Machine Learning Lecture 11 | Multivariate Probability Models 2 [D]
▲ 6 r/ChatGPT+1 crossposts

Machine Learning Lecture 11 | Multivariate Probability Models 2 [D]

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

Hope this adds value to all the beginners trying to understand the mathematical foundations of Machine Learning.

youtu.be
u/Negative_War_65 — 15 hours ago

Linear Gaussian Systems in Machine Learning!

Free Lecture content on Probabilistic Machine Learning Series(Work in Progress!)
Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

Link in shared in comments.

u/Negative_War_65 — 4 days ago

Linear Gaussian Systems in Probabilistic Machine Learning!

Free lectures on Probabilistic Machine Learning Series!

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

Link: https://youtu.be/ViVBWYyL\_8c?si=QppPjeRJbQvu6xYU

u/Negative_War_65 — 4 days ago

Linear Gaussian Systems in Data Science/Machine Learning!

Free Lectures!

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

Link(Free lectures): https://youtu.be/ViVBWYyL\_8c?si=QppPjeRJbQvu6xYU

u/Negative_War_65 — 4 days ago

Linear Gaussian Systems in Machine Learning!

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

These lectures are free BTW.
Link: https://youtu.be/ViVBWYyL\_8c?si=QppPjeRJbQvu6xYU

u/Negative_War_65 — 4 days ago

Linear Gaussian Systems In Machine Learning.

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

Hope they can add good ML Funda’s to your knowledge base, and they are free lectures BTW.

Link: https://youtu.be/ViVBWYyL\_8c?si=QppPjeRJbQvu6xYU

u/Negative_War_65 — 4 days ago

Linear Gaussian Systems in Machine Learning.

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.
Link is shared in the comments, for interested learners. These are FREE lectures BTW

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

u/Negative_War_65 — 4 days ago

Linear Gaussian Systems in Probabilistic Machine Learning [D]

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

These are FREE LECTURES and they will surely add great knowledge value to your ML fundamentals.

Link is shared in the comments

u/Negative_War_65 — 4 days ago

Linear Gaussian Systems!

Dear Folks, sharing Lecture 11 of our Machine Learning series, and this is a bit special to me, because today I cover Conditionals of Multivariate Normals, and Linear Gaussian Systems.

When I first started studying these topics, it took me days to understand. But today I have made a lecture on it, so if you understand the concepts, it’s really good, for I have tried to leave no stone unturned while explaining, deriving the equations, doing it step by step, and tried giving all intuitions I could.

The Gaussian distribution is ubiquitous and important in studying topics as state estimation, tracking, and examples include Autonomous vehicles, robotics and navigation, time-series forecasting, aerospace etc. The breakdown is as:

0-10: Marginals and Conditionals of Multivariate Normals, Matrix Inversion Rules
10-27: Derivation of the Matrix Inverse Rule: Schur Complements(We need this to derive equations for Multivariate Gaussian)
27-45: Deriving the Conditionals of MVN
45-1:03: Example and Imputation of Missing Values
1:03-1:47: Linear Gaussian Systems, and full derivation of Bayes Rule for Gaussians.
1:47-2:19: Inferring an Unknown Scalar and Sequential Updates.
2:19-2:34: Inferring an Unknown vector.
2:37-End: Sensor Fusion.

This lecture is relatively bigger since the concepts are interrelated here. But do not worry, I have tried to explain in the best way I could, and hope it helps you well in your journey to becoming a Machine learning engineer.

These are FREE Lectures, and they can definitely add good knowledge to your ML fundamentals.

Link: https://youtu.be/ViVBWYyL\_8c?si=QppPjeRJbQvu6xYU

u/Negative_War_65 — 4 days ago

Multivariate Probability Models in Machine Learning

Hello Folks, we start our discussion on Lecture 10 of Probabilistic Machine Learning, now starting with Probability Multivariate Models.

Univariate models are toy cases, in real life, ML models are multivariate.

To understand dependence of more than one variables on each other we study ideas as Covariance, Correlations, we delve ourselves into the interesting concept of Simpson’s Paradox, with an example. We define the Multivariate Gaussian distribution, understand the level sets(curves) that we see in our computers while plotting, and gain insights into the geometric shape of the Gaussian density by using “Mahalanobis distance”.

Mathematical foundations are extremely important, in that they make an ML engineer, data scientist stand out. These concepts are becoming so ubiquitous today, that folks from all backgrounds of engineering are interested in the mathematics behind these algorithms.

I hope the learning community finds it helpful, and suggestions are always welcomed.

Link (These are FREE BTW): https://youtu.be/nEhaQlKRAGY?si=OapJH6jMET\_24lYp

u/Negative_War_65 — 6 days ago

Multivariate Probability Models in Machine Learning

Hello Folks, we start our discussion on Lecture 10 of Probabilistic Machine Learning, now starting with Probability Multivariate Models.

Univariate models are toy cases, in real life, ML models are multivariate.

To understand dependence of more than one variables on each other we study ideas as Covariance, Correlations, we delve ourselves into the interesting concept of Simpson’s Paradox, with an example. We define the Multivariate Gaussian distribution, understand the level sets(curves) that we see in our computers while plotting, and gain insights into the geometric shape of the Gaussian density by using “Mahalanobis distance”.

Mathematical foundations are extremely important, in that they make an ML engineer, data scientist stand out. These concepts are becoming so ubiquitous today, that folks from all backgrounds of engineering are interested in the mathematics behind these algorithms.

I hope the learning community finds it helpful, and suggestions are always welcomed.

Link(Lectures are FREE BTW): https://youtu.be/nEhaQlKRAGY?si=OapJH6jMET\_24lYp

u/Negative_War_65 — 6 days ago

Multivariate Probability Models in Machine Learning [D]

Hello Folks, we start our discussion on Lecture 10 of Probabilistic Machine Learning, now starting with Probability Multivariate Models.

Univariate models are toy cases, in real life, ML models are multivariate.

To understand dependence of more than one variables on each other we study ideas as Covariance, Correlations, we delve ourselves into the interesting concept of Simpson’s Paradox, with an example. We define the Multivariate Gaussian distribution, understand the level sets(curves) that we see in our computers while plotting, and gain insights into the geometric shape of the Gaussian density by using “Mahalanobis distance”.

Mathematical foundations are extremely important, in that they make an ML engineer, data scientist stand out. These concepts are becoming so ubiquitous today, that folks from all backgrounds of engineering are interested in the mathematics behind these algorithms.

I hope the learning community finds it helpful, and suggestions are always welcomed.

These are FREE lectures.
Link : https://youtu.be/nEhaQlKRAGY?si=cI6YXnek5USKdKHS

u/Negative_War_65 — 6 days ago

Multivariate Probability Models in Machine Learning [D]

Hello Folks, we start our discussion on Lecture 10 of Probabilistic Machine Learning, now starting with Probability Multivariate Models.

Univariate models are toy cases, in real life, ML models are multivariate.

To understand dependence of more than one variables on each other we study ideas as Covariance, Correlations, we delve ourselves into the interesting concept of Simpson’s Paradox, with an example. We define the Multivariate Gaussian distribution, understand the level sets(curves) that we see in our computers while plotting, and gain insights into the geometric shape of the Gaussian density by using “Mahalanobis distance”.

Mathematical foundations are extremely important, in that they make an ML engineer, data scientist stand out. These concepts are becoming so ubiquitous today, that folks from all backgrounds of engineering are interested in the mathematics behind these algorithms.

I hope the learning community finds it helpful, and suggestions are always welcomed.

Link shared in the comments.

u/Negative_War_65 — 6 days ago

ML Intro Refresher

Hello Folks,

Machine Learning is best understood when approached from a probabilistic perspective, because probabilities are the optimal approach to decision making under uncertainty, and they are widely used in all areas of engineering as well.

Supervised learning, the learning from labelled examples, is ubiquitous today. The Iris dataset was one very simple example from which this concept, EDA, and classifier learning can be understood.

We always end up minimising some loss function in Machine Learning. An approach called Empirical risk minimisation. We also capture uncertainties in ML(both from data and model), and hence we attach a probabilistic perspective to it. Then Maximum likelihood estimation is the technique employed to fit machine learning models.

I explain these concepts with intuition and in detail in my free online video link: https://youtu.be/kMkCOrp8te8?
si=nCRXZnvlj49Gevk-

Edit: I hope giving proper context would make learners more interested in learning.

Note: The contents shared are FREE, and hope they will offer intellectual value to learners.

u/Negative_War_65 — 9 days ago

Machine Learning Concepts

Dear Folks, I have created multiple content on Machine Learning(work in progress). I am a data scientist and a post grad degree holder in AI/ML from IIT. To help the machine learning community with important Machine Learning Concepts, I have created multiple long form videos, and structured topicwise digestible contents structured as playlists for learning.

If you go through the first two playlists:

Introductory Machine Learning Concepts
Probability Foundations: Univariate Models

You might find helpful content, I have tried explaining with intuitions, derivations, and this is work in progress. For code implementations, scikit learn website has great content on them as well. In total they have 60+ topicwise videos so far, and I think they have the potential to help folks a lot in starting with concepts, or getting with mathematical concepts, or whether you are preparing for an AI/ML/Data job interviews etc.

When I sat for my interviews, I was grilled on my project, but majority of questions from my project tested more on foundational concepts and there know how’s.

These are FREE content on youtube.

Link: https://youtube.com/@aayushsugandh4036?si=w8jCGa9gwLXiCyiB

u/Negative_War_65 — 12 days ago

Machine Learning Concepts [D]

Looking for feedback from the Machine Learning Community. Dear Folks, I would be glad if I can get feedback from you all regarding the content?

Dear Folks, I have created multiple content on Machine Learning(work in progress). I am a data scientist and a post grad degree holder in AI/ML. To help the machine learning community with important Machine Learning Concepts, I have created multiple long form videos, and structured topicwise digestible contents structured as playlists for learning.

If you go through the first two playlists:

Introductory Machine Learning Concepts
Probability Foundations: Univariate Models

You might find helpful content, I have tried explaining with intuitions, derivations, and this is work in progress. For code implementations, scikit learn website has great content on them as well. In total they have 60+ topicwise videos so far, and I think they have the potential to help folks a lot in starting with concepts, or getting with mathematical concepts, or whether you are preparing for an AI/ML/Data job interviews etc.

When I sat for my interviews, I was grilled on my project, but majority of questions from my project tested more on foundational concepts and there know how’s.

These are FREE content on youtube.

Link: https://youtube.com/@aayushsugandh4036?si=w5MKORU2fWzLRrAJ

u/Negative_War_65 — 12 days ago

Machine Learning Concepts [D]

Dear Folks, I have created multiple content on Machine Learning(work in progress), and they are free. I am a data scientist and a post grad degree holder in AI/ML. To help the machine learning community with important Machine Learning Concepts, I have created multiple long form videos, and structured topicwise digestible contents structured as playlists for learning.

If you go through the first two playlists:

Introductory Machine Learning Concepts
Probability Foundations: Univariate Models

You might find helpful content, I have tried explaining with intuitions, derivations, and this is work in progress. For code implementations, scikit learn website has great content on them as well. In total they have 60+ topicwise videos so far, and I think they have the potential to help folks a lot in starting with concepts, or getting with mathematical concepts, or whether you are preparing for an AI/ML/Data job interviews etc.

When I sat for my interviews, I was grilled on my project, but majority of questions from my project tested more on foundational concepts and there know how’s.

These are FREE content on youtube, and hope it benefits and helps the ML community.

u/Negative_War_65 — 12 days ago
▲ 36 r/AIMLDiscussion+12 crossposts

Machine Learning Concepts [D]

Dear Folks, I have created multiple content on Machine Learning(work in progress), and they are free. I am a data scientist and a post grad degree holder in AI/ML from IIT. To help the machine learning community with important Machine Learning Concepts, I have created multiple long form videos, and structured topicwise digestible contents structured as playlists for learning.

If you go through the first two playlists:

Introductory Machine Learning Concepts
Probability Foundations: Univariate Models

You might find helpful content, I have tried explaining with intuitions, derivations, and this is work in progress. For code implementations, scikit learn website has great content on them as well. In total they have 60+ topicwise videos so far, and I think they have the potential to help folks a lot in starting with concepts, or getting with mathematical concepts, or whether you are preparing for an AI/ML/Data job interviews etc.

When I sat for my interviews, I was grilled on my project, but majority of questions from my project tested more on foundational concepts and there know how’s.

These are FREE content on youtube. This is for the benefit of the learning community.

Link: https://youtube.com/@aayushsugandh4036?si=w5MKORU2fWzLRrAJ

u/Negative_War_65 — 1 day ago
▲ 309 r/AIMLDiscussion+9 crossposts

Machine Learning Concepts

Dear Folks, I have created multiple content on Machine Learning(work in progress). I am a data scientist and a post grad degree holder in AI/ML. To help the machine learning community with important Machine Learning Concepts, I have created multiple long form videos, and structured topicwise digestible contents structured as playlists for learning.

If you go through the first two playlists:

  1. Introductory Machine Learning Concepts:
  2. Probability Foundations: Univariate Models.

You might find helpful content, I have tried explaining with intuitions, derivations, and this is work in progress. For code implementations, scikit learn website has great content on them as well. In total they have 60+ topicwise videos so far, and I think they have the potential to help folks a lot in starting with concepts, or getting with mathematical concepts, or whether you are preparing for an AI/ML/Data job interviews etc.

When I sat for my interviews, I was grilled on my project, but majority of questions from my project tested more on foundational concepts and there know how’s.

These are FREE content on youtube.

Link : https://youtube.com/@aayushsugandh4036?si=kV-TYjWEKaw00e7-

u/Negative_War_65 — 12 days ago