#10 Machine Learning Specialization [Course 1, Week 1, Lesson 3]

Summary

This video script explains the fundamentals of supervised learning, focusing on how algorithms process input data sets to predict outcomes. It introduces the concept of a training set comprising input features and output targets, which the model learns from. The model, represented as a function 'f', estimates predictions (Y hat) based on input features (X). The script delves into linear regression, a basic form of supervised learning where 'f' is a straight line, and discusses the importance of the cost function in machine learning. It concludes by encouraging viewers to explore an optional lab for hands-on experience with linear regression in Python.

Takeaways

• 📊 Supervised learning algorithms use input data sets to produce a function (f) that can predict output targets.
• 🏠 The training set in supervised learning includes both input features (e.g., size of a house) and output targets (e.g., price of a house).
• 🔢 The model's prediction (y hat) is an estimate of the actual target value (Y), which may differ until confirmed.
• 📉 The function f, often represented as a straight line, is used to make predictions based on the input feature X.
• 📈 The choice of a linear function (F_w,b(x) = Wx + b) simplifies the model and serves as a foundation for more complex models.
• 📚 Linear regression is the specific name for the model when the function f is a straight line, especially with one input variable.
• 🔑 Parameters W and B in the function f are crucial as they determine the slope and intercept of the line, respectively.
• 📝 The script suggests an optional lab for practicing defining a straight line function in Python and fitting it to training data.
• 🤖 Cost function is a critical component in machine learning, used to evaluate and improve the model's performance.
• 🔍 The next step after understanding the basics of linear regression is to learn how to construct a cost function for model optimization.

Q & A

What is the primary goal of a supervised learning algorithm?

The primary goal of a supervised learning algorithm is to learn a function, denoted as 'f', that can take new input data (features) and predict an output (target) based on the training data provided.

What are the two components of a training set in supervised learning?

The two components of a training set in supervised learning are the input features (such as the size of a house) and the output targets (such as the price of the house).

What does the output target represent in the context of supervised learning?

The output target represents the correct answer or the actual true value that the model will learn from during training.

How is the function 'f' in supervised learning typically represented?

In the context of the script, the function 'f' is represented as a straight line equation, which can be mathematically expressed as f(x) = wx + b, where 'w' and 'b' are parameters that need to be learned.

What is the difference between 'y' and 'y-hat' in the script?

'y' represents the actual true value of the target in the training set, while 'y-hat' (notated as ŷ) is the estimated or predicted value of 'y' made by the model.

Why might a linear function be chosen as the initial model in supervised learning?

A linear function is chosen as the initial model because it is relatively simple and easy to work with, which serves as a good foundation for understanding more complex models, including non-linear ones.

What is the term for a linear model with a single input variable?

A linear model with a single input variable is called 'univariate linear regression', where 'univariate' indicates that there is only one variable involved.

What is the purpose of the cost function in the context of supervised learning?

The cost function in supervised learning is used to measure the performance of the model by quantifying the difference between the model's predictions and the actual values in the training set.

Why is the cost function considered an important concept in machine learning?

The cost function is considered an important concept in machine learning because it is a universal tool used to evaluate and improve the model's predictions, and it is fundamental to training many advanced AI models.

What is the next step after defining the model function in supervised learning?

After defining the model function, the next step is to construct a cost function and use it to optimize the parameters of the model to minimize the cost and improve the model's predictions.

Outlines

00:00

📊 Introduction to Supervised Learning

This paragraph introduces the concept of supervised learning, explaining how an algorithm takes a dataset with input features and output targets to learn a function. The function, denoted as 'f', is used to make predictions on new data. The training set includes features like house size and targets like house price. The algorithm's goal is to find a function that can predict the target value (Y hat) based on the input feature (X). The paragraph also touches on the historical term 'hypothesis' for the function 'f' and discusses the importance of the true value (Y) versus the estimated value (Y hat). It ends by hinting at the choice of a linear function to represent 'f', which is a simple yet foundational approach to building more complex models.

05:00

🔍 Linear Regression: The Foundation

The second paragraph delves into the specifics of linear regression, a type of supervised learning where the function 'f' is represented as a straight line. It discusses the use of the linear model with one variable, also known as univariate linear regression, focusing on a single feature such as the size of a house. The paragraph explains the notation for the linear function, f(x) = wx + b, where 'w' and 'b' are parameters that determine the line's slope and intercept, respectively. It also mentions the potential for more complex, non-linear models but emphasizes the simplicity and educational value of starting with linear functions. The paragraph concludes by suggesting an optional lab for viewers to explore defining and fitting a straight line function in Python, which helps in understanding how to adjust 'w' and 'b' to best fit the training data.

Keywords

💡Supervised Learning

Supervised learning is a type of machine learning where the algorithm learns from labeled training data. In the context of the video, supervised learning involves feeding a dataset that includes both input features and output targets to the algorithm. The algorithm then learns to predict the output targets based on the input features. The video script explains that the training set in supervised learning includes input features such as the size of a house and output targets such as the price of the house.

💡Training Set

A training set is a collection of data used to train a machine learning model. It includes both input features and output targets. The video script mentions that the training set is essential for supervised learning as it provides the model with examples to learn from. The model uses this data to make predictions, with the output targets serving as the 'right answers' that the model aims to predict.

💡Input Features

Input features, also known as independent variables, are the attributes that are used as input to a machine learning model. In the video, the size of a house is given as an example of an input feature. These features are the basis on which the model makes predictions, and they are part of the training data that the model learns from.

💡Output Targets

Output targets, or dependent variables, are the values that a supervised learning model aims to predict. The video script uses the price of a house as an example of an output target. These targets are part of the training set and are what the model learns to predict based on the input features.

💡Function f

In the video, function f represents the model that the supervised learning algorithm produces. This function takes a new input and makes a prediction, which is denoted as \( \hat{y} \). The function f is a crucial component of the supervised learning process, as it encapsulates the model's ability to generalize from the training data to make predictions on new, unseen data.

💡Prediction \( \hat{y} \)

The prediction \( \hat{y} \) is the estimated value that the model predicts for the output target y. The video script explains that \( \hat{y} \) is represented by the variable y with a 'hat' symbol on top, indicating that it is an estimate and not the actual true value. In the context of the video, if the model is predicting the price of a house, \( \hat{y} \) would be the model's estimate of that price.

💡Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data. The video script discusses linear regression as a type of model where the function f is represented as a straight line. This model is used to predict the value of y using a linear function of x, which is a simple and foundational approach to understanding more complex models.

💡Univariate Linear Regression

Univariate linear regression is a specific type of linear regression where there is only one independent variable. The video script refers to this as a model with a single input variable, such as the size of a house. This type of regression is used when the prediction is based on a single feature, making the model simpler but still effective for understanding the relationship between the input and output.

💡Cost Function

A cost function is a crucial component in machine learning, used to evaluate the performance of a model. The video script introduces the concept of a cost function as a way to measure how well the model's predictions match the actual output targets. The cost function is used to guide the learning process, helping to adjust the model's parameters to minimize the cost and improve the model's predictions.

💡Model Parameters (w and b)

Model parameters, such as w (weight) and b (bias), are the values that determine the behavior of the model. In the context of the video, these parameters are used in the linear function f to make predictions. The values of w and b are learned by the algorithm during the training process to best fit the training data. The script explains that these parameters are essential for the model to make accurate predictions based on the input features.

Highlights

Supervised learning algorithms input a dataset and output a function to make predictions.

A training set includes input features and output targets, which are the right answers for the model to learn from.

The supervised learning algorithm produces a function, historically called a hypothesis, to make predictions.

The function f takes a new input X and outputs an estimate or prediction, denoted as Y hat.

In machine learning, Y hat represents the estimate or prediction for the true value Y.

The model's prediction is an estimated value of Y, which may differ from the actual true value.

The function f, representing the model, is chosen to be a straight line for simplicity in this context.

The linear function f is represented as F_W,B(X) = W*X + B, where W and B are parameters to be determined.

The values of W and B in the function determine the prediction Y hat based on the input feature X.

Linear regression is used as a foundational model, which can be extended to more complex non-linear models.

The model is called linear regression with one variable, indicating a single input feature.

The term 'univariate linear regression' is used to describe a linear model with a single input variable.

An optional lab is available to practice defining a straight line function in Python and fitting the training data.

Constructing a cost function is crucial for making the model work effectively.

The cost function is a universal concept in machine learning, used in linear regression and advanced AI models.

The next video will explore how to construct a cost function for the learning algorithm.

Transcripts

let's look in this video at the process

of how supervised Learning Works

supervised learning algorithm will input

the data set and then what exactly does

it do and what does it output let's find

out in this video

recall that a training set in supervised

learning includes both the input

features such as the size of the house

and also the output targets such as the

price of the house the output targets

are the right answers to the model we'll

learn from

to train the model you feed the trading

set both the input features and the

output targets to your learning

algorithm

then your supervised learning algorithm

will produce some function

we'll write this function as lowercase f

where F stands for function historically

this function used to be called a

hypothesis but I'm just going to call it

a function f in this clause

and the job of f is to take a new input

X

and upwards an estimate or prediction

which I'm going to call Y hat and it's

written like the variable y with this

little hat symbol on top

in machine learning the convention is

that y hat is the estimate or the

prediction for y

the function f is called the model

X is called the input or the input

feature and the output of the model is

the prediction y hat

the model's prediction is the estimated

value of y

when the symbol is just a letter Y then

that refers to the Target which is the

actual True Value in the training set in

contrast y hat is an estimate it may or

may not be the actual True Value

well if you're helping your client to

sell the house well the true price of

the house is unknown until they sell it

so your model f given the size or

pressure price which is the estimated

that is the prediction of what the true

price will be

now when we design a learning algorithm

a key question is how are we going to

represent the function f or in other

words what is the math formula we're

going to use to compute f

for now let's stick with f being a

straight line

so your function can be written as F

subscript W comma B of x equals I'm

going to use W Times X plus b

I'll Define w and B soon but for now

just know that W and B are numbers and

the values chosen for w and B will

determine the prediction y hat based on

the input feature X so this FWB of X

means f is a function that takes X's

input and depending on the values of w

and b f will output some value of a

prediction y hat

as an alternative to writing this FW

comma B of X I'll sometimes just write f

of x without explicitly including W and

B in the subscript it's just a simple

notation but means exactly the same

thing as FWB of x

let's plot the trading set on the graph

where the input feature X is on the

horizontal axis and the output targets Y

is on the vertical axis remember the

album learns from this data and

generates a best fit line like maybe

this one here

this straight line is the linear

function f w b of x equals W Times X

plus b

or more simply we can drop W and B and

just write f of x equals WX plus b

here's what this function is doing is

making predictions for the value of y

using a straight line function of x

so you may ask why are we choosing a

linear function where linear function is

just a fancy term for a straight line

instead of some nonlinear function like

a curve or a parabola

well sometimes you want to fit more

complex non-linear functions as well

like a curve like this but since this

linear function is relatively simple and

easy to work with let's use a line as a

foundation that will eventually help you

to get to more complex models that are

non-linear

this particular model as a name is

called linear regression more

specifically this is linear regression

with one variable with a phrase one

variable means that there's a single

input variable or feature X namely the

size of the host

another name for a linear model with one

input variable is univariate linear

regression where uni means one in Latin

and where variate means variable so univ

variance is just a fancy way of saying

one variable

in a later video you also see a

variation of regression where you want

to make a prediction based not just on

the size of a hose but on a bunch of

other things that you may know about the

whole such as number of bedrooms and

other features and by the way when

you're done with this video there is

another optional lab you don't need to

write any code just review it run the

code and see what it does that will show

you how to define in Python a straight

line function and the lab will let you

choose the values of wmb to try to fit

the training data

you don't have to do the lab if you

don't want to but I hope you play of it

when you're done watching this video

so that's linear regression in order for

you to make this work one of the most

important things you have to do is

construct a cost function

the idea of a cost function is one of

the most universal and important ideas

in machine learning and is used in both

linear regression and in training many

of the most advanced AI models in the

world so let's go on to the next video

and take a look at how you can construct

a cost function