SlideShare a Scribd company logo
Variational Autoencoders
Generative Models
 They take in data as input and learn to generate new data points from the same
data distribution.
 They learn the hidden representations using unsupervised learning techniques
Variational Autoencoder
 As the name suggests, it is an auto-encoder, which learns attributes from the data
points and represents them in terms of latent variables.
Problems
 How can we make use of the auto-encoder architecture to generate new data points ?
 Assuming we can pass a vector from that learnt latent space to the decoder, how can
guarantee it’s not going to result in a garbage output.
 VAEs address the above problems
1. How do we use the Auto Encoder Architecture for generation ?
So, if we train the Auto encoder network and somehow learn the data distribution of the latent
space, we can then sample from that latent space and pass it down to decoder and generate
data points
But, there is a problem.
2. How can we make sure that if we sample from our latent space, we are going to get new
and meaningful output ?
 VAEs achieve this by constricting the latent space.
 The encoder and decoder parameters are tuned to accommodate for this setup
But,
Calculating Marginal Probability
 If X = (x1, x2, x3) and Z = (z1, z2)
then,
𝑃 𝑍 𝑋 =
𝑃(𝑋|𝑍)∗𝑃(𝑍)
𝑃(𝑋)
Here, the P(X) is very difficult to calculate, especially in higher dimensions.
It takes the form of 𝑧1
𝑧2
𝑃 𝑋1, 𝑋2, 𝑋3, 𝑍1, 𝑍2 𝑑𝑧1 ∗ 𝑑𝑧2 and is intractable.
There are ways to solving this by using,
1. Using Monte Carlo Integration techniques
2. Variational Inference
Variational Inference
As x is already given, log p(x) is a constant.
And KL(q(z) || p(z|x)) is what we wanted to minimize and it is always
>= 0
0 <= p(x) <= 1 and KL >= 0
So, it is equivalent to maximizing the 3rd term.
It is called Variational Lower bound
This is nothing but,
Expectation of p(x|z) w.r.t q(z|x) +
KL(q(z) || p(z|x))
So, Maximizing lower bound means,
Minimizing KL (as >=0), and
For a given q and z, maximize the the likelihood of observing the x
Reparameterization Trick
VAE Architecture
References
 Lecture by Ali Ghodsi https://www.youtube.com/watch?v=uaaqyVS9-rM
 Lecture by Pascal Poupart https://www.youtube.com/watch?v=DWVlEw0D3gA
Hierarchy of Generative Models
Figure from Ian Goodfellow’s tutorial on GANs, NIPS 2016
Internals of a VAE’s learning algorithm
KL Divergence

More Related Content

What's hot

VQ-VAE
VQ-VAEVQ-VAE
VQ-VAE
수철 박
 
Language Model.pptx
Language Model.pptxLanguage Model.pptx
Language Model.pptx
Firas Obeid
 
Attention is All You Need (Transformer)
Attention is All You Need (Transformer)Attention is All You Need (Transformer)
Attention is All You Need (Transformer)
Jeong-Gwan Lee
 
Meta-Learning with Memory-Augmented Neural Networks (MANN)
Meta-Learning with Memory-Augmented Neural Networks (MANN)Meta-Learning with Memory-Augmented Neural Networks (MANN)
Meta-Learning with Memory-Augmented Neural Networks (MANN)
Yeonsu Kim
 
Diffusion models beat gans on image synthesis
Diffusion models beat gans on image synthesisDiffusion models beat gans on image synthesis
Diffusion models beat gans on image synthesis
BeerenSahu
 
[Paper review] BERT
[Paper review] BERT[Paper review] BERT
[Paper review] BERT
JEE HYUN PARK
 
Comparing Incremental Learning Strategies for Convolutional Neural Networks
Comparing Incremental Learning Strategies for Convolutional Neural NetworksComparing Incremental Learning Strategies for Convolutional Neural Networks
Comparing Incremental Learning Strategies for Convolutional Neural Networks
Vincenzo Lomonaco
 
Recurrent Neural Networks. Part 1: Theory
Recurrent Neural Networks. Part 1: TheoryRecurrent Neural Networks. Part 1: Theory
Recurrent Neural Networks. Part 1: Theory
Andrii Gakhov
 
Hyperparameter Tuning
Hyperparameter TuningHyperparameter Tuning
Hyperparameter Tuning
Jon Lederman
 
Interpretable machine learning
Interpretable machine learningInterpretable machine learning
Interpretable machine learning
Sri Ambati
 
クラシックな機械学習入門 1 導入
クラシックな機械学習入門 1 導入クラシックな機械学習入門 1 導入
クラシックな機械学習入門 1 導入
Hiroshi Nakagawa
 
Yurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAI
Yurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAIYurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAI
Yurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAI
Lviv Startup Club
 
BERT
BERTBERT
Latent diffusions vs DALL-E v2
Latent diffusions vs DALL-E v2Latent diffusions vs DALL-E v2
Latent diffusions vs DALL-E v2
Vitaly Bondar
 
Introduction to Transformers for NLP - Olga Petrova
Introduction to Transformers for NLP - Olga PetrovaIntroduction to Transformers for NLP - Olga Petrova
Introduction to Transformers for NLP - Olga Petrova
Alexey Grigorev
 
[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...
[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...
[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...
Deep Learning JP
 
A Review of Deep Contextualized Word Representations (Peters+, 2018)
A Review of Deep Contextualized Word Representations (Peters+, 2018)A Review of Deep Contextualized Word Representations (Peters+, 2018)
A Review of Deep Contextualized Word Representations (Peters+, 2018)
Shuntaro Yada
 
[PR12] intro. to gans jaejun yoo
[PR12] intro. to gans   jaejun yoo[PR12] intro. to gans   jaejun yoo
[PR12] intro. to gans jaejun yoo
JaeJun Yoo
 
Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...
Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...
Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...
Edureka!
 
A Simple Explanation of XLNet
A Simple Explanation of XLNetA Simple Explanation of XLNet
A Simple Explanation of XLNet
Domyoung Lee
 

What's hot (20)

VQ-VAE
VQ-VAEVQ-VAE
VQ-VAE
 
Language Model.pptx
Language Model.pptxLanguage Model.pptx
Language Model.pptx
 
Attention is All You Need (Transformer)
Attention is All You Need (Transformer)Attention is All You Need (Transformer)
Attention is All You Need (Transformer)
 
Meta-Learning with Memory-Augmented Neural Networks (MANN)
Meta-Learning with Memory-Augmented Neural Networks (MANN)Meta-Learning with Memory-Augmented Neural Networks (MANN)
Meta-Learning with Memory-Augmented Neural Networks (MANN)
 
Diffusion models beat gans on image synthesis
Diffusion models beat gans on image synthesisDiffusion models beat gans on image synthesis
Diffusion models beat gans on image synthesis
 
[Paper review] BERT
[Paper review] BERT[Paper review] BERT
[Paper review] BERT
 
Comparing Incremental Learning Strategies for Convolutional Neural Networks
Comparing Incremental Learning Strategies for Convolutional Neural NetworksComparing Incremental Learning Strategies for Convolutional Neural Networks
Comparing Incremental Learning Strategies for Convolutional Neural Networks
 
Recurrent Neural Networks. Part 1: Theory
Recurrent Neural Networks. Part 1: TheoryRecurrent Neural Networks. Part 1: Theory
Recurrent Neural Networks. Part 1: Theory
 
Hyperparameter Tuning
Hyperparameter TuningHyperparameter Tuning
Hyperparameter Tuning
 
Interpretable machine learning
Interpretable machine learningInterpretable machine learning
Interpretable machine learning
 
クラシックな機械学習入門 1 導入
クラシックな機械学習入門 1 導入クラシックな機械学習入門 1 導入
クラシックな機械学習入門 1 導入
 
Yurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAI
Yurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAIYurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAI
Yurii Pashchenko: Zero-shot learning capabilities of CLIP model from OpenAI
 
BERT
BERTBERT
BERT
 
Latent diffusions vs DALL-E v2
Latent diffusions vs DALL-E v2Latent diffusions vs DALL-E v2
Latent diffusions vs DALL-E v2
 
Introduction to Transformers for NLP - Olga Petrova
Introduction to Transformers for NLP - Olga PetrovaIntroduction to Transformers for NLP - Olga Petrova
Introduction to Transformers for NLP - Olga Petrova
 
[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...
[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...
[DL輪読会]“Learning to Predict without Looking Ahead: World Models without Forwa...
 
A Review of Deep Contextualized Word Representations (Peters+, 2018)
A Review of Deep Contextualized Word Representations (Peters+, 2018)A Review of Deep Contextualized Word Representations (Peters+, 2018)
A Review of Deep Contextualized Word Representations (Peters+, 2018)
 
[PR12] intro. to gans jaejun yoo
[PR12] intro. to gans   jaejun yoo[PR12] intro. to gans   jaejun yoo
[PR12] intro. to gans jaejun yoo
 
Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...
Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...
Recurrent Neural Networks (RNN) | RNN LSTM | Deep Learning Tutorial | Tensorf...
 
A Simple Explanation of XLNet
A Simple Explanation of XLNetA Simple Explanation of XLNet
A Simple Explanation of XLNet
 

Similar to Variational Auto Encoder and the Math Behind

Neural networks
Neural networksNeural networks
Neural networks
HarshitGupta367
 
Machine Learning 1
Machine Learning 1Machine Learning 1
Machine Learning 1
cairo university
 
Vector Quantization Vs Scalar Quantization
Vector Quantization Vs Scalar Quantization Vector Quantization Vs Scalar Quantization
Vector Quantization Vs Scalar Quantization
ManasiKaur
 
Matlab-free course by Mohd Esa
Matlab-free course by Mohd EsaMatlab-free course by Mohd Esa
Matlab-free course by Mohd Esa
Mohd Esa
 
Integral Calculus Anti Derivatives reviewer
Integral Calculus Anti Derivatives reviewerIntegral Calculus Anti Derivatives reviewer
Integral Calculus Anti Derivatives reviewer
JoshuaAgcopra
 
Multimedia lossy compression algorithms
Multimedia lossy compression algorithmsMultimedia lossy compression algorithms
Multimedia lossy compression algorithms
Mazin Alwaaly
 
VCE Unit 01 (2).pptx
VCE Unit 01 (2).pptxVCE Unit 01 (2).pptx
VCE Unit 01 (2).pptx
skilljiolms
 
SVM & KNN Presentation.pptx
SVM & KNN Presentation.pptxSVM & KNN Presentation.pptx
SVM & KNN Presentation.pptx
MohamedMonir33
 
Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...
Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...
Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...
Universitat Politècnica de Catalunya
 
Iclr2016 vaeまとめ
Iclr2016 vaeまとめIclr2016 vaeまとめ
Iclr2016 vaeまとめ
Deep Learning JP
 
Tutorial 2
Tutorial     2Tutorial     2
Tutorial 2
Mohamed Yaser
 
maXbox starter67 machine learning V
maXbox starter67 machine learning VmaXbox starter67 machine learning V
maXbox starter67 machine learning V
Max Kleiner
 
nlp dl 1.pdf
nlp dl 1.pdfnlp dl 1.pdf
nlp dl 1.pdf
nyomans1
 
PRML Chapter 4
PRML Chapter 4PRML Chapter 4
PRML Chapter 4
Sunwoo Kim
 
Illustration Clamor Echelon Evaluation via Prime Piece Psychotherapy
Illustration Clamor Echelon Evaluation via Prime Piece PsychotherapyIllustration Clamor Echelon Evaluation via Prime Piece Psychotherapy
Illustration Clamor Echelon Evaluation via Prime Piece Psychotherapy
IJMER
 
Efficient anomaly detection via matrix sketching
Efficient anomaly detection via matrix sketchingEfficient anomaly detection via matrix sketching
Efficient anomaly detection via matrix sketching
Hsing-chuan Hsieh
 
PRML Chapter 5
PRML Chapter 5PRML Chapter 5
PRML Chapter 5
Sunwoo Kim
 
SLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKS
SLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKSSLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKS
SLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKS
IJCI JOURNAL
 
Anomaly detection using deep one class classifier
Anomaly detection using deep one class classifierAnomaly detection using deep one class classifier
Anomaly detection using deep one class classifier
홍배 김
 
Explore ml day 2
Explore ml day 2Explore ml day 2
Explore ml day 2
preetikumara
 

Similar to Variational Auto Encoder and the Math Behind (20)

Neural networks
Neural networksNeural networks
Neural networks
 
Machine Learning 1
Machine Learning 1Machine Learning 1
Machine Learning 1
 
Vector Quantization Vs Scalar Quantization
Vector Quantization Vs Scalar Quantization Vector Quantization Vs Scalar Quantization
Vector Quantization Vs Scalar Quantization
 
Matlab-free course by Mohd Esa
Matlab-free course by Mohd EsaMatlab-free course by Mohd Esa
Matlab-free course by Mohd Esa
 
Integral Calculus Anti Derivatives reviewer
Integral Calculus Anti Derivatives reviewerIntegral Calculus Anti Derivatives reviewer
Integral Calculus Anti Derivatives reviewer
 
Multimedia lossy compression algorithms
Multimedia lossy compression algorithmsMultimedia lossy compression algorithms
Multimedia lossy compression algorithms
 
VCE Unit 01 (2).pptx
VCE Unit 01 (2).pptxVCE Unit 01 (2).pptx
VCE Unit 01 (2).pptx
 
SVM & KNN Presentation.pptx
SVM & KNN Presentation.pptxSVM & KNN Presentation.pptx
SVM & KNN Presentation.pptx
 
Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...
Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...
Deep Generative Models I (DLAI D9L2 2017 UPC Deep Learning for Artificial Int...
 
Iclr2016 vaeまとめ
Iclr2016 vaeまとめIclr2016 vaeまとめ
Iclr2016 vaeまとめ
 
Tutorial 2
Tutorial     2Tutorial     2
Tutorial 2
 
maXbox starter67 machine learning V
maXbox starter67 machine learning VmaXbox starter67 machine learning V
maXbox starter67 machine learning V
 
nlp dl 1.pdf
nlp dl 1.pdfnlp dl 1.pdf
nlp dl 1.pdf
 
PRML Chapter 4
PRML Chapter 4PRML Chapter 4
PRML Chapter 4
 
Illustration Clamor Echelon Evaluation via Prime Piece Psychotherapy
Illustration Clamor Echelon Evaluation via Prime Piece PsychotherapyIllustration Clamor Echelon Evaluation via Prime Piece Psychotherapy
Illustration Clamor Echelon Evaluation via Prime Piece Psychotherapy
 
Efficient anomaly detection via matrix sketching
Efficient anomaly detection via matrix sketchingEfficient anomaly detection via matrix sketching
Efficient anomaly detection via matrix sketching
 
PRML Chapter 5
PRML Chapter 5PRML Chapter 5
PRML Chapter 5
 
SLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKS
SLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKSSLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKS
SLIDING WINDOW SUM ALGORITHMS FOR DEEP NEURAL NETWORKS
 
Anomaly detection using deep one class classifier
Anomaly detection using deep one class classifierAnomaly detection using deep one class classifier
Anomaly detection using deep one class classifier
 
Explore ml day 2
Explore ml day 2Explore ml day 2
Explore ml day 2
 

Recently uploaded

UiPath Test Automation using UiPath Test Suite series, part 3
UiPath Test Automation using UiPath Test Suite series, part 3UiPath Test Automation using UiPath Test Suite series, part 3
UiPath Test Automation using UiPath Test Suite series, part 3
DianaGray10
 
Transcript: Selling digital books in 2024: Insights from industry leaders - T...
Transcript: Selling digital books in 2024: Insights from industry leaders - T...Transcript: Selling digital books in 2024: Insights from industry leaders - T...
Transcript: Selling digital books in 2024: Insights from industry leaders - T...
BookNet Canada
 
Accelerate your Kubernetes clusters with Varnish Caching
Accelerate your Kubernetes clusters with Varnish CachingAccelerate your Kubernetes clusters with Varnish Caching
Accelerate your Kubernetes clusters with Varnish Caching
Thijs Feryn
 
The Future of Platform Engineering
The Future of Platform EngineeringThe Future of Platform Engineering
The Future of Platform Engineering
Jemma Hussein Allen
 
Monitoring Java Application Security with JDK Tools and JFR Events
Monitoring Java Application Security with JDK Tools and JFR EventsMonitoring Java Application Security with JDK Tools and JFR Events
Monitoring Java Application Security with JDK Tools and JFR Events
Ana-Maria Mihalceanu
 
Securing your Kubernetes cluster_ a step-by-step guide to success !
Securing your Kubernetes cluster_ a step-by-step guide to success !Securing your Kubernetes cluster_ a step-by-step guide to success !
Securing your Kubernetes cluster_ a step-by-step guide to success !
KatiaHIMEUR1
 
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdfFIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance
 
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Product School
 
Neuro-symbolic is not enough, we need neuro-*semantic*
Neuro-symbolic is not enough, we need neuro-*semantic*Neuro-symbolic is not enough, we need neuro-*semantic*
Neuro-symbolic is not enough, we need neuro-*semantic*
Frank van Harmelen
 
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Tobias Schneck
 
DevOps and Testing slides at DASA Connect
DevOps and Testing slides at DASA ConnectDevOps and Testing slides at DASA Connect
DevOps and Testing slides at DASA Connect
Kari Kakkonen
 
PCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase TeamPCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase Team
ControlCase
 
Elevating Tactical DDD Patterns Through Object Calisthenics
Elevating Tactical DDD Patterns Through Object CalisthenicsElevating Tactical DDD Patterns Through Object Calisthenics
Elevating Tactical DDD Patterns Through Object Calisthenics
Dorra BARTAGUIZ
 
Key Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdfKey Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdf
Cheryl Hung
 
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Jeffrey Haguewood
 
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMsTo Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
Paul Groth
 
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Thierry Lestable
 
UiPath Test Automation using UiPath Test Suite series, part 4
UiPath Test Automation using UiPath Test Suite series, part 4UiPath Test Automation using UiPath Test Suite series, part 4
UiPath Test Automation using UiPath Test Suite series, part 4
DianaGray10
 
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Albert Hoitingh
 
Epistemic Interaction - tuning interfaces to provide information for AI support
Epistemic Interaction - tuning interfaces to provide information for AI supportEpistemic Interaction - tuning interfaces to provide information for AI support
Epistemic Interaction - tuning interfaces to provide information for AI support
Alan Dix
 

Recently uploaded (20)

UiPath Test Automation using UiPath Test Suite series, part 3
UiPath Test Automation using UiPath Test Suite series, part 3UiPath Test Automation using UiPath Test Suite series, part 3
UiPath Test Automation using UiPath Test Suite series, part 3
 
Transcript: Selling digital books in 2024: Insights from industry leaders - T...
Transcript: Selling digital books in 2024: Insights from industry leaders - T...Transcript: Selling digital books in 2024: Insights from industry leaders - T...
Transcript: Selling digital books in 2024: Insights from industry leaders - T...
 
Accelerate your Kubernetes clusters with Varnish Caching
Accelerate your Kubernetes clusters with Varnish CachingAccelerate your Kubernetes clusters with Varnish Caching
Accelerate your Kubernetes clusters with Varnish Caching
 
The Future of Platform Engineering
The Future of Platform EngineeringThe Future of Platform Engineering
The Future of Platform Engineering
 
Monitoring Java Application Security with JDK Tools and JFR Events
Monitoring Java Application Security with JDK Tools and JFR EventsMonitoring Java Application Security with JDK Tools and JFR Events
Monitoring Java Application Security with JDK Tools and JFR Events
 
Securing your Kubernetes cluster_ a step-by-step guide to success !
Securing your Kubernetes cluster_ a step-by-step guide to success !Securing your Kubernetes cluster_ a step-by-step guide to success !
Securing your Kubernetes cluster_ a step-by-step guide to success !
 
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdfFIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
 
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
 
Neuro-symbolic is not enough, we need neuro-*semantic*
Neuro-symbolic is not enough, we need neuro-*semantic*Neuro-symbolic is not enough, we need neuro-*semantic*
Neuro-symbolic is not enough, we need neuro-*semantic*
 
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
 
DevOps and Testing slides at DASA Connect
DevOps and Testing slides at DASA ConnectDevOps and Testing slides at DASA Connect
DevOps and Testing slides at DASA Connect
 
PCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase TeamPCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase Team
 
Elevating Tactical DDD Patterns Through Object Calisthenics
Elevating Tactical DDD Patterns Through Object CalisthenicsElevating Tactical DDD Patterns Through Object Calisthenics
Elevating Tactical DDD Patterns Through Object Calisthenics
 
Key Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdfKey Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdf
 
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
 
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMsTo Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
 
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
 
UiPath Test Automation using UiPath Test Suite series, part 4
UiPath Test Automation using UiPath Test Suite series, part 4UiPath Test Automation using UiPath Test Suite series, part 4
UiPath Test Automation using UiPath Test Suite series, part 4
 
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
 
Epistemic Interaction - tuning interfaces to provide information for AI support
Epistemic Interaction - tuning interfaces to provide information for AI supportEpistemic Interaction - tuning interfaces to provide information for AI support
Epistemic Interaction - tuning interfaces to provide information for AI support
 

Variational Auto Encoder and the Math Behind

  • 2. Generative Models  They take in data as input and learn to generate new data points from the same data distribution.  They learn the hidden representations using unsupervised learning techniques
  • 3. Variational Autoencoder  As the name suggests, it is an auto-encoder, which learns attributes from the data points and represents them in terms of latent variables.
  • 4. Problems  How can we make use of the auto-encoder architecture to generate new data points ?  Assuming we can pass a vector from that learnt latent space to the decoder, how can guarantee it’s not going to result in a garbage output.  VAEs address the above problems
  • 5. 1. How do we use the Auto Encoder Architecture for generation ? So, if we train the Auto encoder network and somehow learn the data distribution of the latent space, we can then sample from that latent space and pass it down to decoder and generate data points But, there is a problem.
  • 6.
  • 7. 2. How can we make sure that if we sample from our latent space, we are going to get new and meaningful output ?  VAEs achieve this by constricting the latent space.  The encoder and decoder parameters are tuned to accommodate for this setup
  • 9. Calculating Marginal Probability  If X = (x1, x2, x3) and Z = (z1, z2) then, 𝑃 𝑍 𝑋 = 𝑃(𝑋|𝑍)∗𝑃(𝑍) 𝑃(𝑋) Here, the P(X) is very difficult to calculate, especially in higher dimensions. It takes the form of 𝑧1 𝑧2 𝑃 𝑋1, 𝑋2, 𝑋3, 𝑍1, 𝑍2 𝑑𝑧1 ∗ 𝑑𝑧2 and is intractable. There are ways to solving this by using, 1. Using Monte Carlo Integration techniques 2. Variational Inference
  • 11. As x is already given, log p(x) is a constant. And KL(q(z) || p(z|x)) is what we wanted to minimize and it is always >= 0 0 <= p(x) <= 1 and KL >= 0 So, it is equivalent to maximizing the 3rd term. It is called Variational Lower bound
  • 12. This is nothing but, Expectation of p(x|z) w.r.t q(z|x) + KL(q(z) || p(z|x)) So, Maximizing lower bound means, Minimizing KL (as >=0), and For a given q and z, maximize the the likelihood of observing the x
  • 13.
  • 14.
  • 15.
  • 16.
  • 19.
  • 20. References  Lecture by Ali Ghodsi https://www.youtube.com/watch?v=uaaqyVS9-rM  Lecture by Pascal Poupart https://www.youtube.com/watch?v=DWVlEw0D3gA
  • 21. Hierarchy of Generative Models Figure from Ian Goodfellow’s tutorial on GANs, NIPS 2016
  • 22. Internals of a VAE’s learning algorithm KL Divergence