Unit 1.4 | The First Machine Learning Classifier | Part 2 | Making Predictions

Summary

This video script introduces the perceptron, one of the earliest and simplest machine learning algorithms, inspired by the human brain's neuron structure. It explains how a perceptron processes inputs through a 'black box' model to make predictions based on a learned decision boundary. The script covers the perceptron's structure, including input nodes, model parameters (weights and bias), and the computation of the net input (Z value). It emphasizes the perceptron's role as a foundational concept for more complex neural networks, setting the stage for understanding how machine learning algorithms learn and make predictions.

Takeaways

• 🤖 The script introduces the perceptron, one of the earliest and simplest machine learning algorithms, which serves as a foundational concept for more complex models.
• 🧠 The perceptron was inspired by the human brain and its neurons, although it does not precisely replicate brain function.
• 🔍 The algorithm uses a binary classification task to predict outcomes, distinguishing between two classes, represented by blue diamonds and orange triangles.
• 📊 Inputs to the perceptron, or features, are denoted as X, with each feature variable (X1, X2, etc.) associated with a corresponding weight (W1, W2, etc.).
• 🧮 The perceptron computes a net input, or Z value, by applying a weighted sum of the inputs and adding a bias unit, which is a learned model parameter.
• 📉 A decision boundary is established by applying a threshold to the Z value; if Z > 0, it predicts one class, and if Z ≤ 0, it predicts another.
• 🔧 The perceptron 'learns' by adjusting the weights (W) and bias unit (B) through training on a dataset to improve prediction accuracy.
• 🛠️ Historically, the perceptron was first implemented in hardware, but in modern applications, it is implemented programmatically using code.
• 🚀 The script emphasizes that while machine learning algorithms are inspired by the brain, their success in prediction does not rely on exact mimicry, drawing a parallel to how airplanes are inspired by birds but function differently.
• 📚 The perceptron's structure and learning process are foundational to understanding deeper neural networks, which will be explored later in the course.

Q & A

What is the primary purpose of revisiting the example of a two-dimensional dataset in the script?

The purpose is to demonstrate how a machine learning algorithm, specifically the perceptron, learns the decision boundary to make predictions in a binary classification task.

Why is the perceptron significant in the context of machine learning algorithms?

The perceptron is significant because it is one of the simplest machine learning algorithms, providing a foundational understanding before moving on to more complex models like deep learning.

What was the initial inspiration behind the invention of the perceptron?

The perceptron was inspired by how neurons in the human brain work, although it was later discovered that it does not exactly mimic the brain's functionality.

How was the perceptron first implemented, and how does this relate to its modern implementation?

The perceptron was first implemented in hardware as a box with wires, but in modern times, it is implemented programmatically using code.

What is the role of the bias unit in the perceptron?

The bias unit is a value added during the computation of the weighted input (Z value) in the perceptron, which helps in adjusting the decision boundary.

How does the perceptron compute the Z value, also known as the net input?

The Z value is computed by taking the weighted sum of the input features (multiplying each feature by its corresponding weight) and adding the bias unit.

What is the decision rule applied to the Z value in the perceptron?

If the Z value is greater than zero, the perceptron predicts the class as the orange triangle; if Z is less than or equal to zero, it predicts the class as the blue diamond.

What are the model parameters in the context of a perceptron, and how are they learned?

The model parameters are the weights (W1, W2, ...) and the bias unit (B). These are learned from the training dataset through a process that adjusts them to make accurate predictions.

How does the perceptron handle higher-dimensional datasets with more than two features?

For higher-dimensional datasets, the perceptron extends the computation of the Z value to include all features, with each feature having a corresponding weight, and the process is the same as for two-dimensional datasets.

What is the compact mathematical notation used for expressing the weighted sum in the perceptron?

The compact notation uses a summation symbol to represent the multiplication of each input feature by its weight, with the index i starting from 1 and going up to the number of features M, and then adding the bias unit B.

What will be covered in the next video according to the script?

The next video will explain how the perceptron learns the model parameters, specifically how it adjusts the weights and bias to make accurate predictions.

Outlines

00:00

🤖 Introduction to Machine Learning Predictions and the Perceptron

This paragraph introduces the concept of how machine learning algorithms make predictions. It sets the stage for understanding the perceptron, one of the earliest and simplest machine learning algorithms. The perceptron is highlighted as a foundational algorithm that predates more complex deep learning models. The historical context of the perceptron's invention is provided, noting its initial hardware implementation and its inspiration from the human brain's neuron structure. The discussion also touches on the philosophical aspect of machine learning, emphasizing that while these algorithms are inspired by the brain, they don't need to mimic it exactly to be effective, drawing a parallel with how airplanes were inspired by birds but function differently. The paragraph concludes with a brief overview of the perceptron's structure, which includes inputs, a 'black box' for processing, and outputs representing class labels.

05:01

🧠 Deeper Dive into the Perceptron's Operation

This paragraph delves deeper into the workings of the perceptron, focusing on the computation of the 'Z' value, also known as the net input. It explains how the perceptron processes inputs through a series of weighted sums, involving model parameters (weights and bias), to arrive at a decision boundary. The concept of model parameters, including weights and bias, is introduced as the values that the perceptron learns from the training data to make accurate predictions. The paragraph also discusses the perceptron's decision rule, which is based on applying a threshold to the computed 'Z' value to classify the input data into one of two classes. Additionally, the paragraph touches on the perceptron's role as a building block for more complex neural networks, hinting at the broader applications of the principles introduced in this discussion.

Keywords

💡Machine Learning Algorithm

A machine learning algorithm is a set of procedures that enable computers to learn from data, identify patterns, and make decisions with minimal human intervention. In the context of the video, the focus is on how these algorithms make predictions using training data sets. The video aims to demystify the process of how a machine learning algorithm, specifically the perceptron, learns to classify data points into different categories.

💡Perceptron

The perceptron is one of the earliest and simplest types of artificial neural networks, invented around 70 to 80 years ago. It is used for supervised learning of binary classifiers. The video script uses the perceptron as an introductory example to explain how machine learning algorithms can learn from data. The perceptron's operation is foundational to understanding more complex neural networks.

💡Decision Boundary

In machine learning, a decision boundary is a hyperplane that separates different classes in a dataset. The video discusses how a machine learning algorithm, like the perceptron, learns to create a decision boundary to classify data points into different classes, such as blue diamonds and orange triangles in the given example.

💡Feature Variables

Feature variables, also known as input variables or simply features, are the measurable properties of data that are used as input for machine learning algorithms. In the script, the two-dimensional data set has two feature variables, which are used by the perceptron to make predictions.

💡Binary Classification

Binary classification is a type of supervised machine learning problem where the algorithm must determine which of two classes a new, unseen data point belongs to. The video script provides an example of a binary classification task where the perceptron must classify data points into one of two classes: blue diamonds or orange triangles.

💡Model Parameters

Model parameters, in the context of machine learning, are the values that the algorithm learns during training to make accurate predictions. The video explains that the perceptron has model parameters, namely weights (W1, W2) and a bias unit (B), which it learns from the training data set to classify data points correctly.

💡Weights

In machine learning, weights are the numerical values that are assigned to each feature variable and are used to measure the importance of each feature in making a prediction. The video script describes how the perceptron uses weights (W1, W2) for each feature variable to compute the net input (Z value), which is crucial for determining the class label.

💡Bias Unit

The bias unit is an additional parameter in a perceptron that is added to the weighted sum of inputs to help the model fit the training data better. It allows the decision boundary to be shifted. The video script mentions the bias unit as a part of the model parameters that the perceptron learns to adjust its predictions.

💡Net Input

The net input, also referred to as the Z value in the script, is the result of the weighted sum of the input features plus the bias unit. It is a crucial step in the perceptron's process, as it is used to determine the output class label after applying a threshold.

💡Threshold

In the context of the perceptron, a threshold is a value that determines the output of the model. If the net input (Z value) is greater than the threshold, the perceptron predicts one class; if it is less than or equal to the threshold, it predicts another class. The video script uses the threshold as part of the decision rule for classifying data points.

💡Compact Notation

Compact notation is a mathematical shorthand used to simplify complex expressions, especially in the context of summations over multiple terms. The video script introduces compact notation as a way to express the computation of the net input (Z value) for a perceptron with multiple input features, making the formula more manageable and easier to understand.

Highlights

Introduction to how a machine learning algorithm makes predictions.

Overview of using predictions to train a machine learning algorithm.

Discussion on the perceptron, one of the first machine learning algorithms.

Historical context of the perceptron's invention and its initial hardware implementation.

The perceptron's inspiration from the human brain and its simplification for machine learning purposes.

Analogy between the invention of airplanes and the perceptron's inspiration from the brain.

Explanation of the perceptron's structure and its components: inputs, black box, and outputs.

Definition of the decision boundary in a binary classification task.

Process of computing the Z value or net input within the perceptron.

Description of the threshold applied to the Z value for prediction.

Introduction to model parameters and their role in the perceptron's learning process.

Explanation of weights and their association with input features.

Introduction to the bias unit and its function in computing the weighted input.

Generalization of the perceptron model to higher-dimensional data sets.

Compact mathematical notation for expressing the perceptron's weighted sum.

Summary of the perceptron's prediction process using inputs, model parameters, and a threshold.

Anticipation of the next video's focus on how the perceptron learns its parameters.

Transcripts

Now that we are familiar with a typical training data set for a machine learning algorithm,

let's actually take a look at how a machine learning algorithm makes predictions.

And then in the next upcoming videos, we can use these predictions to actually train this

machine learning algorithm to make better predictions.

So revisiting this example of our two dimensional data set here.

So what we have here is we have two measurement variables or feature variables.

And we have a binary classification task where we have two classes, the blue diamonds and

the orange triangles.

So now the big question is, how does the machine learning algorithm learn this decision boundary?

So to see how this works, we will take a look at one of the first machine learning algorithms

called the perceptron, which was invented about 70, 80 years ago.

The reason why we are covering this algorithm is that it's one of the simplest ones and

it will be a good warm up exercise when we implement this in code before we get to the

more complicated deep learning models.

So actually when this perceptron was invented more than 70 years ago, it was first implemented

in hardware.

So back then, it was actually a box with different wires.

Of course, in this course, we will implement all of that programmatically using code.

But it's just like interesting to see how the perceptron came to be, how earlier systems

for machine learning worked.

And when this perceptron was invented, the motivation or inspiration for the perceptron

was how the human brain works.

So the perceptron was implemented analogous to how neurons in the human brain work.

While this sounds very exciting and inspiring, actually it turned out this is not exactly

how the human brain works.

So the perceptron took some inspiration from the human brain and the neurons.

However, how the human brain works, this still remains a big question in research and science.

However, even if machine learning systems don't mimic how the human brain works exactly,

it doesn't mean they are not useful for prediction.

For example, consider airplanes.

When people invented airplanes, they didn't exactly mimic how birds fly.

So airplanes in a sense are inspired by birds, but they don't flap their wings, for example,

and they still fly.

And in the same sense, machine learning algorithms are inspired by how the human brain works.

But in order to make successful predictions, you don't have to mimic it exactly.

Yeah, now enough about the inspiration behind perceptrons.

Let's actually take a look at how they work.

So the overall structure of a perceptron looks like that.

We have inputs here, and the inputs go into a black box, which we will define later, and

out come the predictions.

So we have inputs, our features, our measurements, and the outputs represent our class labels.

And the number of inputs depends on the number of dimensions in our data set.

So in our two-dimensional data set, where we have two measurement variables or feature

variables, we have two input nodes to this perceptron.

And in machine learning terms, we often refer to these measurement or feature variables

as X.

So feature one would be X1, and feature number two would be X2.

So let's pick out a particular point from this data set and see how it's processed by

the perceptron.

So here we're looking at the point with the X1 value of 1.1 and the X2 value of 5.5.

In this particular case, since that's our training data set, we already know the true

answer.

We know that this point is the blue diamond.

However, in real life, when we have a prediction problem, we apply it to new data where we

don't know the answer yet, and it should come up with the predictions.

Now let's take a look at this black box and see what happens inside.

So inside the perceptron computes a so-called Z value, which we also sometimes call the

net input.

We will define how this is computed later.

But for now, consider we are given this value Z, and then we apply a threshold to it.

So we say if Z is greater than zero, predict this orange triangle.

Otherwise, if Z is smaller or equal to zero, then we will predict this blue diamond.

And this is essentially our decision rule.

We have the Z value and we apply a threshold to it.

How do we compute this value Z though?

So for that, we will involve a few parameters.

We call them the model parameters.

And these are essentially the things that the perceptron learns.

So the model parameters here W1, W2, and B are values that are learned from the training

data set.

So the perceptron looks at the training data set and comes up with good values for these

parameters to make good predictions.

That means predictions that are correct.

So these values W, we also refer to them as weights, the model weights.

Each input feature value has a corresponding model weight.

So X1 comes with W1 and X2 comes with W2.

And if we have a higher dimensional data set, this would go on and on and on.

So for each input node, we have an associated model weight.

V here refers to the bias unit.

It's essentially a value that we add on when we compute the weighted input, the value Z.

The bias unit is something we will also encounter later when we work with deeper neural networks.

So everything you see on this slide, you can think of it as a building block for building

deeper neural networks later on in this course.

So now let's step through the process of computing actually the value Z using the inputs and

the model parameters.

So essentially, in a nutshell, we can think of Z as the weighted input.

For that, we multiply the input feature X1 with the model parameter W1.

Then we multiply the second feature value with W2.

And lastly, we add this bias unit to it.

Now in our particular example, we looked at a data set with two feature variables.

However, in many real world cases, we have higher dimensional data sets.

So in this case, we can extend this formula and go up to M features, where M is really

an arbitrary number that stands for the number of dimensions of features in your data set.

And because this becomes unwieldy pretty quick, we often in machine learning make use of more

compact notation.

So in this case, here at the bottom, you see the compact mathematical formula for expressing

the sum above.

So let's zoom in now and just briefly talk about how this equation works, because we

will use that a lot in this course.

So here we have this symbol in the center, which is a sum symbol.

And for that sum symbol, we have an index i equals 1.

That's the index where we start counting.

And we have this M here where we stop counting.

And for each value between i and M, or 1 and M, we do this multiplication between the input

and the weight value.

And once this is completed, we add this value B, the bias unit to it.

So here really this equation represents a more compact notation of the summation that

we have here more explicitly.

In this video, we learned about the perceptron and how the perceptron makes predictions.

Just to summarize how the perceptron makes these predictions, we have inputs where we

have a given number of input variables, here x1 and x2.

We have model parameters w1, w2, and the bias unit.

And we use those together to compute the weighted sum.

Then we apply a threshold to this weighted sum to come up with the class label predictions.

And that, in a nutshell, is how the perceptron works.

The values x are directly derived from the training data set.

However, in order to compute a value z that falls on the right side of this decision threshold,

we also have to find the right values for w1 and w2 in the bias unit.

And we will see in the next video how the perceptron learns these parameters.