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Transcript of Introduction to Model-Based Machine Learning for Transportation
Introduction Probabilistic Programming Case Study
Introduction to Model-Based MachineLearning
A Webinar to TRB ADB40 Big Data Initiative
by
Daniel Emaasit1
1Ph.D. StudentDepartment of Civil and Environmental Engineering
University of Nevada, Las Vegas, [email protected]
September 27 2016
1 / 20
Introduction Probabilistic Programming Case Study
Current Challenges in Adopting Machine Learning
I Generally, current challenges in adopting ML:
I Overwhelming number of traditional ML methods to learnI Deciding which algorithm to use or whyI Some custom problems may not fit with any existing
algorithm
3 / 20
Introduction Probabilistic Programming Case Study
Current Challenges in Adopting Machine Learning
I Generally, current challenges in adopting ML:I Overwhelming number of traditional ML methods to learn
I Deciding which algorithm to use or whyI Some custom problems may not fit with any existing
algorithm
3 / 20
Introduction Probabilistic Programming Case Study
Current Challenges in Adopting Machine Learning
I Generally, current challenges in adopting ML:I Overwhelming number of traditional ML methods to learnI Deciding which algorithm to use or why
I Some custom problems may not fit with any existingalgorithm
3 / 20
Introduction Probabilistic Programming Case Study
Current Challenges in Adopting Machine Learning
I Generally, current challenges in adopting ML:I Overwhelming number of traditional ML methods to learnI Deciding which algorithm to use or whyI Some custom problems may not fit with any existing
algorithm
3 / 20
Introduction Probabilistic Programming Case Study
What is Model-Based Machine Learning?
I A different viewpoint for machine learning proposed byBishop (2013)1, Winn et al. (2015)2
I Goal:
I Provide a single development framework which supports thecreation of a wide range of bespoke models
I The core idea:
I all assumptions about the problem domain are madeexplicit in the form of a model
1Bishop, C. M. (2013). Model-Based Machine Learning. PhilosophicalTransactions of the Royal Society A, 371, pp 1–17
2Winn, J., Bishop, C. M., Diethe, T. (2015). Model-Based MachineLearning. Microsoft Research Cambridge. http://www.mbmlbook.com.
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Introduction Probabilistic Programming Case Study
What is Model-Based Machine Learning?
I A different viewpoint for machine learning proposed byBishop (2013)1, Winn et al. (2015)2
I Goal:
I Provide a single development framework which supports thecreation of a wide range of bespoke models
I The core idea:
I all assumptions about the problem domain are madeexplicit in the form of a model
1Bishop, C. M. (2013). Model-Based Machine Learning. PhilosophicalTransactions of the Royal Society A, 371, pp 1–17
2Winn, J., Bishop, C. M., Diethe, T. (2015). Model-Based MachineLearning. Microsoft Research Cambridge. http://www.mbmlbook.com.
4 / 20
Introduction Probabilistic Programming Case Study
What is Model-Based Machine Learning?
I A different viewpoint for machine learning proposed byBishop (2013)1, Winn et al. (2015)2
I Goal:I Provide a single development framework which supports the
creation of a wide range of bespoke models
I The core idea:
I all assumptions about the problem domain are madeexplicit in the form of a model
1Bishop, C. M. (2013). Model-Based Machine Learning. PhilosophicalTransactions of the Royal Society A, 371, pp 1–17
2Winn, J., Bishop, C. M., Diethe, T. (2015). Model-Based MachineLearning. Microsoft Research Cambridge. http://www.mbmlbook.com.
4 / 20
Introduction Probabilistic Programming Case Study
What is Model-Based Machine Learning?
I A different viewpoint for machine learning proposed byBishop (2013)1, Winn et al. (2015)2
I Goal:I Provide a single development framework which supports the
creation of a wide range of bespoke models
I The core idea:
I all assumptions about the problem domain are madeexplicit in the form of a model
1Bishop, C. M. (2013). Model-Based Machine Learning. PhilosophicalTransactions of the Royal Society A, 371, pp 1–17
2Winn, J., Bishop, C. M., Diethe, T. (2015). Model-Based MachineLearning. Microsoft Research Cambridge. http://www.mbmlbook.com.
4 / 20
Introduction Probabilistic Programming Case Study
What is Model-Based Machine Learning?
I A different viewpoint for machine learning proposed byBishop (2013)1, Winn et al. (2015)2
I Goal:I Provide a single development framework which supports the
creation of a wide range of bespoke models
I The core idea:I all assumptions about the problem domain are made
explicit in the form of a model1Bishop, C. M. (2013). Model-Based Machine Learning. Philosophical
Transactions of the Royal Society A, 371, pp 1–172Winn, J., Bishop, C. M., Diethe, T. (2015). Model-Based Machine
Learning. Microsoft Research Cambridge. http://www.mbmlbook.com.4 / 20
Introduction Probabilistic Programming Case Study
What is a Model in MBML?
I A Model:
I is a set of assumptions, expressed in mathematical/graphicalform
I expresses all parameters, variables as random variablesI shows the dependency between variables
Figure 1: Description of a model5 / 20
Introduction Probabilistic Programming Case Study
What is a Model in MBML?
I A Model:I is a set of assumptions, expressed in mathematical/graphical
form
I expresses all parameters, variables as random variablesI shows the dependency between variables
Figure 1: Description of a model5 / 20
Introduction Probabilistic Programming Case Study
What is a Model in MBML?
I A Model:I is a set of assumptions, expressed in mathematical/graphical
formI expresses all parameters, variables as random variables
I shows the dependency between variables
Figure 1: Description of a model5 / 20
Introduction Probabilistic Programming Case Study
What is a Model in MBML?
I A Model:I is a set of assumptions, expressed in mathematical/graphical
formI expresses all parameters, variables as random variablesI shows the dependency between variables
Figure 1: Description of a model5 / 20
Introduction Probabilistic Programming Case Study
Key Ideas of MBML?
I MBML is built upon 3 key ideas
I the use of Probabilistic Graphical Models (PGM)
I the adoption of Bayesian ML
I the application of fast, deterministic inference algorithms
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Introduction Probabilistic Programming Case Study
Key Ideas of MBML?
I MBML is built upon 3 key ideasI the use of Probabilistic Graphical Models (PGM)
I the adoption of Bayesian ML
I the application of fast, deterministic inference algorithms
6 / 20
Introduction Probabilistic Programming Case Study
Key Ideas of MBML?
I MBML is built upon 3 key ideasI the use of Probabilistic Graphical Models (PGM)
I the adoption of Bayesian ML
I the application of fast, deterministic inference algorithms
6 / 20
Introduction Probabilistic Programming Case Study
Key Ideas of MBML?
I MBML is built upon 3 key ideasI the use of Probabilistic Graphical Models (PGM)
I the adoption of Bayesian ML
I the application of fast, deterministic inference algorithms
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Introduction Probabilistic Programming Case Study
Key Idea 1: Probabilistic Graphical Models
I Combine probability theory with graphs (e.g Factor Graphs)
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Introduction Probabilistic Programming Case Study
Key Idea 2: Bayesian Machine Learning
I Everything follows from two simple rules of probabilitytheory
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Introduction Probabilistic Programming Case Study
Key Idea 3: Inference Algorithms
I the application of fast, approximate inference algorithms bylocal message passing
I Variational BayesI Belief Propagation, Loopy Belief PropagationI Expectation Propagation
(a) Learning by local messagepassing
(b) Inference algorithms
Figure 2: MCMC vs Approximate methods9 / 20
Introduction Probabilistic Programming Case Study
Key Idea 3: Inference Algorithms
I the application of fast, approximate inference algorithms bylocal message passing
I Variational Bayes
I Belief Propagation, Loopy Belief PropagationI Expectation Propagation
(a) Learning by local messagepassing
(b) Inference algorithms
Figure 2: MCMC vs Approximate methods9 / 20
Introduction Probabilistic Programming Case Study
Key Idea 3: Inference Algorithms
I the application of fast, approximate inference algorithms bylocal message passing
I Variational BayesI Belief Propagation, Loopy Belief Propagation
I Expectation Propagation
(a) Learning by local messagepassing
(b) Inference algorithms
Figure 2: MCMC vs Approximate methods9 / 20
Introduction Probabilistic Programming Case Study
Key Idea 3: Inference Algorithms
I the application of fast, approximate inference algorithms bylocal message passing
I Variational BayesI Belief Propagation, Loopy Belief PropagationI Expectation Propagation
(a) Learning by local messagepassing
(b) Inference algorithms
Figure 2: MCMC vs Approximate methods9 / 20
Introduction Probabilistic Programming Case Study
Stages of MBML
I 3 stages of MBML
I Build the model: Joint probability distribution of all therelevant variables (e.g as a graph)
I Incorporate the observed data
I Perform inference to learn parameters of the latentvariables
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Introduction Probabilistic Programming Case Study
Stages of MBML
I 3 stages of MBMLI Build the model: Joint probability distribution of all the
relevant variables (e.g as a graph)
I Incorporate the observed data
I Perform inference to learn parameters of the latentvariables
10 / 20
Introduction Probabilistic Programming Case Study
Stages of MBML
I 3 stages of MBMLI Build the model: Joint probability distribution of all the
relevant variables (e.g as a graph)
I Incorporate the observed data
I Perform inference to learn parameters of the latentvariables
10 / 20
Introduction Probabilistic Programming Case Study
Stages of MBML
I 3 stages of MBMLI Build the model: Joint probability distribution of all the
relevant variables (e.g as a graph)
I Incorporate the observed data
I Perform inference to learn parameters of the latentvariables
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Introduction Probabilistic Programming Case Study
Special cases of MBML
(a) Special cases
(b) For sequential data
Figure 3: Special Cases of Models
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Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approach
I Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
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Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutions
I Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledge
I Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled manner
I Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfitting
I Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problems
I Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative models
I Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternatives
I It’s general purpose: No need to learn the 1000s of existingML algorithms
I Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithms
I Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
Benefits of MBML
I Potential benefits of this approachI Provides a systematic process of creating ML solutionsI Allows for incorporation of prior knowledgeI Allows for handling uncertainity in a principled mannerI Does not suffer from overfittingI Custom solutions are built for specific problemsI Allows for quick building of several alternative modelsI Easy to compare those alternativesI It’s general purpose: No need to learn the 1000s of existing
ML algorithmsI Separates model from inference/training code
12 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:
I random variablesI constraints on variablesI inference
I Examples of PP software packages
I Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:
I random variablesI constraints on variablesI inference
I Examples of PP software packages
I Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variables
I constraints on variablesI inference
I Examples of PP software packages
I Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variables
I inference
I Examples of PP software packages
I Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variablesI inference
I Examples of PP software packages
I Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variablesI inference
I Examples of PP software packages
I Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variablesI inference
I Examples of PP software packagesI Infer.Net (C#, C++)
I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variablesI inference
I Examples of PP software packagesI Infer.Net (C#, C++)I Stan (R, python, C++)
I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variablesI inference
I Examples of PP software packagesI Infer.Net (C#, C++)I Stan (R, python, C++)I BUGS
I churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variablesI inference
I Examples of PP software packagesI Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI church
I PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
What is Probabilistic Programming?
I A software package that takes the model and thenautomatically generate inference routines (even source code!)to solve a wide variety of models
I Takes programming languages and adds support for:I random variablesI constraints on variablesI inference
I Examples of PP software packagesI Infer.Net (C#, C++)I Stan (R, python, C++)I BUGSI churchI PyMC (python)
14 / 20
Introduction Probabilistic Programming Case Study
How Probabilistic Programming works
Figure 4: How infer.NET works
15 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily TravelI Analysing the distribution of an individual cyclist’s daily
travel time to work
I Identify the variables of interestttn - travel time in the
nth dayat - average travel-timetu - uncertainty
ttn
at
tu
N
17 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily TravelI Analysing the distribution of an individual cyclist’s daily
travel time to workI Identify the variables of interest
ttn - travel time in thenth day
at - average travel-timetu - uncertainty
ttn
at
tu
N
17 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily TravelI Analysing the distribution of an individual cyclist’s daily
travel time to workI Specify relationships between variables
ttn - travel time in thenth day
at - average travel-timetu - uncertainty
ttn
at
tu
N
I Joint distribution is given by
p(tt, at, tu) = p(at) p(tu)︸ ︷︷ ︸priors
×N∏
n=1p(ttn|at, tu)︸ ︷︷ ︸likelihood
18 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily TravelI Analysing the distribution of an individual cyclist’s daily
travel time to workI Specify relationships between variables
ttn - travel time in thenth day
at - average travel-timetu - uncertainty
ttn
at
tu
N
I Joint distribution is given by
p(tt, at, tu) = p(at) p(tu)︸ ︷︷ ︸priors
×N∏
n=1p(ttn|at, tu)︸ ︷︷ ︸likelihood
18 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily Travel
I Analysing the distribution of an individual cyclist’s dailytravel time to work
I Joint distribution is given by
p(tt, as, tu) = p(at) p(tu)︸ ︷︷ ︸priors
×N∏
n=1p(ttn|at, tu)︸ ︷︷ ︸likelihood
I How should we define the likelihood p(ttn|at, tu)?
I the distribution’s mean is the cyclist’s average travel timeI the distribution’s variance determines how much the travel
time varies from day to day (e.g. variations in trafficconditions)
I What distributions should p(at) and p(tu) have?I conjugate priors! (well, at least most of the times...)
19 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily Travel
I Analysing the distribution of an individual cyclist’s dailytravel time to work
I Joint distribution is given by
p(tt, as, tu) = p(at) p(tu)︸ ︷︷ ︸priors
×N∏
n=1p(ttn|at, tu)︸ ︷︷ ︸likelihood
I How should we define the likelihood p(ttn|at, tu)?I the distribution’s mean is the cyclist’s average travel timeI the distribution’s variance determines how much the travel
time varies from day to day (e.g. variations in trafficconditions)
I What distributions should p(at) and p(tu) have?I conjugate priors! (well, at least most of the times...)
19 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily Travel
I Analysing the distribution of an individual cyclist’s dailytravel time to work
I Joint distribution is given by
p(tt, as, tu) = p(at) p(tu)︸ ︷︷ ︸priors
×N∏
n=1p(ttn|at, tu)︸ ︷︷ ︸likelihood
I How should we define the likelihood p(ttn|at, tu)?I the distribution’s mean is the cyclist’s average travel timeI the distribution’s variance determines how much the travel
time varies from day to day (e.g. variations in trafficconditions)
I What distributions should p(at) and p(tu) have?
I conjugate priors! (well, at least most of the times...)
19 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily Travel
I Analysing the distribution of an individual cyclist’s dailytravel time to work
I Joint distribution is given by
p(tt, as, tu) = p(at) p(tu)︸ ︷︷ ︸priors
×N∏
n=1p(ttn|at, tu)︸ ︷︷ ︸likelihood
I How should we define the likelihood p(ttn|at, tu)?I the distribution’s mean is the cyclist’s average travel timeI the distribution’s variance determines how much the travel
time varies from day to day (e.g. variations in trafficconditions)
I What distributions should p(at) and p(tu) have?I conjugate priors! (well, at least most of the times...)
19 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily Travel
I Likelihood given byp(ttn |at, tu) = N (ttn |at, tu)
I We now know what distribution forms to assign to thepriors...
p(at) = N (at|µ, σ2)p(tu) = InvGamma(tu|α, β)
I Set the hyper-parameters based on our prior knowledge ofthe domain (e.g. µ = 12, σ2 = 10, α = 2.0, β = 1.0)
I The choice of the initial parameters of the prior is significantonly if you have a small number of observations
I As the number of observations increases, the influence of theinitial prior on the posterior declines
20 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily Travel
I Likelihood given byp(ttn |at, tu) = N (ttn |at, tu)
I We now know what distribution forms to assign to thepriors...
p(at) = N (at|µ, σ2)p(tu) = InvGamma(tu|α, β)
I Set the hyper-parameters based on our prior knowledge ofthe domain (e.g. µ = 12, σ2 = 10, α = 2.0, β = 1.0)
I The choice of the initial parameters of the prior is significantonly if you have a small number of observations
I As the number of observations increases, the influence of theinitial prior on the posterior declines
20 / 20
Introduction Probabilistic Programming Case Study
A Bicyclist’s Daily Travel
I Likelihood given byp(ttn |at, tu) = N (ttn |at, tu)
I We now know what distribution forms to assign to thepriors...
p(at) = N (at|µ, σ2)p(tu) = InvGamma(tu|α, β)
I Set the hyper-parameters based on our prior knowledge ofthe domain (e.g. µ = 12, σ2 = 10, α = 2.0, β = 1.0)
I The choice of the initial parameters of the prior is significantonly if you have a small number of observations
I As the number of observations increases, the influence of theinitial prior on the posterior declines
20 / 20