if we passed our model an `X`

value of 17.0?

```
# Make a prediction with the model
model.predict([17.0])
```

1/1 [==============================] - 0s 115ms/step

array([[-16.701845]], dtype=float32)

It doesn't go very well... it should've output something close to 27.0.

🤔

Question:What's Keras? I thought we were working with TensorFlow but every time we write TensorFlow code,`keras`

comes after`tf`

(e.g.`tf.keras.layers.Dense()`

)?

Before TensorFlow 2.0+, Keras was an API designed to be able to build deep learning models with ease. Since TensorFlow 2.0+, its functionality has been tightly integrated within the TensorFlow library.

## Improving a model¶

How do you think you'd improve upon our current model?

If you guessed by tweaking some of the things we did above, you'd be correct.

To improve our model, we alter almost every part of the 3 steps we went through before.

**Creating a model**- here you might want to add more layers, increase the number of hidden units (also called neurons) within each layer, change the activation functions of each layer.**Compiling a model**- you might want to choose optimization function or perhaps change the**learning rate**of the optimization function.**Fitting a model**- perhaps you could fit a model for more**epochs**(leave it training for longer) or on more data (give the model more examples to learn from).

*There are many different ways to potentially improve a neural network. Some of the most common include: increasing the number of layers (making the network deeper), increasing the number of hidden units (making the network wider) and changing the learning rate. Because these values are all human-changeable, they're referred to as hyperparameters) and the practice of trying to find the best hyperparameters is referred to as hyperparameter tuning.*

Woah. We just introduced a bunch of possible steps. The important thing to remember is how you alter each of these will depend on the problem you're working on.

And the good thing is, over the next few problems, we'll get hands-on with all of them.

For now, let's keep it simple, all we'll do is train our model for longer (everything else will stay the same).

```
# Set random seed
tf.random.set_seed(42)
# Create a model (same as above)
model = tf.keras.Sequential([
tf.keras.layers.Dense(1)
])
# Compile model (same as above)
model.compile(loss=tf.keras.losses.mae,
optimizer=tf.keras.optimizers.SGD(),
metrics=["mae"])
# Fit model (this time we'll train for longer)
model.fit(tf.expand_dims(X, axis=-1), y, epochs=100) # train for 100 epochs not 10
```

Epoch 1/100 1/1 [==============================] - 1s 604ms/step - loss: 12.9936 - mae: 12.9936 Epoch 2/100 1/1 [==============================] - 0s 14ms/step - loss: 12.8611 - mae: 12.8611 Epoch 3/100 1/1 [==============================] - 0s 16ms/step - loss: 12.7286 - mae: 12.7286 Epoch 4/100 1/1 [==============================] - 0s 16ms/step - loss: 12.5961 - mae: 12.5961 Epoch 5/100 1/1 [==============================] - 0s 15ms/step - loss: 12.4636 - mae: 12.4636 Epoch 6/100 1/1 [==============================] - 0s 15ms/step - loss: 12.3311 - mae: 12.3311 Epoch 7/100 1/1 [==============================] - 0s 15ms/step - loss: 12.1986 - mae: 12.1986 Epoch 8/100 1/1 [==============================] - 0s 16ms/step - loss: 12.0661 - mae: 12.0661 Epoch 9/100 1/1 [==============================] - 0s 13ms/step - loss: 11.9336 - mae: 11.9336 Epoch 10/100 1/1 [==============================] - 0s 14ms/step - loss: 11.8011 - mae: 11.8011 Epoch 11/100 1/1 [==============================] - 0s 12ms/step - loss: 11.6686 - mae: 11.6686 Epoch 12/100 1/1 [==============================] - 0s 13ms/step - loss: 11.5361 - mae: 11.5361 Epoch 13/100 1/1 [==============================] - 0s 13ms/step - loss: 11.4036 - mae: 11.4036 Epoch 14/100 1/1 [==============================] - 0s 13ms/step - loss: 11.2711 - mae: 11.2711 Epoch 15/100 1/1 [==============================] - 0s 13ms/step - loss: 11.1386 - mae: 11.1386 Epoch 16/100 1/1 [==============================] - 0s 12ms/step - loss: 11.0061 - mae: 11.0061 Epoch 17/100 1/1 [==============================] - 0s 12ms/step - loss: 10.8736 - mae: 10.8736 Epoch 18/100 1/1 [==============================] - 0s 12ms/step - loss: 10.7411 - mae: 10.7411 Epoch 19/100 1/1 [==============================] - 0s 12ms/step - loss: 10.6086 - mae: 10.6086 Epoch 20/100 1/1 [==============================] - 0s 12ms/step - loss: 10.4761 - mae: 10.4761 Epoch 21/100 1/1 [==============================] - 0s 12ms/step - loss: 10.3436 - mae: 10.3436 Epoch 22/100 1/1 [==============================] - 0s 12ms/step - loss: 10.2111 - mae: 10.2111 Epoch 23/100 1/1 [==============================] - 0s 18ms/step - loss: 10.0786 - mae: 10.0786 Epoch 24/100 1/1 [==============================] - 0s 10ms/step - loss: 9.9461 - mae: 9.9461 Epoch 25/100 1/1 [==============================] - 0s 9ms/step - loss: 9.8136 - mae: 9.8136 Epoch 26/100 1/1 [==============================] - 0s 10ms/step - loss: 9.6811 - mae: 9.6811 Epoch 27/100 1/1 [==============================] - 0s 10ms/step - loss: 9.5486 - mae: 9.5486 Epoch 28/100 1/1 [==============================] - 0s 10ms/step - loss: 9.4161 - mae: 9.4161 Epoch 29/100 1/1 [==============================] - 0s 11ms/step - loss: 9.2836 - mae: 9.2836 Epoch 30/100 1/1 [==============================] - 0s 11ms/step - loss: 9.1511 - mae: 9.1511 Epoch 31/100 1/1 [==============================] - 0s 9ms/step - loss: 9.0186 - mae: 9.0186 Epoch 32/100 1/1 [==============================] - 0s 9ms/step - loss: 8.8861 - mae: 8.8861 Epoch 33/100 1/1 [==============================] - 0s 10ms/step - loss: 8.7536 - mae: 8.7536 Epoch 34/100 1/1 [==============================] - 0s 10ms/step - loss: 8.6211 - mae: 8.6211 Epoch 35/100 1/1 [==============================] - 0s 12ms/step - loss: 8.4886 - mae: 8.4886 Epoch 36/100 1/1 [==============================] - 0s 10ms/step - loss: 8.3561 - mae: 8.3561 Epoch 37/100 1/1 [==============================] - 0s 9ms/step - loss: 8.2236 - mae: 8.2236 Epoch 38/100 1/1 [==============================] - 0s 8ms/step - loss: 8.0911 - mae: 8.0911 Epoch 39/100 1/1 [==============================] - 0s 10ms/step - loss: 7.9586 - mae: 7.9586 Epoch 40/100 1/1 [==============================] - 0s 9ms/step - loss: 7.8261 - mae: 7.8261 Epoch 41/100 1/1 [==============================] - 0s 9ms/step - loss: 7.6936 - mae: 7.6936 Epoch 42/100 1/1 [==============================] - 0s 9ms/step - loss: 7.5611 - mae: 7.5611 Epoch 43/100 1/1 [==============================] - 0s 9ms/step - loss: 7.4286 - mae: 7.4286 Epoch 44/100 1/1 [==============================] - 0s 9ms/step - loss: 7.2961 - mae: 7.2961 Epoch 45/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1700 - mae: 7.1700 Epoch 46/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1644 - mae: 7.1644 Epoch 47/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1588 - mae: 7.1588 Epoch 48/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1531 - mae: 7.1531 Epoch 49/100 1/1 [==============================] - 0s 10ms/step - loss: 7.1475 - mae: 7.1475 Epoch 50/100 1/1 [==============================] - 0s 10ms/step - loss: 7.1419 - mae: 7.1419 Epoch 51/100 1/1 [==============================] - 0s 8ms/step - loss: 7.1363 - mae: 7.1363 Epoch 52/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1306 - mae: 7.1306 Epoch 53/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1250 - mae: 7.1250 Epoch 54/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1194 - mae: 7.1194 Epoch 55/100 1/1 [==============================] - 0s 11ms/step - loss: 7.1138 - mae: 7.1138 Epoch 56/100 1/1 [==============================] - 0s 10ms/step - loss: 7.1081 - mae: 7.1081 Epoch 57/100 1/1 [==============================] - 0s 9ms/step - loss: 7.1025 - mae: 7.1025 Epoch 58/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0969 - mae: 7.0969 Epoch 59/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0913 - mae: 7.0913 Epoch 60/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0856 - mae: 7.0856 Epoch 61/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0800 - mae: 7.0800 Epoch 62/100 1/1 [==============================] - 0s 8ms/step - loss: 7.0744 - mae: 7.0744 Epoch 63/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0688 - mae: 7.0688 Epoch 64/100 1/1 [==============================] - 0s 8ms/step - loss: 7.0631 - mae: 7.0631 Epoch 65/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0575 - mae: 7.0575 Epoch 66/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0519 - mae: 7.0519 Epoch 67/100 1/1 [==============================] - 0s 10ms/step - loss: 7.0463 - mae: 7.0463 Epoch 68/100 1/1 [==============================] - 0s 11ms/step - loss: 7.0406 - mae: 7.0406 Epoch 69/100 1/1 [==============================] - 0s 10ms/step - loss: 7.0350 - mae: 7.0350 Epoch 70/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0294 - mae: 7.0294 Epoch 71/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0238 - mae: 7.0238 Epoch 72/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0181 - mae: 7.0181 Epoch 73/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0125 - mae: 7.0125 Epoch 74/100 1/1 [==============================] - 0s 9ms/step - loss: 7.0069 - mae: 7.0069 Epoch 75/100 1/1 [==============================] - 0s 10ms/step - loss: 7.0013 - mae: 7.0013 Epoch 76/100 1/1 [==============================] - 0s 10ms/step - loss: 6.9956 - mae: 6.9956 Epoch 77/100 1/1 [==============================] - 0s 10ms/step - loss: 6.9900 - mae: 6.9900 Epoch 78/100 1/1 [==============================] - 0s 10ms/step - loss: 6.9844 - mae: 6.9844 Epoch 79/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9788 - mae: 6.9788 Epoch 80/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9731 - mae: 6.9731 Epoch 81/100 1/1 [==============================] - 0s 10ms/step - loss: 6.9675 - mae: 6.9675 Epoch 82/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9619 - mae: 6.9619 Epoch 83/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9563 - mae: 6.9563 Epoch 84/100 1/1 [==============================] - 0s 8ms/step - loss: 6.9506 - mae: 6.9506 Epoch 85/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9450 - mae: 6.9450 Epoch 86/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9394 - mae: 6.9394 Epoch 87/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9338 - mae: 6.9338 Epoch 88/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9281 - mae: 6.9281 Epoch 89/100 1/1 [==============================] - 0s 10ms/step - loss: 6.9225 - mae: 6.9225 Epoch 90/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9169 - mae: 6.9169 Epoch 91/100 1/1 [==============================] - 0s 9ms/step - loss: 6.9113 - mae: 6.9113 Epoch 92/100 1/1 [==============================] - 0s 10ms/step - loss: 6.9056 - mae: 6.9056 Epoch 93/100 1/1 [==============================] - 0s 8ms/step - loss: 6.9000 - mae: 6.9000 Epoch 94/100 1/1 [==============================] - 0s 11ms/step - loss: 6.8944 - mae: 6.8944 Epoch 95/100 1/1 [==============================] - 0s 9ms/step - loss: 6.8888 - mae: 6.8888 Epoch 96/100 1/1 [==============================] - 0s 9ms/step - loss: 6.8831 - mae: 6.8831 Epoch 97/100 1/1 [==============================] - 0s 10ms/step - loss: 6.8775 - mae: 6.8775 Epoch 98/100 1/1 [==============================] - 0s 15ms/step - loss: 6.8719 - mae: 6.8719 Epoch 99/100 1/1 [==============================] - 0s 10ms/step - loss: 6.8663 - mae: 6.8663 Epoch 100/100 1/1 [==============================] - 0s 9ms/step - loss: 6.8606 - mae: 6.8606

<keras.callbacks.History at 0x7f0065eabcd0>

You might've noticed the loss value decrease from before (and keep decreasing as the number of epochs gets higher).

What do you think this means for when we make a prediction with our model?

How about we try predict on 17.0 again?

```
# Remind ourselves of what X and y are
X, y
```

(<tf.Tensor: shape=(8,), dtype=float32, numpy=array([-7., -4., -1., 2., 5., 8., 11., 14.], dtype=float32)>, <tf.Tensor: shape=(8,), dtype=float32, numpy=array([ 3., 6., 9., 12., 15., 18., 21., 24.], dtype=float32)>)

```
# Try and predict what y would be if X was 17.0
model.predict([17.0]) # the right answer is 27.0 (y = X + 10)
```

1/1 [==============================] - 0s 61ms/step

array([[29.499516]], dtype=float32)

Much better!

We got closer this time. But we could still be better.

Now we've trained a model, how could we evaluate it?

## Evaluating a model¶

A typical workflow you'll go through when building neural networks is:

```
Build a model -> evaluate it -> build (tweak) a model -> evaulate it -> build (tweak) a model -> evaluate it...
```

The tweaking comes from maybe not building a model from scratch but adjusting an existing one.

### Visualize, visualize, visualize¶

When it comes to evaluation, you'll want to remember the words: "visualize, visualize, visualize."

This is because you're probably better looking at something (doing) than you are thinking about something.

It's a good idea to visualize:

**The data**- what data are you working with? What does it look like?**The model itself**- what does the architecture look like? What are the different shapes?**The training of a model**- how does a model perform while it learns?**The predictions of a model**- how do the predictions of a model line up against the ground truth (the original labels)?

Let's start by visualizing the model.

But first, we'll create a little bit of a bigger dataset and a new model we can use (it'll be the same as before, but the more practice the better).

```
# Make a bigger dataset
X = np.arange(-100, 100, 4)
X
```

array([-100, -96, -92, -88, -84, -80, -76, -72, -68, -64, -60, -56, -52, -48, -44, -40, -36, -32, -28, -24, -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96])

```
# Make labels for the dataset (adhering to the same pattern as before)
y = np.arange(-90, 110, 4)
y
```

array([-90, -86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42, -38, -34, -30, -26, -22, -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106])

Since $y=X+10$, we could make the labels like so:

```
# Same result as above
y = X + 10
y
```

array([-90, -86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42, -38, -34, -30, -26, -22, -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106])

## Split data into training/test set¶

One of the other most common and important steps in a machine learning project is creating a training and test set (and when required, a validation set).

Each set serves a specific purpose:

**Training set**- the model learns from this data, which is typically 70-80% of the total data available (like the course materials you study during the semester).**Validation set**- the model gets tuned on this data, which is typically 10-15% of the total data available (like the practice exam you take before the final exam).**Test set**- the model gets evaluated on this data to test what it has learned, it's typically 10-15% of the total data available (like the final exam you take at the end of the semester).

For now, we'll just use a training and test set, this means we'll have a dataset for our model to learn on as well as be evaluated on.

We can create them by splitting our `X`

and `y`

arrays.

🔑

Note:When dealing with real-world data, this step is typically done right at the start of a project (the test set should always be kept separate from all other data). We want our model to learn on training data and then evaluate it on test data to get an indication of how well itgeneralizesto unseen examples.

```
# Check how many samples we have
len(X)
```

50

```
# Split data into train and test sets
X_train = X[:40] # first 40 examples (80% of data)
y_train = y[:40]
X_test = X[40:] # last 10 examples (20% of data)
y_test = y[40:]
len(X_train), len(X_test)
```

(40, 10)

## Visualizing the data¶

Now we've got our training and test data, it's a good idea to visualize it.

Let's plot it with some nice colours to differentiate what's what.

```
plt.figure(figsize=(10, 7))
# Plot training data in blue
plt.scatter(X_train, y_train, c='b', label='Training data')
# Plot test data in green
plt.scatter(X_test, y_test, c='g', label='Testing data')
# Show the legend
plt.legend();
```

Beautiful! Any time you can visualize your data, your model, your anything, it's a good idea.

With this graph in mind, what we'll be trying to do is build a model which learns the pattern in the blue dots (`X_train`

) to draw the green dots (`X_test`

).

Time to build a model. We'll make the exact same one from before (the one we trained for longer).

```
# Set random seed
tf.random.set_seed(42)
# Create a model (same as above)
model = tf.keras.Sequential([
tf.keras.layers.Dense(1)
])
# Compile model (same as above)
model.compile(loss=tf.keras.losses.mae,
optimizer=tf.keras.optimizers.SGD(),
metrics=["mae"])
# Fit model (same as above)
#model.fit(X_train, y_train, epochs=100) # commented out on purpose (not fitting it just yet)
```

## Visualizing the model¶

After you've built a model, you might want to take a look at it (especially if you haven't built many before).

You can take a look at the layers and shapes of your model by calling `summary()`

on it.

🔑

Note:Visualizing a model is particularly helpful when you run into input and output shape mismatches.

```
# Doesn't work (model not fit/built)
model.summary()
```

--------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-22-7d09d31d4e66> in <cell line: 2>() 1 # Doesn't work (model not fit/built) ----> 2 model.summary() /usr/local/lib/python3.10/dist-packages/keras/engine/training.py in summary(self, line_length, positions, print_fn, expand_nested, show_trainable, layer_range) 3227 """ 3228 if not self.built: -> 3229 raise ValueError( 3230 "This model has not yet been built. " 3231 "Build the model first by calling `build()` or by calling " ValueError: This model has not yet been built. Build the model first by calling `build()` or by calling the model on a batch of data.

Ahh, the cell above errors because we haven't fit or built our model.

We also haven't told it what input shape it should be expecting.

Remember above, how we discussed the input shape was just one number?

We can let our model know the input shape of our data using the `input_shape`

parameter to the first layer (usually if `input_shape`

isn't defined, Keras tries to figure it out automatically).

```
# Set random seed
tf.random.set_seed(42)
# Create a model (same as above)
model = tf.keras.Sequential([
tf.keras.layers.Dense(1, input_shape=[1]) # define the input_shape to our model
])
# Compile model (same as above)
model.compile(loss=tf.keras.losses.mae,
optimizer=tf.keras.optimizers.SGD(),
metrics=["mae"])
```

```
# This will work after specifying the input shape
model.summary()
```

Model: "sequential_3" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense_3 (Dense) (None, 1) 2 ================================================================= Total params: 2 Trainable params: 2 Non-trainable params: 0 _________________________________________________________________

Calling `summary()`

on our model shows us the layers it contains, the output shape and the number of parameters.

**Total params**- total number of parameters in the model.**Trainable parameters**- these are the parameters (patterns) the model can update as it trains.**Non-trainable parameters**- these parameters aren't updated during training (this is typical when you bring in the already learned patterns from other models during transfer learning).

📖

Resource:For a more in-depth overview of the trainable parameters within a layer, check out MIT's introduction to deep learning video.

🛠

Exercise:Try playing around with the number of hidden units in the`Dense`

layer (e.g.`Dense(2)`

,`Dense(3)`

). How does this change the Total/Trainable params? Investigate what's causing the change.

For now, all you need to think about these parameters is that their learnable patterns in the data.

Let's fit our model to the training data.

```
# Fit the model to the training data
model.fit(X_train, y_train, epochs=100, verbose=0) # verbose controls how much gets output
```

<keras.callbacks.History at 0x7f0065dd80d0>

```
# Check the model summary
model.summary()
```

Model: "sequential_3" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense_3 (Dense) (None, 1) 2 ================================================================= Total params: 2 Trainable params: 2 Non-trainable params: 0 _________________________________________________________________

Alongside summary, you can also view a 2D plot of the model using `plot_model()`

.

```
from tensorflow.keras.utils import plot_model
plot_model(model, show_shapes=True)
```

In our case, the model we used only has an input and an output but visualizing more complicated models can be very helpful for debugging.

## Visualizing the predictions¶

Now we've got a trained model, let's visualize some predictions.

To visualize predictions, it's always a good idea to plot them against the ground truth labels.

Often you'll see this in the form of `y_test`

vs. `y_pred`

(ground truth vs. predictions).

First, we'll make some predictions on the test data (`X_test`

), remember the model has never seen the test data.

```
# Make predictions
y_preds = model.predict(X_test)
```

1/1 [==============================] - 0s 45ms/step

```
# View the predictions
y_preds
```

array([[44.544697], [47.427135], [50.309574], [53.192013], [56.07445 ], [58.95689 ], [61.839325], [64.72176 ], [67.60421 ], [70.48664 ]], dtype=float32)

Okay, we get a list of numbers but how do these compare to the ground truth labels?

Let's build a plotting function to find out.

🔑

Note:If you think you're going to be visualizing something a lot, it's a good idea to functionize it so you can use it later.

```
def plot_predictions(train_data=X_train,
train_labels=y_train,
test_data=X_test,
test_labels=y_test,
predictions=y_preds):
"""
Plots training data, test data and compares predictions.
"""
plt.figure(figsize=(10, 7))
# Plot training data in blue
plt.scatter(train_data, train_labels, c="b", label="Training data")
# Plot test data in green
plt.scatter(test_data, test_labels, c="g", label="Testing data")
# Plot the predictions in red (predictions were made on the test data)
plt.scatter(test_data, predictions, c="r", label="Predictions")
# Show the legend
plt.legend();
```

```
plot_predictions(train_data=X_train,
train_labels=y_train,
test_data=X_test,
test_labels=y_test,
predictions=y_preds)
```

From the plot we can see our predictions aren't totally outlandish but they definitely aren't anything special either.

## Evaluating predictions¶

Alongisde visualizations, evaulation metrics are your alternative best option for evaluating your model.

Depending on the problem you're working on, different models have different evaluation metrics.

Two of the main metrics used for regression problems are:

**Mean absolute error (MAE)**- the mean difference between each of the predictions.**Mean squared error (MSE)**- the squared mean difference between of the predictions (use if larger errors are more detrimental than smaller errors).

The lower each of these values, the better.

You can also use `model.evaluate()`

which will return the loss of the model as well as any metrics setup during the compile step.

```
# Evaluate the model on the test set
model.evaluate(X_test, y_test)
```

1/1 [==============================] - 0s 132ms/step - loss: 30.4843 - mae: 30.4843

[30.484329223632812, 30.484329223632812]

In our case, since we used MAE for the loss function as well as MAE for the metrics, `model.evaulate()`

returns them both.

TensorFlow also has built in functions for MSE and MAE.

For many evaluation functions, the premise is the same: compare predictions to the ground truth labels.

```
# Calculate the mean absolute error
mae = tf.metrics.mean_absolute_error(y_true=y_test,
y_pred=y_preds)
mae
```

<tf.Tensor: shape=(10,), dtype=float32, numpy= array([43.455303, 40.572865, 37.690426, 34.807987, 31.925549, 29.04311 , 26.160675, 23.278236, 20.39579 , 17.610687], dtype=float32)>

Huh? That's strange, MAE should be a single output.

Instead, we get 10 values.

This is because our `y_test`

and `y_preds`

tensors are different shapes.

```
# Check the test label tensor values
y_test
```

array([ 70, 74, 78, 82, 86, 90, 94, 98, 102, 106])

```
# Check the predictions tensor values (notice the extra square brackets)
y_preds
```

array([[44.544697], [47.427135], [50.309574], [53.192013], [56.07445 ], [58.95689 ], [61.839325], [64.72176 ], [67.60421 ], [70.48664 ]], dtype=float32)

```
# Check the tensor shapes
y_test.shape, y_preds.shape
```

((10,), (10, 1))

Remember how we discussed dealing with different input and output shapes is one the most common issues you'll come across, this is one of those times.

But not to worry.

We can fix it using `squeeze()`

, it'll remove the the `1`

dimension from our `y_preds`

tensor, making it the same shape as `y_test`

.

🔑

Note:If you're comparing two tensors, it's important to make sure they're the right shape(s) (you won't always have to manipulate the shapes, but always be on the look out,manyerrors are the result of mismatched tensors, especially mismatched input and output shapes).

```
# Shape before squeeze()
y_preds.shape
```

(10, 1)

```
# Shape after squeeze()
y_preds.squeeze().shape
```

(10,)

```
# What do they look like?
y_test, y_preds.squeeze()
```

(array([ 70, 74, 78, 82, 86, 90, 94, 98, 102, 106]), array([44.544697, 47.427135, 50.309574, 53.192013, 56.07445 , 58.95689 , 61.839325, 64.72176 , 67.60421 , 70.48664 ], dtype=float32))

Okay, now we know how to make our `y_test`

and `y_preds`

tenors the same shape, let's use our evaluation metrics.

```
# Calcuate the MAE
mae = tf.metrics.mean_absolute_error(y_true=y_test,
y_pred=y_preds.squeeze()) # use squeeze() to make same shape
mae
```

<tf.Tensor: shape=(), dtype=float32, numpy=30.48433>

```
# Calculate the MSE
mse = tf.metrics.mean_squared_error(y_true=y_test,
y_pred=y_preds.squeeze())
mse
```

<tf.Tensor: shape=(), dtype=float32, numpy=939.59827>

We can also calculate the MAE using pure TensorFlow functions.

```
# Returns the same as tf.metrics.mean_absolute_error()
tf.reduce_mean(tf.abs(y_test-y_preds.squeeze()))
```

<tf.Tensor: shape=(), dtype=float64, numpy=30.484329986572266>

Again, it's a good idea to functionize anything you think you might use over again (or find yourself using over and over again).

Let's make functions for our evaluation metrics.

```
def mae(y_test, y_pred):
"""
Calculuates mean absolute error between y_test and y_preds.
"""
return tf.metrics.mean_absolute_error(y_test,
y_pred)
def mse(y_test, y_pred):
"""
Calculates mean squared error between y_test and y_preds.
"""
return tf.metrics.mean_squared_error(y_test,
y_pred)
```

## Running experiments to improve a model¶

After seeing the evaluation metrics and the predictions your model makes, it's likely you'll want to improve it.

Again, there are many different ways you can do this, but 3 of the main ones are:

**Get more data**- get more examples for your model to train on (more opportunities to learn patterns).**Make your model larger (use a more complex model)**- this might come in the form of more layers or more hidden units in each layer.**Train for longer**- give your model more of a chance to find the patterns in the data.

Since we created our dataset, we could easily make more data but this isn't always the case when you're working with real-world datasets.

So let's take a look at how we can improve our model using 2 and 3.

To do so, we'll build 3 models and compare their results:

`model_1`

- same as original model, 1 layer, trained for 100 epochs.`model_2`

- 2 layers, trained for 100 epochs.`model_3`

- 2 layers, trained for 500 epochs.

**Build model_1**

```
# Set random seed
tf.random.set_seed(42)
# Replicate original model
model_1 = tf.keras.Sequential([
tf.keras.layers.Dense(1)
])
# Compile the model
model_1.compile(loss=tf.keras.losses.mae,
optimizer=tf.keras.optimizers.SGD(),
metrics=['mae'])
# Fit the model
model_1.fit(tf.expand_dims(X_train, axis=-1), y_train, epochs=100)
```

Epoch 1/100 2/2 [==============================] - 0s 19ms/step - loss: 30.0988 - mae: 30.0988 Epoch 2/100 2/2 [==============================] - 0s 8ms/step - loss: 8.4388 - mae: 8.4388 Epoch 3/100 2/2 [==============================] - 0s 6ms/step - loss: 10.5960 - mae: 10.5960 Epoch 4/100 2/2 [==============================] - 0s 6ms/step - loss: 13.1312 - mae: 13.1312 Epoch 5/100 2/2 [==============================] - 0s 7ms/step - loss: 12.1970 - mae: 12.1970 Epoch 6/100 2/2 [==============================] - 0s 6ms/step - loss: 9.4357 - mae: 9.4357 Epoch 7/100 2/2 [==============================] - 0s 7ms/step - loss: 8.5754 - mae: 8.5754 Epoch 8/100 2/2 [==============================] - 0s 7ms/step - loss: 9.0484 - mae: 9.0484 Epoch 9/100 2/2 [==============================] - 0s 6ms/step - loss: 18.7568 - mae: 18.7568 Epoch 10/100 2/2 [==============================] - 0s 7ms/step - loss: 10.1199 - mae: 10.1199 Epoch 11/100 2/2 [==============================] - 0s 7ms/step - loss: 8.4027 - mae: 8.4027 Epoch 12/100 2/2 [==============================] - 0s 6ms/step - loss: 10.6692 - mae: 10.6692 Epoch 13/100 2/2 [==============================] - 0s 7ms/step - loss: 9.8023 - mae: 9.8023 Epoch 14/100 2/2 [==============================] - 0s 6ms/step - loss: 16.0152 - mae: 16.0152 Epoch 15/100 2/2 [==============================] - 0s 8ms/step - loss: 11.4080 - mae: 11.4080 Epoch 16/100 2/2 [==============================] - 0s 7ms/step - loss: 8.5437 - mae: 8.5437 Epoch 17/100 2/2 [==============================] - 0s 7ms/step - loss: 13.6405 - mae: 13.6405 Epoch 18/100 2/2 [==============================] - 0s 7ms/step - loss: 11.4690 - mae: 11.4690 Epoch 19/100 2/2 [==============================] - 0s 7ms/step - loss: 17.9154 - mae: 17.9154 Epoch 20/100 2/2 [==============================] - 0s 6ms/step - loss: 15.0500 - mae: 15.0500 Epoch 21/100 2/2 [==============================] - 0s 7ms/step - loss: 11.0231 - mae: 11.0231 Epoch 22/100 2/2 [==============================] - 0s 7ms/step - loss: 8.1580 - mae: 8.1580 Epoch 23/100 2/2 [==============================] - 0s 7ms/step - loss: 9.5191 - mae: 9.5191 Epoch 24/100 2/2 [==============================] - 0s 6ms/step - loss: 7.6655 - mae: 7.6655 Epoch 25/100 2/2 [==============================] - 0s 6ms/step - loss: 13.1908 - mae: 13.1908 Epoch 26/100 2/2 [==============================] - 0s 8ms/step - loss: 16.4217 - mae: 16.4217 Epoch 27/100 2/2 [==============================] - 0s 7ms/step - loss: 13.1672 - mae: 13.1672 Epoch 28/100 2/2 [==============================] - 0s 13ms/step - loss: 14.2568 - mae: 14.2568 Epoch 29/100 2/2 [==============================] - 0s 7ms/step - loss: 10.0703 - mae: 10.0703 Epoch 30/100 2/2 [==============================] - 0s 6ms/step - loss: 16.3398 - mae: 16.3398 Epoch 31/100 2/2 [==============================] - 0s 7ms/step - loss: 23.6485 - mae: 23.6485 Epoch 32/100 2/2 [==============================] - 0s 6ms/step - loss: 7.6261 - mae: 7.6261 Epoch 33/100 2/2 [==============================] - 0s 6ms/step - loss: 9.3267 - mae: 9.3267 Epoch 34/100 2/2 [==============================] - 0s 6ms/step - loss: 13.7369 - mae: 13.7369 Epoch 35/100 2/2 [==============================] - 0s 7ms/step - loss: 11.1301 - mae: 11.1301 Epoch 36/100 2/2 [==============================] - 0s 7ms/step - loss: 13.3224 - mae: 13.3224 Epoch 37/100 2/2 [==============================] - 0s 7ms/step - loss: 9.4813 - mae: 9.4813 Epoch 38/100 2/2 [==============================] - 0s 7ms/step - loss: 10.1438 - mae: 10.1438 Epoch 39/100 2/2 [==============================] - 0s 7ms/step - loss: 10.1818 - mae: 10.1818 Epoch 40/100 2/2 [==============================] - 0s 7ms/step - loss: 10.9152 - mae: 10.9152 Epoch 41/100 2/2 [==============================] - 0s 7ms/step - loss: 7.9088 - mae: 7.9088 Epoch 42/100 2/2 [==============================] - 0s 7ms/step - loss: 10.0967 - mae: 10.0967 Epoch 43/100 2/2 [==============================] - 0s 7ms/step - loss: 8.7052 - mae: 8.7052 Epoch 44/100 2/2 [==============================] - 0s 7ms/step - loss: 12.2103 - mae: 12.2103 Epoch 45/100 2/2 [==============================] - 0s 7ms/step - loss: 13.7978 - mae: 13.7978 Epoch 46/100 2/2 [==============================] - 0s 7ms/step - loss: 8.4711 - mae: 8.4711 Epoch 47/100 2/2 [==============================] - 0s 7ms/step - loss: 9.1381 - mae: 9.1381 Epoch 48/100 2/2 [==============================] - 0s 7ms/step - loss: 10.6247 - mae: 10.6247 Epoch 49/100 2/2 [==============================] - 0s 7ms/step - loss: 7.7550 - mae: 7.7550 Epoch 50/100 2/2 [==============================] - 0s 6ms/step - loss: 9.5461 - mae: 9.5461 Epoch 51/100 2/2 [==============================] - 0s 7ms/step - loss: 9.1627 - mae: 9.1627 Epoch 52/100 2/2 [==============================] - 0s 7ms/step - loss: 16.3674 - mae: 16.3674 Epoch 53/100 2/2 [==============================] - 0s 7ms/step - loss: 14.1315 - mae: 14.1315 Epoch 54/100 2/2 [==============================] - 0s 7ms/step - loss: 21.1233 - mae: 21.1233 Epoch 55/100 2/2 [==============================] - 0s 7ms/step - loss: 16.4010 - mae: 16.4010 Epoch 56/100 2/2 [==============================] - 0s 6ms/step - loss: 9.9366 - mae: 9.9366 Epoch 57/100 2/2 [==============================] - 0s 7ms/step - loss: 9.6189 - mae: 9.6189 Epoch 58/100 2/2 [==============================] - 0s 6ms/step - loss: 8.9519 - mae: 8.9519 Epoch 59/100 2/2 [==============================] - 0s 7ms/step - loss: 10.1374 - mae: 10.1374 Epoch 60/100 2/2 [==============================] - 0s 6ms/step - loss: 8.4572 - mae: 8.4572 Epoch 61/100 2/2 [==============================] - 0s 8ms/step - loss: 9.3126 - mae: 9.3126 Epoch 62/100 2/2 [==============================] - 0s 7ms/step - loss: 7.0772 - mae: 7.0772 Epoch 63/100 2/2 [==============================] - 0s 7ms/step - loss: 8.6268 - mae: 8.6268 Epoch 64/100 2/2 [==============================] - 0s 7ms/step - loss: 9.2062 - mae: 9.2062 Epoch 65/100 2/2 [==============================] - 0s 7ms/step - loss: 10.4393 - mae: 10.4393 Epoch 66/100 2/2 [==============================] - 0s 7ms/step - loss: 15.7070 - mae: 15.7070 Epoch 67/100 2/2 [==============================] - 0s 7ms/step - loss: 10.0863 - mae: 10.0863 Epoch 68/100 2/2 [==============================] - 0s 7ms/step - loss: 9.0451 - mae: 9.0451 Epoch 69/100 2/2 [==============================] - 0s 7ms/step - loss: 12.5786 - mae: 12.5786 Epoch 70/100 2/2 [==============================] - 0s 9ms/step - loss: 8.9553 - mae: 8.9553 Epoch 71/100 2/2 [==============================] - 0s 7ms/step - loss: 9.9295 - mae: 9.9295 Epoch 72/100 2/2 [==============================] - 0s 8ms/step - loss: 9.9702 - mae: 9.9702 Epoch 73/100 2/2 [==============================] - 0s 8ms/step - loss: 12.4305 - mae: 12.4305 Epoch 74/100 2/2 [==============================] - 0s 7ms/step - loss: 10.5927 - mae: 10.5927 Epoch 75/100 2/2 [==============================] - 0s 7ms/step - loss: 9.6281 - mae: 9.6281 Epoch 76/100 2/2 [==============================] - 0s 7ms/step - loss: 11.0915 - mae: 11.0915 Epoch 77/100 2/2 [==============================] - 0s 7ms/step - loss: 8.2769 - mae: 8.2769 Epoch 78/100 2/2 [==============================] - 0s 7ms/step - loss: 8.9623 - mae: 8.9623 Epoch 79/100 2/2 [==============================] - 0s 7ms/step - loss: 19.8117 - mae: 19.8117 Epoch 80/100 2/2 [==============================] - 0s 6ms/step - loss: 17.8036 - mae: 17.8036 Epoch 81/100 2/2 [==============================] - 0s 7ms/step - loss: 7.0915 - mae: 7.0915 Epoch 82/100 2/2 [==============================] - 0s 7ms/step - loss: 10.4045 - mae: 10.4045 Epoch 83/100 2/2 [==============================] - 0s 7ms/step - loss: 9.8260 - mae: 9.8260 Epoch 84/100 2/2 [==============================] - 0s 7ms/step - loss: 7.9471 - mae: 7.9471 Epoch 85/100 2/2 [==============================] - 0s 7ms/step - loss: 9.4590 - mae: 9.4590 Epoch 86/100 2/2 [==============================] - 0s 7ms/step - loss: 9.5023 - mae: 9.5023 Epoch 87/100 2/2 [==============================] - 0s 7ms/step - loss: 11.4498 - mae: 11.4498 Epoch 88/100 2/2 [==============================] - 0s 7ms/step - loss: 9.9486 - mae: 9.9486 Epoch 89/100 2/2 [==============================] - 0s 7ms/step - loss: 7.2579 - mae: 7.2579 Epoch 90/100 2/2 [==============================] - 0s 6ms/step - loss: 12.7103 - mae: 12.7103 Epoch 91/100 2/2 [==============================] - 0s 7ms/step - loss: 7.3206 - mae: 7.3206 Epoch 92/100 2/2 [==============================] - 0s 12ms/step - loss: 7.6849 - mae: 7.6849 Epoch 93/100 2/2 [==============================] - 0s 8ms/step - loss: 7.1229 - mae: 7.1229 Epoch 94/100 2/2 [==============================] - 0s 7ms/step - loss: 12.5571 - mae: 12.5571 Epoch 95/100 2/2 [==============================] - 0s 6ms/step - loss: 9.9330 - mae: 9.9330 Epoch 96/100 2/2 [==============================] - 0s 7ms/step - loss: 9.1413 - mae: 9.1413 Epoch 97/100 2/2 [==============================] - 0s 7ms/step - loss: 12.0806 - mae: 12.0806 Epoch 98/100 2/2 [==============================] - 0s 7ms/step - loss: 9.0788 - mae: 9.0788 Epoch 99/100 2/2 [==============================] - 0s 8ms/step - loss: 8.4999 - mae: 8.4999 Epoch 100/100 2/2 [==============================] - 0s 7ms/step - loss: 14.4517 - mae: 14.4517

<keras.callbacks.History at 0x7f0065a91180>

```
# Make and plot predictions for model_1
y_preds_1 = model_1.predict(X_test)
plot_predictions(predictions=y_preds_1)
```

1/1 [==============================] - 0s 45ms/step

```
# Calculate model_1 metrics
mae_1 = mae(y_test, y_preds_1.squeeze()).numpy()
mse_1 = mse(y_test, y_preds_1.squeeze()).numpy()
mae_1, mse_1
```

(30.638134, 949.13086)

**Build model_2**

This time we'll add an extra dense layer (so now our model will have 2 layers) whilst keeping everything else the same.

```
# Set random seed
tf.random.set_seed(42)
# Replicate model_1 and add an extra layer
model_2 = tf.keras.Sequential([
tf.keras.layers.Dense(1),
tf.keras.layers.Dense(1) # add a second layer
])
# Compile the model
model_2.compile(loss=tf.keras.losses.mae,
optimizer=tf.keras.optimizers.SGD(),
metrics=['mae'])
# Fit the model
model_2.fit(tf.expand_dims(X_train, axis=-1), y_train, epochs=100, verbose=0) # set verbose to 0 for less output
```

<keras.callbacks.History at 0x7f00643ba560>

```
# Make and plot predictions for model_2
y_preds_2 = model_2.predict(X_test)
plot_predictions(predictions=y_preds_2)
```

WARNING:tensorflow:5 out of the last 5 calls to <function Model.make_predict_function.<locals>.predict_function at 0x7f006436f880> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has reduce_retracing=True option that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for more details.

1/1 [==============================] - 0s 51ms/step

Woah, that's looking better already! And all it took was an extra layer.

```
# Calculate model_2 metrics
mae_2 = mae(y_test, y_preds_2.squeeze()).numpy()
mse_2 = mse(y_test, y_preds_2.squeeze()).numpy()
mae_2, mse_2
```

(10.610324, 120.35542)

**Build model_3**

For our 3rd model, we'll keep everything the same as `model_2`

except this time we'll train for longer (500 epochs instead of 100).

This will give our model more of a chance to learn the patterns in the data.

```
# Set random seed
tf.random.set_seed(42)
# Replicate model_2
model_3 = tf.keras.Sequential([
tf.keras.layers.Dense(1),
tf.keras.layers.Dense(1)
])
# Compile the model
model_3.compile(loss=tf.keras.losses.mae,
optimizer=tf.keras.optimizers.SGD(),
metrics=['mae'])
# Fit the model (this time for 500 epochs, not 100)
model_3.fit(tf.expand_dims(X_train, axis=-1), y_train, epochs=500, verbose=0) # set verbose to 0 for less output
```

<keras.callbacks.History at 0x7f0065a5c8e0>

```
# Make and plot predictions for model_3
y_preds_3 = model_3.predict(X_test)
plot_predictions(predictions=y_preds_3)
```

WARNING:tensorflow:6 out of the last 6 calls to <function Model.make_predict_function.<locals>.predict_function at 0x7f00641280d0> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has reduce_retracing=True option that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for more details.

1/1 [==============================] - 0s 55ms/step

Strange, we trained for longer but our model performed worse?

As it turns out, our model might've trained too long and has thus resulted in worse results (we'll see ways to prevent training for too long later on).

```
# Calculate model_3 metrics
mae_3 = mae(y_test, y_preds_3.squeeze()).numpy()
mse_3 = mse(y_test, y_preds_3.squeeze()).numpy()
mae_3, mse_3
```

(67.224594, 4601.822)

## Comparing results¶

Now we've got results for 3 similar but slightly different results, let's compare them.

```
model_results = [["model_1", mae_1, mse_1],
["model_2", mae_2, mse_2],
["model_3", mae_3, mae_3]]
```

```
import pandas as pd
all_results = pd.DataFrame(model_results, columns=["model", "mae", "mse"])
all_results
```

model | mae | mse | |
---|---|---|---|

0 | model_1 | 30.638134 | 949.130859 |

1 | model_2 | 10.610324 | 120.355423 |

2 | model_3 | 67.224594 | 67.224594 |