Xgboost Regression In-Depth Intuition Explained- Machine Learning Algorithms 🔥🔥🔥🔥

Summary

In this YouTube tutorial, the host Krishna dives into the workings of the XGBoost Regressor, an ensemble machine learning technique. He explains how decision trees are constructed within XGBoost, detailing the process from creating a base model to calculating residuals and constructing sequential binary trees. Krishna also covers the calculation of similarity weights and information gain, crucial for optimizing splits in the tree. The video is educational, aiming to provide in-depth intuition into XGBoost's regression capabilities.

Takeaways

• 🌟 XGBoost is an ensemble technique that uses boosting methods, specifically extreme gradient boosting.
• 📊 The script explains how decision trees are constructed in XGBoost, starting with creating a base model that uses the average of the target variable.
• 🔍 Residuals are calculated by subtracting the base model's output from the actual values, which are then used to train the decision trees.
• 📈 The script discusses the calculation of similarity weights in XGBoost, which is a key component in determining how to split nodes in the trees.
• 📉 Lambda is introduced as a hyperparameter that can adjust the similarity weight, thus influencing the complexity of the model.
• 📝 The process of calculating information gain for different splits is detailed, which helps in deciding the best splits for the decision trees.
• 🌳 The script walks through an example of constructing a decision tree using the 'experience' feature and comparing it with other potential splits.
• 🔧 The concept of gain, which is the improvement in model performance from a split, is calculated and used to decide which features and splits to use.
• 🔄 The script mentions the use of multiple decision trees in XGBoost, each contributing to the final prediction with a learning rate (alpha) applied.
• 🛠 The role of hyperparameters like gamma in post-pruning to prevent overfitting is discussed, highlighting the importance of tuning these parameters for optimal model performance.

Q & A

What is the main topic of the video?

The main topic of the video is an in-depth discussion on the XGBoost Regressor, focusing on how decision trees are created in XGBoost and the mathematical formulas involved.

What is XGBoost and what does it stand for?

XGBoost stands for eXtreme Gradient Boosting. It is an ensemble machine learning algorithm that uses a boosting technique to build and combine multiple decision trees.

What is the role of the base model in XGBoost?

The base model in XGBoost is used to calculate the average output, which serves as the initial prediction before any decision trees are applied. It helps in computing residuals that are used to train the subsequent decision trees.

How does the script define 'residual' in the context of XGBoost?

In the context of XGBoost, 'residual' refers to the difference between the actual value and the predicted value by the base model. It represents the error that the model is trying to correct.

What is the significance of the lambda parameter in XGBoost?

The lambda parameter in XGBoost is a hyperparameter that controls the complexity of the model. It is used in the calculation of similarity weight, which in turn affects the decision of splitting nodes in the decision trees.

What is the purpose of calculating similarity weight in XGBoost?

The similarity weight in XGBoost is calculated to measure the quality of a split in a decision tree. It is used to determine the best split that maximizes the reduction in the weighted sum of squared residuals.

How does the script describe the process of creating a decision tree in XGBoost?

The script describes the process of creating a decision tree in XGBoost by first creating a base model, then calculating residuals, and using these residuals to determine the best splits for the decision tree nodes based on similarity weight and gain.

What is the role of the learning rate (alpha) in the XGBoost algorithm?

The learning rate (alpha) in the XGBoost algorithm determines the contribution of each decision tree to the final prediction. It is used to control the impact of each tree, allowing the model to update predictions incrementally.

What is the purpose of the gamma parameter mentioned in the script?

The gamma parameter in the script is used for post-pruning in the decision trees. If the information gain after a split is less than the gamma value, the split is pruned, which helps in preventing overfitting.

How does the script explain the process of calculating the output for a decision tree in XGBoost?

The script explains that the output for a decision tree in XGBoost is calculated by taking the average of the residuals that fall into a particular node, and then using this output to update the predictions for the corresponding records.

What is the final output of the XGBoost model as described in the script?

The final output of the XGBoost model is the sum of the base model output and the outputs from each decision tree, each multiplied by their respective learning rates (alphas).

Outlines

00:00

🌟 Introduction to XGBoost Regressor

The speaker, Krishna, introduces the topic of the video, which is an in-depth exploration of the XGBoost Regressor. He explains that the video will cover the creation of decision trees within XGBoost and the mathematical formulas involved. Krishna references a previous video on the HDBSCAN classifier and encourages viewers to watch it for context. The video then delves into a problem statement involving three features: experience, gap, and salary. The aim is to demonstrate how decision trees are constructed in XGBoost, starting with the creation of a base model using the average salary as a predictor.

05:01

📊 Constructing Decision Trees in XGBoost

Krishna explains the process of creating sequential decision trees in XGBoost, beginning with the calculation of residuals based on the average salary. He then discusses how the first decision tree is constructed using the features 'experience' and 'gap', along with the residuals. The video illustrates how to split the data at the root node based on the 'experience' feature, creating two branches: one for values less than or equal to 2 and another for values greater than 2. Krishna also introduces the concept of similarity weight, which is calculated using the sum of residual squares and a hyperparameter called lambda. The goal is to find the best split that maximizes the information gain, which is the difference between the sum of similarity weights of the left and right nodes and the similarity weight of the root node.

10:04

🔍 Calculating Information Gain and Decision Tree Output

The speaker continues by calculating the information gain for different splits in the decision tree, comparing the gains to determine the most effective split. He emphasizes the importance of choosing the split that yields the highest gain. Krishna then explains how to calculate the output of the decision tree nodes, using the average of the residuals for each node. The video demonstrates how the base model output is combined with the decision tree output, adjusted by a learning rate, to produce the final predictions. The process is repeated for each record, and Krishna clarifies a mistake made in the calculation, ensuring accuracy in the demonstration.

15:05

🛠️ Advanced XGBoost Techniques and Conclusion

In the final part of the video, Krishna discusses advanced techniques in XGBoost, such as the use of the gamma parameter for post-pruning to prevent overfitting. He explains that if the information gain after a split is less than the gamma value, the split is pruned. Krishna summarizes the process of constructing an XGBoost model, which involves creating multiple decision trees and combining their outputs with the base model output, each multiplied by a learning rate. He concludes by encouraging viewers to subscribe to the channel for more content and thanks them for watching.

Keywords

💡XGBoost Regressor

XGBoost Regressor is an ensemble machine learning technique that uses boosting for regression tasks. It constructs sequential decision trees, each correcting the errors from the previous one, improving the overall model accuracy. In the script, the speaker explains how XGBoost Regressor is used to model relationships between features like experience and salary.

💡Boosting Technique

Boosting is a machine learning method where multiple weak learners (often decision trees) are combined to create a strong learner. Each model in the sequence focuses on correcting the errors of the previous ones. XGBoost is one such boosting technique, and the video emphasizes how it uses boosting to improve model performance.

💡Decision Tree

A decision tree is a flowchart-like structure used to model decisions based on feature values. In XGBoost, decision trees are sequentially created, with each tree learning from the residual errors of the previous tree. The script describes how decision trees are created in XGBoost Regressor to predict outcomes like salary based on experience and gap.

💡Residuals

Residuals represent the difference between the predicted and actual values in a regression model. In XGBoost, residuals from the base model are used to train subsequent decision trees. The video shows how residuals are calculated after the base model's prediction of the average salary and how they influence the training of the next tree.

💡Similarity Weight

Similarity weight is a measure used in XGBoost to determine the best splits in decision trees. It is calculated based on the residuals and helps to quantify how similar or different the data points in a split are. The speaker demonstrates how similarity weights are computed for different splits to decide the optimal node division.

💡Lambda

Lambda is a hyperparameter in XGBoost that controls the regularization term applied to the similarity weight calculation. It helps prevent overfitting by penalizing overly complex models. The script mentions that increasing the lambda value decreases the similarity weight, thus influencing the decision-making process in tree construction.

💡Information Gain

Information gain measures the improvement in accuracy or reduction in uncertainty after a split in a decision tree. It is calculated by comparing the similarity weights before and after the split. In the video, the speaker explains how the total gain from a split is computed, and the split with the highest gain is selected.

💡Hyperparameter Tuning

Hyperparameter tuning involves adjusting the settings of a machine learning algorithm to optimize performance. In XGBoost, parameters like lambda and gamma control model complexity and pruning. The speaker explains how tuning lambda and gamma values can affect the similarity weights and post-pruning of decision trees.

💡Learning Rate

The learning rate (alpha) in XGBoost controls the contribution of each new tree to the final model. A smaller learning rate makes the model learn more slowly but can improve performance by avoiding overfitting. In the video, the speaker uses a learning rate of 0.5 to adjust the output of the trees in the XGBoost Regressor.

💡Pruning

Pruning is the process of removing nodes from a decision tree to avoid overfitting and improve model generalization. In XGBoost, pruning is influenced by the gamma hyperparameter. The speaker discusses how gamma is used to decide whether a split should be pruned based on the information gain and its effect on the overall model.

Highlights

Introduction to XGBoost Regressor and its ensemble technique using boosting.

Explanation of how decision trees are created in XGBoost.

Discussion on the Mean Absolute Percentage Error (MAPE) formula involved in XGBoost.

Overview of the base model creation process in XGBoost.

Calculation of residuals based on the base model output.

Introduction to the concept of similarity weight in XGBoost Regressor.

Calculation of similarity weight for different splits in the decision tree.

Explanation of information gain in the context of XGBoost Regressor.

Demonstration of how to choose the best split point in a decision tree.

Construction of a binary tree with experience as a continuous feature.

Use of lambda as a hyperparameter to adjust similarity weight.

Calculation of the output for each node in the decision tree.

Description of how to pass a record through the decision tree to get the output.

Introduction to the concept of learning rate in the context of XGBoost.

Explanation of how residuals are recalculated after each iteration.

Discussion on the role of gamma as a hyperparameter for post-pruning in XGBoost.

Final output calculation using the XGBoost formula with multiple decision trees.

Encouragement for viewers to subscribe for more in-depth tutorials on XGBoost.

Transcripts

hello all my name is krishna welcome to

my youtube channel so guys today in this

particular video we are going to discuss

about xg boost regressor we'll try to

understand how the decision tree

is actually created in xgboost and apart

from that we'll also try to see

the maps formula that are actually

involved in xg boost now this will be an

xg boost regression in-depth intuition

my previous video i had already covered

with respects to hdbush classifier

if you have not seen that guys please go

ahead and see that again the link of

that particular video will be given in

the description

okay now to begin with what i'm going to

do is that again if you don't know about

xgboost it is an ensemble technique it

uses boosting technique

and there are many other algorithms in

boosting technique like

boost gradient boosting extreme gradient

boosting i've covered all these three

and again there are some more boosting

techniques which i'm going to cover in

the upcoming sessions

so to begin with i'm going to actually

take this simple problem statement

this paper i have actually done all the

computation and

suppose if i miss out any calculation

i'll just verify it from here okay

so in this particular problem statement

i have three features

like experience gap and salary

so this basically says that a person if

he's having an experience of two years

and suppose if he has gap

gap is basically a categorical feature

if he has a gap the salary will be

somewhere around 40k

okay it may be in dollars then 2.5 yes

41k if he does not have gap usually

based on experience the salary will

become more

okay so this is the complete data set i

have okay

if you remember if you have gone through

my xg boost classifier

you know there i've actually shown you

how to construct the decision tree

similarly i'll try to show you how you

can construct a decision entry in exibus

regressor

so let's begin now over here always

remember

as in xgboost what we do is that we

create sequential decision trees

so first of all we'll try to create a

base model this base model

will actually give you the output what

kind of output it will give

so based on this average salary suppose

uh by default you know the first base

model will take the average of all this

salary

40k 41k 52k 60k and 62k

if i calculate the average of this the

average salary will be somewhere on 51k

okay then based on this 51k i will try

to find out the residual

okay this will be my residual one

because i'm finding out for the first

residual

and if i whenever i talk about boosting

techniques guys the decision tree gets

trained

based on this particular residual values

so i'll try to subtract 40 k

minus 51k so this will be nothing but 9k

sorry minus 9k then if i sorry it should

not be 9

minus 9 but instead it should be minus

11k

right if i subtract 41 with 51 it should

be minus 10

right if i subtract 52 with 51 it should

be 1.

if i subtract 60 with 51 it should be 9

and if i subtract 62 uh with 51

then at that particular point of time it

should be actually

51 11 11 1162 right it should be 11

okay now these are all my values with

respect to residual ones

let me consider guys one thing let me

just make a small change over here

instead of writing 41k

i will try to write 42k okay

just a small change this just to make my

calculation easier

but again it will not matter if you also

write 41k

now if i try to find out the difference

this will be somewhere around

9k just to make my calculation easier i

have just written it as 40k

now what we will do the xg boost

regressor we have created the base model

the base model output is 51k based on

that we have got the residuals residual

basically means error

right now in the first decision tree

that is basically getting created

we are going to take this independent

feature experience gap and salary

sorry not salary experience gap and

residual

so first of all we will try to take the

root node we will try to see in which

road node we will try to divide

okay so suppose if i take experience

now in experience okay i know all my

output values what are my output values

it is minus 11k then it is minus 9

then it is 1 then 9 and 11

right i have this and remember

experience is a continuous feature right

it is not a category feature it is a

continuous feature two two point five

three four four point five

so in a continuous feature how a

decision tree is basically constructed

suppose

every time remember in extreme boost we

create a binary trees only

so here i will try to create a binary

tree

the first tree over here i'll say that

the condition will be less than or equal

to the first record that is 2

okay then in my next record i will say

this will be greater than

2. okay so i have actually taken this it

will be less than or equal to 2 it will

be greater than 2

that basically means the first record

will go over here remaining all the

records will go in this side

right now if i try to get all the values

over here

right what will be the values if i have

less than or equal to

2 that is only this one residual so here

i will be getting minus 11

and remaining or i will be getting minus

9 1

9 comma 11. so all these values will be

coming over here which is greater than 2

pretty much simple pretty much easy okay

this is one way

you can also take like this first of all

you can take first two records you can

calculate the average

then less than or equal to average all

the records you put it on the left hand

side

otherwise you put it on the right hand

side but here what i've done is that

i've taken the first record i've written

greater than less than or equal to two

made it as one branch the other branch

will be this now this is the first step

now in the second step we basically

calculate

something called as similarity weight

now if you remember in xd boost

classifier

the similarity weight was defined as

summation of residual square

in exhibit classifier again i'm telling

you guys classifier

summation of residual square summation

of probability

minus 1 minus probability and this

probability used to be 0.5

now in case of sg bush regressor this

formula will change little bit

okay here we'll basically say that

number of residuals number of residuals

plus a parameter hyper parameter which

is called as lambda

okay this lambda value will definitely

if we increase the lambda value this

will decrease the

similarity weight in short okay so this

can be treated as a hyper parameter

so let me go ahead and let me start

computing the similarity weight

in exhibit regressor also we create we

calculate the similarity weight

now suppose for this we'll try to

calculate the similarity weight

because i need to basically understand

if i am taking experience as my root

node how do i have to split

right now i've just taken the first

record in the left hand side and

remaining greater than 2 in the right

hand side

right whether this record is the best

record to split

right for that we'll calculate the

similarity to g weight after that we'll

calculate the information gain

or we'll say all as gain okay so here

we'll try to calculate the similarity

weight okay so here some residual square

i have only one residual so this will

become 121

minus 11 is nothing minus 11 square is

nothing but 121

number of residual is again 1 plus in

this particular case let me consider

that i am going to take lambda as 1

so if i try to write 121 divided by 2

this would be nothing but

six zero and then uh five zero 0.5 so my

similarity weight in this case is 65.5

so i've calculated

it i'll write it over here so my

similarity weight

is 65.5 remember my lambda is equal to

1.

now similarly i will try to calculate

the similarity weight for

this how will i calculate i'll take all

the residual

summation of this minus 1 9 plus 1

plus 9 plus 11 whole square

divided by how many numbers are there it

is basically 4

4 plus 1 right now if i try to compute

this

right and this 9 and this 9 will get

cancelled 12 12 is nothing but 144

divided by 5 right so if i try to do

this

ok how many records i will be getting

five ones are five twos are ten

then five eights are 40 88 28.5

so i will get the sims this similarity

weight as 28.5

if there is little bit mistake don't

worry okay just calculate the

similarities weight will be 28.5

if it is getting coming some other value

you can let me know in the description

so i'm going to just going to write 28.5

so here i'm going to write 28.5

now the third thing that i'm going to do

is basically

i also have to compute the similarity

weight of the root

right this root so here i will be taking

again

minus 11 minus 9 9 11 this will get

cancelled

only 1 will be remaining so this will be

1 square divided by how many numbers i

have 5

5 plus 1 so this is nothing but 1 by 6

1 by 6 is nothing but if i say that it

is somewhere around

0.1 um 0.16

okay so i'm going to take this 0.16 so

i will write over here my similarity

weight

is nothing but 0.16

now if i really want to calculate the

information gain or again i'll say

then we have to take this left

similarity weight

add it with right similarity weight

subtract with the root similarity weight

okay so here if i try to calculate this

is

20 um suppose 5 5 1 13 14

14 and 94 minus 0.16

okay and here if i try to subtract 2094

minus

0.16 you know so this will be somewhere

around four

eight three ninety three point eight

four

ninety three point eight four so the

total gain

that i am getting from this split is

basically 93.84

so here i'm just going to note down this

one and i'll say that the total gain

that i'm going to get is

93.84 okay so this is my

gain now similarly what i'll do

i have done this now i'll go with the

next split in next plate i'll say that

okay

instead of making see guys with one

split we got the gain 98.4 so let me

just write it down somewhere here

okay so for the first record split i

got somewhere around 98.34

okay so i hope i'm writing it right okay

now

in my second split what i'm going to do

is that i'm going to just drop this

and now i'll go to my second record

i'll go to my second record now second

record is nothing but 2.5 so here i'll

say that

less than or equal to 2.5 and greater

than

2.5 now when i do this less than or

equal to 2.5 how many records are there

one 2 so here i am going to write minus

11 minus 9

okay here again there will be 3 records

1 9 11

okay 1 9 11 now when we try to calculate

the similarity weight again over here it

will be minus 11 minus 9 whole square

divided by 2 which is nothing but 400

sorry 2 plus 1 right because alpha value

is also there

so 400 divided by 3 this will be

somewhere around

3 1 are three threes or three threes are

0.33 so it will be nothing but 133.33 so

this similarity weight over here

will be 133.33

okay then for this similarity weight

again i will try to

add up all these things 1 plus 9 is 10

10 plus 11 is 21

21 whole square will be 441 441 divided

by 3 plus 1 which is nothing but

4 okay so if i write 441 divided by 4

it will be nothing but 1 1 0

or 0.25 so 1 1 0.25 so i'm going to take

this similarity weight as

1 1 0.25

okay now i'll try to i know my root

similarity

now if i really want to find out the

gain it will be 133.33

plus 110.25 minus

0.16 okay so once i do this

probably how much it will come so let me

add it for you

133.33 110.25

okay so this will be 85.34 143.58

and if i try to subtract with 1 6

this will be nothing but 4 143.42

so here the total gain that i will be

getting is

143.42 and obviously this gain is

better than this gain so i'll definitely

not do the split from here

i'll do the split from here and

similarly i'll try to compare with all

the splits

and suppose i find out that i have to do

the split from this record

i will take this and i will try to

create it now once i decided okay this

is the split that i have to use

after this what i'll do is that i will

go with the next category feature

now suppose over here i go with gap as

yes and no

in gap if it is yes suppose this is yes

right and this is no in yes because both

these values are in yes so this becomes

the root node so i will not go with this

splitting

right then next with this splitting i'll

go with gap

again i'll write yes or no so how many

in this records which is greater than

2.5 there are two nodes

two nodes over here right two nodes and

these are nothing but one and nine

so i'll write it as one nine nine here i

will write it as

um remaining one is eleven then again

i'll try to calculate the similarity

score

i'll try to calculate the gain okay now

suppose if i go with this split right

now

okay and then i'll try to compare like

whichever will be having the highest

gain i'll be taking that

now suppose this is the overall tree

structure that has been created for the

first tree

how will i calculate the output now

suppose in this particular path if it is

going the output over here

will be the average of this value so

minus 11 minus 9 is nothing but 20

20 divided by 2 will be nothing but 10

so this output of this node

will be actually 20. so here i'm going

to write it as

output as 20 okay

in this particular output since this is

a single node it will be 11

in this it will be the 5 because this

average is nothing but 5

right when i have done this when i have

done this now suppose

i take this record and i try to

calculate what will be the output now

right i know that first

after this base model then will

concatenate basically will

then pass through this tree only after

the base model

so as soon as i pass this record suppose

i am passing this first record

first of all it will go to the base

model the base model will be giving me

the value as 51

because this is 51k then suppose i

consider my learning rate parameter

that is alpha is 0.5 okay now this 0.5

multiplied by the output of this tree

now suppose this is 2 2 basically means

will come here

right this path will be taken here and

once we find out the output is 20

so here i will write it as 20 right

this is with respect to one decision

tree like this i can create any number

of decision trees like i can create

with the help of gap as my root node

with the help of experience on some

other records

right i can create multiple decision

tree so this will be my

alpha t one then again i can have alpha

this can be alpha one t one this can be

alpha two t

2 alpha 3 t 3 like this i can have any

number of trees

now in this particular case i have since

i have constructed only one decision

tree

i am just going to use this so what will

be the value 51 plus

0.5 into 2 is nothing but 10.

sorry the output uh sorry this output

will be

i'm extremely sorry guys this output

will be minus

minus 20 by 2 minus 10 okay

i made one mistake the average output

for this will be minus 10

okay minus 10 so here i will write it as

0.5

multiplied by minus 10 right

when i subtract it it will be nothing

but minus 0.5

sorry minus minus 5 okay

this will be minus 5 so here my total

value will be 46 that basically means

once i pass this particular output my

real output now

my real output now will be 46

then again if i try to pass with respect

to 42 k 42 to k will again pass in this

path

again this will also become 46 right

plus 0.5

minus multiplied by minus 10 similarly

we have to pass all these particular

records

calculate our value suppose this value

is somewhere around for this value let

me compute okay what will be this value

okay see three is basically passing

through this road

node right now negative is no no is

basically getting passed over here

the output is 5 so i will write 51

k plus 0.5 which is my learning rate

multiplied by 5

okay and here i can write 51 plus

0.25 right five five two sorry it should

not be 0.25 it should be

2.5 2.5 so here i will be having

53.5 so this will be my output over here

right and similarly i will be trying to

write all these values i'm just going to

rub this guys

i'm just going to rub this okay

similarly i'm going to find out like

this so it'll be here will be 62

and here probably will be 63. then again

i'll try to calculate my residual 2

some value will be again coming now in

my next iteration i'll create one more

tree

where i'll be taking this two input

features and this will be my dependent

feature and again i'll be trying to

create a decision tree

this will be my second decision tree my

first decision tree is basically getting

created here

i have this particular output like this

over here and after that this will be my

second decision tree after this i will

try to add it again my formula will be

like what

my base model output right plus

alpha 1 t 1 plus alpha 2

t 2 like this plus alpha and

t n and like this will be my complete

x j boost output that it will be coming

up you know

and that is the how we have to say there

is also one more parameter which is

called as gamma

gamma basically says that suppose if i

say gamma is 140

or let me just write it as okay gamma is

somewhere around 150.5

and suppose after this split the

information gain i got it as 140.

if i try to subtract 150 with 140 uh if

i

try to subtract this 140 with 150.5

if it is negative value then we can

postpone this

we can prune basically we can cut that

particular tree if it is a positive

value

it will be no we should not prune it and

again this is the kind of hyper

parameter

that we can set for doing the post

pruning technique only when it is trying

to get over fitted

but most of the scenarios some value of

alpha or gamma will be actually set

the default value you can again see in

the scale who are there also

in that particular library some default

value will be getting set

so i hope you understood how xgboost

aggressor work

please do subscribe the channel if you

have not already subscribe i'll see you

in the next video

have a great day ahead thank you bye bye