Soumettre la recherche
Mettre en ligne
02 cv mil_intro_to_probability
•
Télécharger en tant que PPTX, PDF
•
0 j'aime
•
357 vues
Z
zukun
Suivre
Technologie
Formation
Signaler
Partager
Signaler
Partager
1 sur 27
Télécharger maintenant
Recommandé
Dsp presentation
Dsp presentation
ILA SHARMA
Window_of_Economic_Statistics_MDPS_AE_Q3_2013Window of economic_statistics_md...
Window_of_Economic_Statistics_MDPS_AE_Q3_2013Window of economic_statistics_md...
Mahmoud Abozaid
Devops kc
Devops kc
Philip Thompson
Data Portals in National Statistics Offices: Case of Developing Countries
Data Portals in National Statistics Offices: Case of Developing Countries
Rajiv Ranjan
Chap019
Chap019
Dhamo daran
Spatial Statistics on the Geospatial Web
Spatial Statistics on the Geospatial Web
Matthias Hinz
Six sigma
Six sigma
Alaa Youssef
Fourier transform
Fourier transform
Department of Technical Education, Ministry of Education
Recommandé
Dsp presentation
Dsp presentation
ILA SHARMA
Window_of_Economic_Statistics_MDPS_AE_Q3_2013Window of economic_statistics_md...
Window_of_Economic_Statistics_MDPS_AE_Q3_2013Window of economic_statistics_md...
Mahmoud Abozaid
Devops kc
Devops kc
Philip Thompson
Data Portals in National Statistics Offices: Case of Developing Countries
Data Portals in National Statistics Offices: Case of Developing Countries
Rajiv Ranjan
Chap019
Chap019
Dhamo daran
Spatial Statistics on the Geospatial Web
Spatial Statistics on the Geospatial Web
Matthias Hinz
Six sigma
Six sigma
Alaa Youssef
Fourier transform
Fourier transform
Department of Technical Education, Ministry of Education
Probability and random processes project based learning template.pdf
Probability and random processes project based learning template.pdf
Vedant Srivastava
Economics Statistics Worktext
Economics Statistics Worktext
Jameson Estrada Pangasinan State University
Key Economic & Social Statistics - India
Key Economic & Social Statistics - India
Federation of Indian Chambers of Commerce & Industry (FICCI)
Quantative analysis
Quantative analysis
Dhruti Gadhiya
Analytical Design in Applied Marketing Research
Analytical Design in Applied Marketing Research
Kelly Page
Hollywood Motion Picture Cluster
Hollywood Motion Picture Cluster
Aliaksey Narko
Noida Master Plan 2021
Noida Master Plan 2021
Vijay Meena
Data Analysis
Data Analysis
sikander kushwaha
Application fields of R in classical industrial analytics
Application fields of R in classical industrial analytics
eoda GmbH
Lean knowledge
Lean knowledge
NsbmUcd
Ola fopl stats project
Ola fopl stats project
Stephen Abram
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...
Hemantha Kulathilake
Multivariate data analysis regression, cluster and factor analysis on spss
Multivariate data analysis regression, cluster and factor analysis on spss
Aditya Banerjee
Applied Statistics - Introduction
Applied Statistics - Introduction
Julio Huato
WSC 2011, advanced tutorial on simulation in Statistics
WSC 2011, advanced tutorial on simulation in Statistics
Christian Robert
Bhavishya- Technical Analysis
Bhavishya- Technical Analysis
shivamantri
Hadoop Operations Powered By ... Hadoop (Hadoop Summit 2014 Amsterdam)
Hadoop Operations Powered By ... Hadoop (Hadoop Summit 2014 Amsterdam)
Adam Kawa
Application of machine learning in industrial applications
Application of machine learning in industrial applications
Anish Das
Introduction to Probability
Introduction to Probability
Lukas Tencer
03 cv mil_probability_distributions
03 cv mil_probability_distributions
zukun
Common Probability Distibution
Common Probability Distibution
Lukas Tencer
05 cv mil_normal_distribution
05 cv mil_normal_distribution
zukun
Contenu connexe
En vedette
Probability and random processes project based learning template.pdf
Probability and random processes project based learning template.pdf
Vedant Srivastava
Economics Statistics Worktext
Economics Statistics Worktext
Jameson Estrada Pangasinan State University
Key Economic & Social Statistics - India
Key Economic & Social Statistics - India
Federation of Indian Chambers of Commerce & Industry (FICCI)
Quantative analysis
Quantative analysis
Dhruti Gadhiya
Analytical Design in Applied Marketing Research
Analytical Design in Applied Marketing Research
Kelly Page
Hollywood Motion Picture Cluster
Hollywood Motion Picture Cluster
Aliaksey Narko
Noida Master Plan 2021
Noida Master Plan 2021
Vijay Meena
Data Analysis
Data Analysis
sikander kushwaha
Application fields of R in classical industrial analytics
Application fields of R in classical industrial analytics
eoda GmbH
Lean knowledge
Lean knowledge
NsbmUcd
Ola fopl stats project
Ola fopl stats project
Stephen Abram
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...
Hemantha Kulathilake
Multivariate data analysis regression, cluster and factor analysis on spss
Multivariate data analysis regression, cluster and factor analysis on spss
Aditya Banerjee
Applied Statistics - Introduction
Applied Statistics - Introduction
Julio Huato
WSC 2011, advanced tutorial on simulation in Statistics
WSC 2011, advanced tutorial on simulation in Statistics
Christian Robert
Bhavishya- Technical Analysis
Bhavishya- Technical Analysis
shivamantri
Hadoop Operations Powered By ... Hadoop (Hadoop Summit 2014 Amsterdam)
Hadoop Operations Powered By ... Hadoop (Hadoop Summit 2014 Amsterdam)
Adam Kawa
Application of machine learning in industrial applications
Application of machine learning in industrial applications
Anish Das
En vedette
(18)
Probability and random processes project based learning template.pdf
Probability and random processes project based learning template.pdf
Economics Statistics Worktext
Economics Statistics Worktext
Key Economic & Social Statistics - India
Key Economic & Social Statistics - India
Quantative analysis
Quantative analysis
Analytical Design in Applied Marketing Research
Analytical Design in Applied Marketing Research
Hollywood Motion Picture Cluster
Hollywood Motion Picture Cluster
Noida Master Plan 2021
Noida Master Plan 2021
Data Analysis
Data Analysis
Application fields of R in classical industrial analytics
Application fields of R in classical industrial analytics
Lean knowledge
Lean knowledge
Ola fopl stats project
Ola fopl stats project
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...
Multivariate data analysis regression, cluster and factor analysis on spss
Multivariate data analysis regression, cluster and factor analysis on spss
Applied Statistics - Introduction
Applied Statistics - Introduction
WSC 2011, advanced tutorial on simulation in Statistics
WSC 2011, advanced tutorial on simulation in Statistics
Bhavishya- Technical Analysis
Bhavishya- Technical Analysis
Hadoop Operations Powered By ... Hadoop (Hadoop Summit 2014 Amsterdam)
Hadoop Operations Powered By ... Hadoop (Hadoop Summit 2014 Amsterdam)
Application of machine learning in industrial applications
Application of machine learning in industrial applications
Similaire à 02 cv mil_intro_to_probability
Introduction to Probability
Introduction to Probability
Lukas Tencer
03 cv mil_probability_distributions
03 cv mil_probability_distributions
zukun
Common Probability Distibution
Common Probability Distibution
Lukas Tencer
05 cv mil_normal_distribution
05 cv mil_normal_distribution
zukun
04 cv mil_fitting_probability_models
04 cv mil_fitting_probability_models
zukun
08 cv mil_regression
08 cv mil_regression
zukun
10 cv mil_graphical_models
10 cv mil_graphical_models
zukun
09 cv mil_classification
09 cv mil_classification
zukun
07 cv mil_modeling_complex_densities
07 cv mil_modeling_complex_densities
zukun
15 cv mil_models_for_transformations
15 cv mil_models_for_transformations
zukun
11 cv mil_models_for_chains_and_trees
11 cv mil_models_for_chains_and_trees
zukun
06 cv mil_learning_and_inference
06 cv mil_learning_and_inference
zukun
17 cv mil_models_for_shape
17 cv mil_models_for_shape
zukun
16 cv mil_multiple_cameras
16 cv mil_multiple_cameras
zukun
12 cv mil_models_for_grids
12 cv mil_models_for_grids
zukun
02 Introduction to probability ノート
02 Introduction to probability ノート
Gen Sasaki
20 cv mil_models_for_words
20 cv mil_models_for_words
zukun
Representation Learning & Generative Modeling with Variational Autoencoder(VA...
Representation Learning & Generative Modeling with Variational Autoencoder(VA...
changedaeoh
19 cv mil_temporal_models
19 cv mil_temporal_models
zukun
Graphical Models for chains, trees and grids
Graphical Models for chains, trees and grids
potaters
Similaire à 02 cv mil_intro_to_probability
(20)
Introduction to Probability
Introduction to Probability
03 cv mil_probability_distributions
03 cv mil_probability_distributions
Common Probability Distibution
Common Probability Distibution
05 cv mil_normal_distribution
05 cv mil_normal_distribution
04 cv mil_fitting_probability_models
04 cv mil_fitting_probability_models
08 cv mil_regression
08 cv mil_regression
10 cv mil_graphical_models
10 cv mil_graphical_models
09 cv mil_classification
09 cv mil_classification
07 cv mil_modeling_complex_densities
07 cv mil_modeling_complex_densities
15 cv mil_models_for_transformations
15 cv mil_models_for_transformations
11 cv mil_models_for_chains_and_trees
11 cv mil_models_for_chains_and_trees
06 cv mil_learning_and_inference
06 cv mil_learning_and_inference
17 cv mil_models_for_shape
17 cv mil_models_for_shape
16 cv mil_multiple_cameras
16 cv mil_multiple_cameras
12 cv mil_models_for_grids
12 cv mil_models_for_grids
02 Introduction to probability ノート
02 Introduction to probability ノート
20 cv mil_models_for_words
20 cv mil_models_for_words
Representation Learning & Generative Modeling with Variational Autoencoder(VA...
Representation Learning & Generative Modeling with Variational Autoencoder(VA...
19 cv mil_temporal_models
19 cv mil_temporal_models
Graphical Models for chains, trees and grids
Graphical Models for chains, trees and grids
Plus de zukun
My lyn tutorial 2009
My lyn tutorial 2009
zukun
ETHZ CV2012: Tutorial openCV
ETHZ CV2012: Tutorial openCV
zukun
ETHZ CV2012: Information
ETHZ CV2012: Information
zukun
Siwei lyu: natural image statistics
Siwei lyu: natural image statistics
zukun
Lecture9 camera calibration
Lecture9 camera calibration
zukun
Brunelli 2008: template matching techniques in computer vision
Brunelli 2008: template matching techniques in computer vision
zukun
Modern features-part-4-evaluation
Modern features-part-4-evaluation
zukun
Modern features-part-3-software
Modern features-part-3-software
zukun
Modern features-part-2-descriptors
Modern features-part-2-descriptors
zukun
Modern features-part-1-detectors
Modern features-part-1-detectors
zukun
Modern features-part-0-intro
Modern features-part-0-intro
zukun
Lecture 02 internet video search
Lecture 02 internet video search
zukun
Lecture 01 internet video search
Lecture 01 internet video search
zukun
Lecture 03 internet video search
Lecture 03 internet video search
zukun
Icml2012 tutorial representation_learning
Icml2012 tutorial representation_learning
zukun
Advances in discrete energy minimisation for computer vision
Advances in discrete energy minimisation for computer vision
zukun
Gephi tutorial: quick start
Gephi tutorial: quick start
zukun
EM algorithm and its application in probabilistic latent semantic analysis
EM algorithm and its application in probabilistic latent semantic analysis
zukun
Object recognition with pictorial structures
Object recognition with pictorial structures
zukun
Iccv2011 learning spatiotemporal graphs of human activities
Iccv2011 learning spatiotemporal graphs of human activities
zukun
Plus de zukun
(20)
My lyn tutorial 2009
My lyn tutorial 2009
ETHZ CV2012: Tutorial openCV
ETHZ CV2012: Tutorial openCV
ETHZ CV2012: Information
ETHZ CV2012: Information
Siwei lyu: natural image statistics
Siwei lyu: natural image statistics
Lecture9 camera calibration
Lecture9 camera calibration
Brunelli 2008: template matching techniques in computer vision
Brunelli 2008: template matching techniques in computer vision
Modern features-part-4-evaluation
Modern features-part-4-evaluation
Modern features-part-3-software
Modern features-part-3-software
Modern features-part-2-descriptors
Modern features-part-2-descriptors
Modern features-part-1-detectors
Modern features-part-1-detectors
Modern features-part-0-intro
Modern features-part-0-intro
Lecture 02 internet video search
Lecture 02 internet video search
Lecture 01 internet video search
Lecture 01 internet video search
Lecture 03 internet video search
Lecture 03 internet video search
Icml2012 tutorial representation_learning
Icml2012 tutorial representation_learning
Advances in discrete energy minimisation for computer vision
Advances in discrete energy minimisation for computer vision
Gephi tutorial: quick start
Gephi tutorial: quick start
EM algorithm and its application in probabilistic latent semantic analysis
EM algorithm and its application in probabilistic latent semantic analysis
Object recognition with pictorial structures
Object recognition with pictorial structures
Iccv2011 learning spatiotemporal graphs of human activities
Iccv2011 learning spatiotemporal graphs of human activities
Dernier
The State of Passkeys with FIDO Alliance.pptx
The State of Passkeys with FIDO Alliance.pptx
LoriGlavin3
Arizona Broadband Policy Past, Present, and Future Presentation 3/25/24
Arizona Broadband Policy Past, Present, and Future Presentation 3/25/24
Mark Goldstein
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptx
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptx
LoriGlavin3
Transcript: New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
Transcript: New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
BookNet Canada
TrustArc Webinar - How to Build Consumer Trust Through Data Privacy
TrustArc Webinar - How to Build Consumer Trust Through Data Privacy
TrustArc
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
ThousandEyes
How to write a Business Continuity Plan
How to write a Business Continuity Plan
Databarracks
Scale your database traffic with Read & Write split using MySQL Router
Scale your database traffic with Read & Write split using MySQL Router
Mydbops
Data governance with Unity Catalog Presentation
Data governance with Unity Catalog Presentation
Knoldus Inc.
A Journey Into the Emotions of Software Developers
A Journey Into the Emotions of Software Developers
Nicole Novielli
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
LoriGlavin3
Why device, WIFI, and ISP insights are crucial to supporting remote Microsoft...
Why device, WIFI, and ISP insights are crucial to supporting remote Microsoft...
panagenda
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
LoriGlavin3
Assure Ecommerce and Retail Operations Uptime with ThousandEyes
Assure Ecommerce and Retail Operations Uptime with ThousandEyes
ThousandEyes
The Ultimate Guide to Choosing WordPress Pros and Cons
The Ultimate Guide to Choosing WordPress Pros and Cons
Pixlogix Infotech
How AI, OpenAI, and ChatGPT impact business and software.
How AI, OpenAI, and ChatGPT impact business and software.
Curtis Poe
TeamStation AI System Report LATAM IT Salaries 2024
TeamStation AI System Report LATAM IT Salaries 2024
Lonnie McRorey
2024 April Patch Tuesday
2024 April Patch Tuesday
Ivanti
Moving Beyond Passwords: FIDO Paris Seminar.pdf
Moving Beyond Passwords: FIDO Paris Seminar.pdf
LoriGlavin3
Connecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdf
Neo4j
Dernier
(20)
The State of Passkeys with FIDO Alliance.pptx
The State of Passkeys with FIDO Alliance.pptx
Arizona Broadband Policy Past, Present, and Future Presentation 3/25/24
Arizona Broadband Policy Past, Present, and Future Presentation 3/25/24
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptx
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptx
Transcript: New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
Transcript: New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
TrustArc Webinar - How to Build Consumer Trust Through Data Privacy
TrustArc Webinar - How to Build Consumer Trust Through Data Privacy
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
How to write a Business Continuity Plan
How to write a Business Continuity Plan
Scale your database traffic with Read & Write split using MySQL Router
Scale your database traffic with Read & Write split using MySQL Router
Data governance with Unity Catalog Presentation
Data governance with Unity Catalog Presentation
A Journey Into the Emotions of Software Developers
A Journey Into the Emotions of Software Developers
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
Why device, WIFI, and ISP insights are crucial to supporting remote Microsoft...
Why device, WIFI, and ISP insights are crucial to supporting remote Microsoft...
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
Assure Ecommerce and Retail Operations Uptime with ThousandEyes
Assure Ecommerce and Retail Operations Uptime with ThousandEyes
The Ultimate Guide to Choosing WordPress Pros and Cons
The Ultimate Guide to Choosing WordPress Pros and Cons
How AI, OpenAI, and ChatGPT impact business and software.
How AI, OpenAI, and ChatGPT impact business and software.
TeamStation AI System Report LATAM IT Salaries 2024
TeamStation AI System Report LATAM IT Salaries 2024
2024 April Patch Tuesday
2024 April Patch Tuesday
Moving Beyond Passwords: FIDO Paris Seminar.pdf
Moving Beyond Passwords: FIDO Paris Seminar.pdf
Connecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdf
02 cv mil_intro_to_probability
1.
Computer vision: models, learning
and inference Chapter 2 Introduction to probability Please send errata to s.prince@cs.ucl.ac.uk
2.
Random variables • A
random variable x denotes a quantity that is uncertain • May be result of experiment (flipping a coin) or a real world measurements (measuring temperature) • If observe several instances of x we get different values • Some values occur more than others and this information is captured by a probability distribution Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 2
3.
Discrete Random Variables
Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 3
4.
Continuous Random Variable
Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 4
5.
Joint Probability • Consider
two random variables x and y • If we observe multiple paired instances, then some combinations of outcomes are more likely than others • This is captured in the joint probability distribution • Written as Pr(x,y) • Can read Pr(x,y) as “probability of x and y” Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 5
6.
Joint Probability Computer vision:
models, learning and inference. ©2011 Simon J.D. Prince 6
7.
Marginalization We can recover
probability distribution of any variable in a joint distribution by integrating (or summing) over the other variables Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 7
8.
Marginalization We can recover
probability distribution of any variable in a joint distribution by integrating (or summing) over the other variables Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 8
9.
Marginalization We can recover
probability distribution of any variable in a joint distribution by integrating (or summing) over the other variables Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 9
10.
Marginalization We can recover
probability distribution of any variable in a joint distribution by integrating (or summing) over the other variables Works in higher dimensions as well – leaves joint distribution between whatever variables are left Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 10
11.
Conditional Probability • Conditional
probability of x given that y=y1 is relative propensity of variable x to take different outcomes given that y is fixed to be equal to y1. • Written as Pr(x|y=y1) 11 Computer vision: models, learning and inference. ©2011 Simon J.D. Prince
12.
Conditional Probability • Conditional
probability can be extracted from joint probability • Extract appropriate slice and normalize Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 12
13.
Conditional Probability • More
usually written in compact form • Can be re-arranged to give Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 13
14.
Conditional Probability • This
idea can be extended to more than two variables Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 14
15.
Bayes’ Rule From before: Combining: Re-arranging:
Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 15
16.
Bayes’ Rule Terminology
Likelihood – propensity for Prior – what we know observing a certain value of about y before seeing x x given a certain value of y Posterior – what we Evidence –a constant to know about y after ensure that the left hand seeing x side is a valid distribution Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 16
17.
Independence • If two
variables x and y are independent then variable x tells us nothing about variable y (and vice-versa) Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 17
18.
Independence • If two
variables x and y are independent then variable x tells us nothing about variable y (and vice-versa) Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 18
19.
Independence • When variables
are independent, the joint factorizes into a product of the marginals: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 19
20.
Expectation Expectation tell us
the expected or average value of some function f [x] taking into account the distribution of x Definition: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 20
21.
Expectation Expectation tell us
the expected or average value of some function f [x] taking into account the distribution of x Definition in two dimensions: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 21
22.
Expectation: Common Cases
Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 22
23.
Expectation: Rules Rule 1: Expected
value of a constant is the constant Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 23
24.
Expectation: Rules Rule 2: Expected
value of constant times function is constant times expected value of function Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 24
25.
Expectation: Rules Rule 3: Expectation
of sum of functions is sum of expectation of functions Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 25
26.
Expectation: Rules Rule 4: Expectation
of product of functions in variables x and y is product of expectations of functions if x and y are independent Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 26
27.
Conclusions • Rules of
probability are compact and simple • Concepts of marginalization, joint and conditional probability, Bayes rule and expectation underpin all of the models in this book • One remaining concept – conditional expectation – discussed later Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 27
Télécharger maintenant