Andrew Ng Naive Bayes Generative Learning Algorithms
Summary
TLDRThis video delves into generative learning algorithms, contrasting them with discriminative ones like logistic regression. It highlights the simplicity, quick implementation, and scalability of generative algorithms, especially Naive Bayes, which is ideal for a 'quick and dirty' approach to machine learning problems. The script explains the concepts of discriminative learning, which tries to find a boundary to separate classes, and generative learning, which models each class individually. It also covers the mathematical foundation of generative algorithms, including Bayes' rule, and provides a numerical example to illustrate how these models make predictions.
Takeaways
- 📚 The video discusses different types of learning algorithms beyond linear and logistic regression, focusing on generative learning algorithms.
- 🔍 Generative learning algorithms are advantageous when there are few training examples and are simple, quick to implement, and efficient, even for large datasets.
- 🛠️ The philosophy of implementing a 'quick and dirty' solution and then iterating to improve is highlighted as a practical approach in machine learning.
- 🤖 Most learning algorithms are categorized into discriminative learning algorithms and generative learning algorithms, with the latter being the focus of the video.
- 🔍 Discriminative learning algorithms, such as logistic regression, try to find a boundary to separate different classes, while generative learning algorithms model each class separately.
- 📈 The video provides an intuitive example of how a generative learning algorithm might classify new data points by comparing them to models of 'benign' and 'malignant' tumors.
- 🧠 Discriminative learning algorithms estimate the probability of Y given X directly, whereas generative learning algorithms learn the probability of X given Y and the class prior (P of Y).
- 📝 Bayes' rule is integral to generative learning algorithms, allowing the computation of the posterior probability P(Y=1|X) for classification.
- 📉 The video explains the process of calculating the posterior probability using the terms learned from the generative model.
- 📝 Modeling P(X|Y) and P(Y) are key decisions in building a generative model, which will be further explored in the development of the naive Bayes algorithm in subsequent videos.
- 🔑 The naive Bayes algorithm is introduced as an example of a generative learning algorithm that simplifies the modeling of P(X|Y) and P(Y).
Q & A
What is the main topic discussed in this video script?
-The main topic discussed in this video script is generative learning algorithms, with a focus on their advantages and how they differ from discriminative learning algorithms.
Why might generative learning algorithms be preferred when there are very few training examples?
-Generative learning algorithms may be preferred when there are very few training examples because they can work better with limited data and are simple, quick to implement, and efficient, which allows them to scale easily even to massive datasets.
What is the philosophy of implementing something 'quick and dirty' and then iterating to improve it?
-The philosophy of implementing something 'quick and dirty' is about starting with a simple solution and then refining it through iteration. This approach can be particularly useful in machine learning when you want to quickly get something working and then improve upon it based on feedback and performance.
What are the two main categories of learning algorithms discussed in the script?
-The two main categories of learning algorithms discussed in the script are discriminative learning algorithms and generative learning algorithms.
How does a discriminative learning algorithm like logistic regression work?
-A discriminative learning algorithm like logistic regression works by trying to find a decision boundary that separates different classes. It does this by fitting a model that estimates the probability of the target variable given the input features.
What is the difference between discriminative and generative learning algorithms in terms of what they model?
-Discriminative learning algorithms model the probability of the target variable given the input features (P(Y|X)), while generative learning algorithms model the input features given the target variable (P(X|Y)) and also learn the prior probabilities of the target variable (P(Y)).
How does a generative learning algorithm make a classification prediction?
-A generative learning algorithm makes a classification prediction by building models for each class and then comparing a new example to these models to determine which class it looks more like, based on the computed probabilities.
What is Bayes' rule and how is it used in the context of generative learning algorithms?
-Bayes' rule is a fundamental theorem in probability that describes the probability of an event based on prior knowledge of conditions that might be related to the event. In the context of generative learning algorithms, Bayes' rule is used to compute the posterior probability P(Y|X), which is used for making predictions.
What are the key terms a generative learning algorithm needs to model?
-The key terms a generative learning algorithm needs to model are P(X|Y), which is the probability of the input features given the target variable, and P(Y), which is the prior probability of the target variable.
Can you provide an example of how a generative model computes P(Y=1|X) for a new test example?
-Sure, given a new test example X, a generative model computes P(Y=1|X) by using the values of P(X|Y=1), P(Y=1), P(X|Y=0), and P(Y=0). It applies Bayes' rule to calculate the posterior probability, which is then used for classification.
What is the naive Bayes algorithm and how does it relate to the discussion in the script?
-The naive Bayes algorithm is a specific type of generative learning algorithm that makes a strong (naive) assumption of feature independence given the target variable. The script discusses the naive Bayes algorithm as an example of how to model P(X|Y) and P(Y) in a generative learning context.
Outlines
📚 Introduction to Generative Learning Algorithms
This paragraph introduces the concept of generative learning algorithms, contrasting them with discriminative learning algorithms like logistic regression. It highlights the advantages of generative algorithms, such as their efficiency, simplicity, and quick implementation, which make them ideal for situations with limited training examples. The paragraph also touches on the philosophy of implementing a 'quick and dirty' solution and iterating for improvement, using the naive Bayes algorithm as an example of a simple yet effective generative model. The distinction between discriminative and generative learning is further clarified by explaining how discriminative algorithms, like logistic regression, aim to find a boundary to separate data, whereas generative algorithms build models for each class separately and then make predictions by comparing new examples to these models.
🔍 Deep Dive into Generative Learning: Naive Bayes
The second paragraph delves deeper into the workings of generative learning algorithms, focusing on the naive Bayes model. It explains the process of learning the probability of features given the class (P(X|Y)) and the class prior probability (P(Y)). The paragraph illustrates how these probabilities are used in conjunction with Bayes' rule to compute the posterior probability (P(Y|X)) for classification. The explanation includes a step-by-step guide on how to calculate this probability using the learned model parameters. The importance of modeling P(X|Y) and P(Y) accurately is emphasized, as these are the core components of a generative model. The paragraph concludes by setting the stage for further exploration of the naive Bayes algorithm in subsequent videos.
📉 Numerical Example of a Generative Model in Action
The final paragraph provides a numerical example to demonstrate how a generative model, specifically the naive Bayes algorithm, can be applied to make predictions. It outlines the process of using the model's learned probabilities for P(X|Y) and P(Y) to calculate the posterior probability P(Y=1|X) for a new test example. The example includes a step-by-step calculation that simplifies the computation by taking advantage of equal prior probabilities for the classes. The paragraph concludes by emphasizing the importance of choosing the right modeling approach for P(X|Y) and P(Y), which will be further discussed in upcoming videos.
Mindmap
Keywords
💡Learning Algorithm
💡Generative Learning Algorithms
💡Naive Bayes
💡Discriminative Learning Algorithms
💡Logistic Regression
💡Gradient Descent
💡Bayes' Rule
💡Conditional Probability
💡Class Prior
💡Feature Space
💡Modeling
Highlights
Introduction to generative learning algorithms as an alternative to linear and logistic regression.
Generative learning algorithms are advantageous when there are few training examples and are simple to implement and run.
Generative algorithms are efficient and can easily scale to massive datasets.
Naive Bayes as a quick and dirty implementation for initial machine learning solutions.
Philosophy of implementing a simple model first and iterating for improvement.
Discriminative learning algorithms versus generative learning algorithms.
Discriminative algorithms like logistic regression search for a boundary to separate classes.
Generative learning focuses on building models for each class separately.
Explanation of how a generative model classifies new examples based on comparison to built models.
Formal definition of discriminative learning algorithms learning P(Y|X) directly.
Formal definition of generative learning algorithms learning P(X|Y) and P(Y).
Use of Bayes' rule to compute P(Y=1|X) for classification predictions.
Calculation of P(X) using the joint distribution of X and Y.
The importance of modeling P(X|Y) and P(Y) in a generative learning algorithm.
A numerical example demonstrating the computation of P(Y=1|X) using a generative model.
The key decision in building a generative model is how to model P(X|Y) and P(Y).
Introduction to the development of the Naive Bayes algorithm in upcoming videos.
Transcripts
in this video we're going to talk about
the different type of learning algorithm
than the one so far like linear
regression and logistic regression in
particular we want to talk about
generative learning algorithms
generative learning algorithms may work
better if we have very few training
examples and there are a second
advantage is that they're very simple
and very quick to implement and also
very quick to run and because they're so
efficient they often scale very easily
even to massive datasets
moreover turns out sometimes if you're
facing some machine learning problem you
just want to get something to work on
well the thing the best thing to do
sometimes isn't to overthink or to
over-design the algorithm but rather to
implement something quick and dirty and
then to iterate and to improve the
algorithm from there I'll say more about
this later of philosophy of implementing
something quick and dirty and iterating
and improving but because the algorithm
we're going to talk about naive Bayes is
so simple to implement and because it
runs so quickly scales even well to
massive datasets this generative
learning algorithm naive Bayes is often
a good candidate for a quick and dirty
implementation of something it turns out
most learning algorithms categorize into
two classes the first of them is what we
call discriminative learning algorithms
and the second is generative learning
algorithms and discriminative learning
algorithms is what we've seen so far
such as logistic regression which we may
fit with gradient descent right then
I'll say more what general I'll say
later what generative learning hours are
so here's the intuition given a training
set
what a discriminative learning algorithm
does by logistic regression is maybe try
to search for a straight line to
separate the two concepts right in
particular it turns out if you say
initialize logistic regressions
parameters randomly maybe initially you
end
with a vision bounty like that well
that's not such a good one so when you
start to do gradient descent with my
discretion
maybe one after one innovation you get
that design boundary of the two
iterations you get that not there bunch
of iterations you get that decision
boundary weave separates the data and so
there's a sense that logistic regression
is trying to search for a straight line
to separate the two courses and so you
know where where once again if these are
what malignant tumors and these are
benign humans we're basically looking at
all of our data and trying to find a
straight line that separates the
malignant humans from the benign tumors
that's what the discriminative learning
algorithm does in contrast this is what
a generative learning algorithm does
which is rather than looking at both
classes and trying to find something
separate them
we'll say well let's just focus on the
benign tumors to start right these are
the benign tumors and you know looking
only at these blue circles let's build a
model for what benign tumors look like
right so let's say you know build a
model and say well the most benign
tumors tend to lie in this region of
space and then we'll turn our attention
and then having built in a model of what
benign tumors look like will then turn
our attention to the malignant tumors
and now we just focus our attention on
the malignant tumors and only look at
the malignant tumors and ask you know
try to build a model of what the
malignant tumors look like it looks
looks like most of malignant tumors live
in that region of space now let me get
rid of the training set now if a new
patient comes in and you know if you
plot their features x1 x2 if it lies
there say you say oh look this black dot
it looks looks like as well though it
looks like the benign tumors I've seen
so classified this is benign whereas in
your patient whose features live there
you say oh look this looks like this
line in my red oval and a red circle
this looks like the malignant tumors
I've seen before so I'm going to
classify that example
malignant in other words well what
genitive album does is it builds a model
of each of the two classes and then mix
classification predictions based on
looking at your example and comparing it
to your two models to see whether it
looks like more like your benign or like
your malignant tumour model let's
formalize this notion of discriminative
and generative learning algorithms what
a discriminative learning algorithm does
is it learns P of Y given X directly and
this is you know the probability of Y
given X and so the justic regression
right uses the sigmoid of logistic
function to estimate this directly and I
should say there are also some
discriminative learning algorithms that
try to learn you know hypotheses that
outputs a value 0 or 1 directly or so
for example if you were to take logistic
regression and threshold this output 0.5
so the hypothesis outputs either 0 1
that would oppose a classification
prediction 0 1 directly that would be
another this ruins an album but the
intuition is yeah we so I've tried to
estimate where Y is directly as a
function of X we try to estimate the
probability of Y directly as a function
of X in contrast what a generative
learning algorithm does is instead
learns P of X given Y and it turns out
that it also learns P of Y if with the
first term is this is more important
maybe interesting one just say what that
means in our earlier example Y the class
label indicates whether a tumor is
malignant or benign and X are the
features right and so what this
algorithm is is doing is learning well
what are the features like conditioned
on a tumor being
lignin say so say what what what do
malignant tumors look like what are the
features like condition on y equals one
or is asking what are the features like
conditions on y equals zero so in other
words what do benign breast cancer
tumors look like okay
and then the other term on P of Y this
is called the class prior and this just
the you know a priori oh is the prior
probability of y equals 0 or y equals 1
in other words think of it as if a
patient walks into your office and you
don't know any features about them you
haven't measured anything yet you have
no idea right what are the odds did the
next patient to walk that your office
won't be will have a malignant versus
benign tumor or for a different example
if you're doing your spam classification
you know this is well not having seen
the next email you get tomorrow yet what
are the odds that the next piece of
email you get will be spam or non-spam
that's what the cost prior is now
modeling these two terms P of X given Y
and P of Y are the two ketones we'll
need to model in a generative learning
algorithm so suppose that we have come
up with a way to model P of x given Y
and P of Y it turns out that given the
new example X we can then compute P of y
equals 1 given X as follows in
particular this is what we need to
compute if we want to make a prediction
on a new test example X right so this
thing on the left is equal to this one
of a P of X and this is owned by Bayes
rule depending on how much probability
remember this rule here is called Bayes
rule where so P of y equals when you're
like this P of X given Y times P of Y
divided by P of X in case this doesn't
look familiar if you multiply both sides
by P of X then
no you know this becomes so the rule of
conditional probability but hopefully
maybe remember what Bayes rule is and
then let's see and howdy Callum so these
two terms in the numerator P of x given
Y and P of Y and we can get directly
from our model right because our model
tries to your estimate P of X in the
line P of Y and the denominator well
turns out you can compute that too so by
the definition of them how you
marginalize probability distributions P
of X is sum of Y of the Joint
Distribution between x and y and the
Joint Distribution and this is therefore
equal to we can also write this out as P
of x given y equals 0 oops usually P of
y equals 1 times P of y equals 1 plus P
of x given y equals 0 times P of y
equals 0 ok and so you know this is a
through some manipulations of
probability you can show that this is
equal to this which is therefore equal
to that and the reason I did this of
course is because each of these terms P
of x given Y and also these terms P of Y
but both of these are the terms that our
model gives us and so you can you know
put plug these into these four terms as
well in order to compute P of X and
using that you can then compute P of y
equals 1 given X and therefore make a
prediction on make a classification
prediction on what Y will be given X
finally to wrap up this video let's work
through I'd like to ask you to work
through a numerical example supposed to
train a generative model and so if we've
trained a generative model what that
really means is what build models of P
of X given Y and P of Y and suppose we
now going to new test example X let's
say our model tells us you know these
things P of X given
zero y equals one and so on P of Y are
equal to these quantities one is P of y
equals one conditions on X hopefully you
got that this is a right answer and just
very quickly set through the calculation
P of y equals 1 given X by the rule we
worked on just now it is equal to this
times P of 1 plus 1 divided by P of x
given y equals 1 times P of y equals 1
plus P of x given y equals 0 times P of
y equals 0 but because in our example P
of y equals 1 equals P of y equals 0
equals 0.5 you know we can cancel out
these terms in the numerator and
denominator because all three of those
one thing is I just 0.5 and so this
leaves us with the numerator P of x
given y equals 1 is 0.03 divided by and
then the other terms are go point O 3
plus this term plus 0.01 which is just
0.75 and this shows how using these
quantities learn from a generative model
we can then compute P of Y given X and
of course when deciding in building the
generative model the key decision is how
do you model P of X given Y and how do
you model P of Y and in the next few
videos we'll develop the naive Bayes
algorithm which is one way of modeling
these two terms
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