Mudanças entre as edições de "Stochastic Processes"
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− | This is the main page of an undergraduate-level course in stochastic processes targeted at engineering students (mainly computer engineering and its interface with mechanical engineering), being taught in | + | This is the main page of an undergraduate-level course in stochastic processes targeted at engineering students (mainly computer engineering and its interface with mechanical engineering), being taught in 2020 PAE (emergencial semester during the COVID-19 pandemic) at the Polytechnic Institute [http://pt.wikipedia.org/wiki/IPRJ IPRJ]/UERJ. |
− | * Course pages for previous years: '''[[PE2012|2012]]''' | + | * Course pages for previous years: '''[[PE2020 (canceled)|2020/1a (Canceled due to COVID-19)]], [[PE2019|2019]], [[PE2018|2018]], [[PE2012|2012]]''' |
[[Image:Mocap_transfer.png|right|250px|thumb|Recent application of [https://en.wikipedia.org/wiki/Gaussian_process Gaussian stochastic processes] for 3D motion capture transfer [http://openaccess.thecvf.com/content_cvpr_2017/papers/Boukhayma_Surface_Motion_Capture_CVPR_2017_paper.pdf (CVPR 2017)] ]] | [[Image:Mocap_transfer.png|right|250px|thumb|Recent application of [https://en.wikipedia.org/wiki/Gaussian_process Gaussian stochastic processes] for 3D motion capture transfer [http://openaccess.thecvf.com/content_cvpr_2017/papers/Boukhayma_Surface_Motion_Capture_CVPR_2017_paper.pdf (CVPR 2017)] ]] | ||
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== General Info == | == General Info == | ||
* Instructor: prof. [http://www.lems.brown.edu/~rfabbri Ricardo Fabbri], Ph.D. Brown University | * Instructor: prof. [http://www.lems.brown.edu/~rfabbri Ricardo Fabbri], Ph.D. Brown University | ||
− | * Meeting times: Tuesdays 1:20pm-3:10pm Thursdays 1:20pm - 3:10pm, room | + | * Meeting times: Tuesdays 1:20pm-3:10pm, room 206; Thursdays 1:20pm - 3:10pm, room 208. |
− | + | * Forum for file exchange and discussion: lista do google groups: [https://groups.google.com/forum/#!forum/iprj-estocasticos-2020-pae <tt>iprj-estocasticos-2020-PAE@googlegroups.com</tt>] | |
− | * Forum for file exchange and discussion: lista do google groups: [https://groups.google.com/forum/#! | + | |
* Chat: IRC #labmacambira for random chat | * Chat: IRC #labmacambira for random chat | ||
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=== Software === | === Software === | ||
The R programming language and data exploration environment will be used for learning, with others used occasionally. Students can also choose to do their homework in Python, Scilab, Matlab or similar languages. The R language has received growing attention, specially in the past couple of years, but it is simple enough so that the student can adapt the code to his preferred language. '''Students are expected to learn any of these languages on their own as needed, by doing tutorials and asking questions''' | The R programming language and data exploration environment will be used for learning, with others used occasionally. Students can also choose to do their homework in Python, Scilab, Matlab or similar languages. The R language has received growing attention, specially in the past couple of years, but it is simple enough so that the student can adapt the code to his preferred language. '''Students are expected to learn any of these languages on their own as needed, by doing tutorials and asking questions''' | ||
+ | * [https://www.rstudio.com/products/rstudio/download/preview/ R studio]: recommended IDE for R. | ||
+ | * [http://rich-iannone.github.io/DiagrammeR Diagrammer]: beautiful tool to draw and interact with graphs in R. | ||
== Approximate Content == | == Approximate Content == | ||
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=== Lectures === | === Lectures === | ||
Lectures roughly follow the sequence of our main book, with some additional material as needed. All necessary background will be covered as needed. Advanced material will be covered partly. | Lectures roughly follow the sequence of our main book, with some additional material as needed. All necessary background will be covered as needed. Advanced material will be covered partly. | ||
− | # Overview & Course Logistics ( | + | |
+ | # Overview & Course Logistics (15Sep20) | ||
+ | |||
+ | ==== Public Youtube Playlist (Portuguese) ==== | ||
+ | Prof. Fabbri's lectures are available online at: | ||
+ | https://www.youtube.com/playlist?list=PL1tkMA9lsTiVw9PzRcxpUBN4aArh948sK | ||
+ | |||
+ | Partial listing: | ||
+ | |||
+ | * Aula 1 parte 1 Introdução ao Curso https://youtu.be/qTZkZ5y_MJc | ||
+ | * Aula 1 parte 2 O que são Processos Estocásticos? https://youtu.be/hDVdjPTVJtw | ||
+ | * Aula 1 parte 3 O que significa "estocástico"? https://youtu.be/xUSvDqRXAL4 | ||
+ | * Aula 1 parte 4 Formalismo e revisão de probabilidades https://youtu.be/pawQt7TtIf0 | ||
+ | * Aula 1 parte 5 Exemplos Iniciais https://youtu.be/L5zH-uSDejc | ||
+ | * Aula 1 parte 6 Exemplos 2, Difusões https://youtu.be/tYD0ezDfYxM | ||
+ | * Aula 2 parte 1 Revisão de Probabilidade parte 2 | ||
+ | * Aula 2 parte 2 Revisão de Distribuições - Revisão de Probabilidade parte 3 https://youtu.be/admtZDT2iok | ||
+ | * Aula 3 parte 1 Pagerank https://youtu.be/45wx3yZh7SI | ||
+ | * Aula 3 parte 2 Grafos - Revisão https://youtu.be/cE834FfnnuY | ||
+ | * Aula 4 parte 1 Cadeias de Markov e exemplo em Metástase do Câncer https://youtu.be/N0R83bBUSf8 | ||
+ | ** Paper: Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites., Newton, P., Mason, J., Venkatappa, N. et al., Nature npj Breast Cancer 1, 15018 (2015). https://doi.org/10.1038/npjbcancer.2015.18 | ||
+ | ** Paper: A Stochastic Markov Chain Model to Describe Lung Cancer Growth and Metastasis | ||
+ | Newton PK, Mason J, Bethel K, Bazhenova LA, Nieva J, et al. (2012) A Stochastic Markov Chain Model to Describe Lung Cancer Growth and Metastasis. PLOS ONE 7(4): e34637. https://doi.org/10.1371/journal.pone.0034637 | ||
+ | * Remaining lectures ongoing at: https://www.youtube.com/playlist?list=PL1tkMA9lsTiVw9PzRcxpUBN4aArh948sK | ||
+ | |||
+ | ==== Lecture Notes ==== | ||
+ | |||
+ | * Fabbri's lecture notes on long term markov chains (based on Dobrow's Chapter 3) [https://drive.google.com/file/d/1FVCbiH32Up4_NHzBLhuFd6tn0GN2FmX0/view?usp=sharing pdf] | ||
==== Tentative listing ==== | ==== Tentative listing ==== | ||
* Intro, overview of main processes and quick review | * Intro, overview of main processes and quick review | ||
* Markov Chains | * Markov Chains | ||
− | |||
* Markov Chain Monte Carlo: MCMC | * Markov Chain Monte Carlo: MCMC | ||
* Poisson Process | * Poisson Process | ||
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* If you do the homework in two different languages, you get double the homework grade (bonus of 100%) | * If you do the homework in two different languages, you get double the homework grade (bonus of 100%) | ||
* Late homework will be accepted but penalized at the professor's will according to how late it is | * Late homework will be accepted but penalized at the professor's will according to how late it is | ||
+ | * '''All electronic material must be sent to the professors' email, with the string "[iprj-pe]" as part of the subject of the email. You will receive an automatic confirmation.''' | ||
+ | |||
+ | === Assignment -1: se inscrever na lista de discussão (data: quarta 16set20) === | ||
+ | * Enviar email para: <tt>iprj-estocasticos-2020-PAE+subscribe@googlegroups.com</tt> | ||
+ | * Responder ao email do professor sobre o PDFs dos livros com "OK" | ||
+ | * Quem ja realizou esta tarefa como parte do periodo cancelado, favor re-enviar | ||
=== Assignment 0 === | === Assignment 0 === | ||
* Ex 1.1 of the main book | * Ex 1.1 of the main book | ||
− | * Handrwitten | + | * Handrwitten and scanned |
− | * Due date: | + | * Due date: 22set20 (sugerida) |
=== Assignment 1 === | === Assignment 1 === | ||
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''Simulating Discrete Random Variables'' (pp 51, 52, 53) | ''Simulating Discrete Random Variables'' (pp 51, 52, 53) | ||
* Type your solutions in Latex | * Type your solutions in Latex | ||
− | * Due date: | + | * Due date: 29set20 (suggested), extendido para 13Out20 |
* No need to read this book for this exercise. You will review discrete random variables in the context of Markov chains for natural language processing; this is basic for most AI bots nowadays. If you're curious about the applications, you can read the book chapter just for fun. | * No need to read this book for this exercise. You will review discrete random variables in the context of Markov chains for natural language processing; this is basic for most AI bots nowadays. If you're curious about the applications, you can read the book chapter just for fun. | ||
=== Assignment 2: Exercise list for chapter 1 === | === Assignment 2: Exercise list for chapter 1 === | ||
− | Exercises: 1.3, 1.5, 1.6, 1.7, 1.9, 1.10, 1.19 | + | 7 Exercises: 1.3, 1.5, 1.6, 1.7, 1.9, 1.10, 1.19 |
− | * Due date: | + | * Due date: 29Set20 (suggested) |
=== Assignment 3: Exercise list for chapter 2 === | === Assignment 3: Exercise list for chapter 2 === | ||
− | Exercises: 2.1, 2.4, 2.6, 2.8, 2.9, 2.10, 2.12, 2.14, 2.15, 2.18 | + | 11 Exercises: 2.1, 2.4, 2.6, 2.8, 2.9, 2.10, 2.12, 2.14, 2.15, 2.18 |
Computer: 2.26 | Computer: 2.26 | ||
− | * Due date: | + | * Due date: 6Out20 (suggested), extendido para 13Out20 |
=== Assignment 4: Exercise list for chapter 3 === | === Assignment 4: Exercise list for chapter 3 === | ||
− | Exercises: 3.2, 3. | + | Exercises: 3.2, 3.5a-c, 3.10a-d, 3.16i-iv, 3.25a-b, 3.37, 3.58 |
− | * Due date: | + | * Due date: before P1 (suggested) |
+ | |||
+ | === Assignment 5: Exercise list for chapter 5 (MCMC) === | ||
+ | 4 Exercises: 5.1, 5.2, 5.5, 5.6 | ||
+ | * Due date: inicio da P2 | ||
+ | |||
+ | === Assignment 6: Exercise list for chapter 6 === | ||
+ | 2 Exercises: 6.3, 6.4 | ||
+ | 2 Bonus exercises (extra grading): 6.7, 6.8 | ||
+ | * Due date: inicio da P2 | ||
== Exams == | == Exams == | ||
− | * '''P1 (easy):''' | + | * '''P1 (easy):''' 27Out20 |
− | * '''P2 (harder):''' | + | * '''P2 (harder):''' 8Dez20 |
− | * '''Final-Sub:''' | + | * '''Final-Sub:''' 14Dez20 |
== Evaluation criteria == | == Evaluation criteria == | ||
− | + | Ver este [https://drive.google.com/file/d/1iimWFLNjwr5ktBGWcKVRvGZi_NonoCIg PDF] | |
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== Awesome Links == | == Awesome Links == |
Edição atual tal como às 19h13min de 22 de outubro de 2020
This is the main page of an undergraduate-level course in stochastic processes targeted at engineering students (mainly computer engineering and its interface with mechanical engineering), being taught in 2020 PAE (emergencial semester during the COVID-19 pandemic) at the Polytechnic Institute IPRJ/UERJ.
- Course pages for previous years: 2020/1a (Canceled due to COVID-19), 2019, 2018, 2012
Índice
- 1 General Info
- 2 Approximate Content
- 3 Main Resources
- 4 Homework
- 4.1 Assignment -1: se inscrever na lista de discussão (data: quarta 16set20)
- 4.2 Assignment 0
- 4.3 Assignment 1
- 4.4 Assignment 2: Exercise list for chapter 1
- 4.5 Assignment 3: Exercise list for chapter 2
- 4.6 Assignment 4: Exercise list for chapter 3
- 4.7 Assignment 5: Exercise list for chapter 5 (MCMC)
- 4.8 Assignment 6: Exercise list for chapter 6
- 5 Exams
- 6 Evaluation criteria
- 7 Awesome Links
- 8 Keywords
General Info
- Instructor: prof. Ricardo Fabbri, Ph.D. Brown University
- Meeting times: Tuesdays 1:20pm-3:10pm, room 206; Thursdays 1:20pm - 3:10pm, room 208.
- Forum for file exchange and discussion: lista do google groups: iprj-estocasticos-2020-PAE@googlegroups.com
- Chat: IRC #labmacambira for random chat
Pre-requisites
- Undergraduate-level mathematics and probability (will review as needed)
- Desirable: Intermediate programming experience with any numerics scripting language such as Scilab, Python, R or Matlab. Knowing at least one of them will help you learn any new language needed in the course.
Software
The R programming language and data exploration environment will be used for learning, with others used occasionally. Students can also choose to do their homework in Python, Scilab, Matlab or similar languages. The R language has received growing attention, specially in the past couple of years, but it is simple enough so that the student can adapt the code to his preferred language. Students are expected to learn any of these languages on their own as needed, by doing tutorials and asking questions
- R studio: recommended IDE for R.
- Diagrammer: beautiful tool to draw and interact with graphs in R.
Approximate Content
This year's course will focus on a modern approach bridging theory and practice. As engineers and scientists, you should not learn theory here without also considering broader applications. Recent applications in artificial intelligence, machine learning, robotics, autonomous driving, material science and other topics will be considered. These applications are often too hard to tackle at the level of this course, but having contact with them will help motivate the abstract theory. We will try to focus on key concepts and more realistic applications than most courses (that come from the 1900's), that will prompt us to elaborate theory.
Main Resources
Textbooks
Main book
Introduction to Stochastic Processes with R, Robert Dobrow, 2016 (5 stars on Amazon)
Additional books used in the course
Learning stochastic processes will require aditional books, including more traditional ones:
- Markov Chains: gibbs fields, monte carlo simulation and queues, Pierre Bremaud
- An Introduction to Stochastic Modeling, Taylor & Karlin
- Pattern Theory: The Stochastic Analysis of Real-World Signals, David Mumford and Agnes Desolneux - the first chapters already cover many types of stochastic processes in text, signal and image AI
- My own machine learning and computational modeling book draft, co-written with prof. Francisco Duarte Moura Neto and focused on diffusion processes on graphs like PageRank. There is a probability chapter which is the basis for this course. We have many copies at IPRJ's library.
Other books to look at
Basic probability and statistics
- I recommend you review from the above books. They all include a review. But you might have to see:
- Elementary Statistics, Mario Triola (passed down to me by a great scientist and statistician)
Interesting books
Machine Learning
- Pattern Theory: From Representation to Inference, Ulf Grenader
Lectures
Lectures roughly follow the sequence of our main book, with some additional material as needed. All necessary background will be covered as needed. Advanced material will be covered partly.
- Overview & Course Logistics (15Sep20)
Public Youtube Playlist (Portuguese)
Prof. Fabbri's lectures are available online at:
https://www.youtube.com/playlist?list=PL1tkMA9lsTiVw9PzRcxpUBN4aArh948sK
Partial listing:
- Aula 1 parte 1 Introdução ao Curso https://youtu.be/qTZkZ5y_MJc
- Aula 1 parte 2 O que são Processos Estocásticos? https://youtu.be/hDVdjPTVJtw
- Aula 1 parte 3 O que significa "estocástico"? https://youtu.be/xUSvDqRXAL4
- Aula 1 parte 4 Formalismo e revisão de probabilidades https://youtu.be/pawQt7TtIf0
- Aula 1 parte 5 Exemplos Iniciais https://youtu.be/L5zH-uSDejc
- Aula 1 parte 6 Exemplos 2, Difusões https://youtu.be/tYD0ezDfYxM
- Aula 2 parte 1 Revisão de Probabilidade parte 2
- Aula 2 parte 2 Revisão de Distribuições - Revisão de Probabilidade parte 3 https://youtu.be/admtZDT2iok
- Aula 3 parte 1 Pagerank https://youtu.be/45wx3yZh7SI
- Aula 3 parte 2 Grafos - Revisão https://youtu.be/cE834FfnnuY
- Aula 4 parte 1 Cadeias de Markov e exemplo em Metástase do Câncer https://youtu.be/N0R83bBUSf8
- Paper: Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites., Newton, P., Mason, J., Venkatappa, N. et al., Nature npj Breast Cancer 1, 15018 (2015). https://doi.org/10.1038/npjbcancer.2015.18
- Paper: A Stochastic Markov Chain Model to Describe Lung Cancer Growth and Metastasis
Newton PK, Mason J, Bethel K, Bazhenova LA, Nieva J, et al. (2012) A Stochastic Markov Chain Model to Describe Lung Cancer Growth and Metastasis. PLOS ONE 7(4): e34637. https://doi.org/10.1371/journal.pone.0034637
- Remaining lectures ongoing at: https://www.youtube.com/playlist?list=PL1tkMA9lsTiVw9PzRcxpUBN4aArh948sK
Lecture Notes
- Fabbri's lecture notes on long term markov chains (based on Dobrow's Chapter 3) pdf
Tentative listing
- Intro, overview of main processes and quick review
- Markov Chains
- Markov Chain Monte Carlo: MCMC
- Poisson Process
- Queue theory
- Brownian Motion
- Stochastic Calculus
Homework
- All homework can be done in any language. Most are either in the R programming language or in Scilab/Matlab and Python.
- If you do the homework in two different languages, you get double the homework grade (bonus of 100%)
- Late homework will be accepted but penalized at the professor's will according to how late it is
- All electronic material must be sent to the professors' email, with the string "[iprj-pe]" as part of the subject of the email. You will receive an automatic confirmation.
Assignment -1: se inscrever na lista de discussão (data: quarta 16set20)
- Enviar email para: iprj-estocasticos-2020-PAE+subscribe@googlegroups.com
- Responder ao email do professor sobre o PDFs dos livros com "OK"
- Quem ja realizou esta tarefa como parte do periodo cancelado, favor re-enviar
Assignment 0
- Ex 1.1 of the main book
- Handrwitten and scanned
- Due date: 22set20 (sugerida)
Assignment 1
- Exercise 1 Ch1 of the Pattern Theory book by Mumford & Desolneux,
Simulating Discrete Random Variables (pp 51, 52, 53)
- Type your solutions in Latex
- Due date: 29set20 (suggested), extendido para 13Out20
- No need to read this book for this exercise. You will review discrete random variables in the context of Markov chains for natural language processing; this is basic for most AI bots nowadays. If you're curious about the applications, you can read the book chapter just for fun.
Assignment 2: Exercise list for chapter 1
7 Exercises: 1.3, 1.5, 1.6, 1.7, 1.9, 1.10, 1.19
- Due date: 29Set20 (suggested)
Assignment 3: Exercise list for chapter 2
11 Exercises: 2.1, 2.4, 2.6, 2.8, 2.9, 2.10, 2.12, 2.14, 2.15, 2.18 Computer: 2.26
- Due date: 6Out20 (suggested), extendido para 13Out20
Assignment 4: Exercise list for chapter 3
Exercises: 3.2, 3.5a-c, 3.10a-d, 3.16i-iv, 3.25a-b, 3.37, 3.58
- Due date: before P1 (suggested)
Assignment 5: Exercise list for chapter 5 (MCMC)
4 Exercises: 5.1, 5.2, 5.5, 5.6
- Due date: inicio da P2
Assignment 6: Exercise list for chapter 6
2 Exercises: 6.3, 6.4 2 Bonus exercises (extra grading): 6.7, 6.8
- Due date: inicio da P2
Exams
- P1 (easy): 27Out20
- P2 (harder): 8Dez20
- Final-Sub: 14Dez20
Evaluation criteria
Ver este PDF
Awesome Links
- Course on robotic path planning with applications of stochastic processes: https://natanaso.github.io/ece276b/schedule.html
- Paper: Markovian robots: minimal navigation strategies for active particles, Arxiv 2017
- Paper: Stochastic processes in vision: from Langevin to Beltrami https://ieeexplore.ieee.org/document/937531/
- Cool applications: https://math.stackexchange.com/questions/1543211/which-research-groups-use-stochastic-processes-and-or-stochastic-differential-eq
- Paper: Building Blocks for Computer Vision with Stochastic Partial Differential Equations https://link.springer.com/article/10.1007/s11263-008-0145-5
- Paper: Variational Bayesian Multiple Instance Learning with Gaussian Processes, CVPR 2017
- Paper: Correlational Gaussian Processes for Cross-domain Visual Recognition, CVPR 2017
Neural Nets and Stochastic Processes
- Generative Models for Stochastic Processes Using Convolutional Neural Networks, arxiv, pesquisadores brasileiros (USP)
- Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding, Cipolla et. al arxiv 2016
Keywords
random fields, stochastic modeling, data science, queue theory, machine learning, poisson process, markov chains, Gaussian processes, Bernoulli processes, soft computing, random process, Brownian motion, robot path planning, artificial intelligence, simulation, sampling, pattern formation, signal processing, text processing, image processing, dimentionality reduction, diffusion, Markov Chain Monte Carlo MCMC, tracking, branching process, stochastic calculus, SDEs