MACHINE LEARNING A BAYESIAN AND
OPTIMIZATION PERSPECTIVE UPDATED
ACTUAL QUESTIONS AND CORRECT
ANSWERS COMPLETE STUDY GUIDE FULL
SOLUTION
●● What is the Sample Subspace
Answer: Set out Outcomes
●● What is an Event
Answer: Subset of the sample space
●● What is the Conditional Probability
Answer:
●● What is the Sum Rule
Answer: P(A) = Sum P(A, B)
●● What is Bayes Rule
Answer:
,●● What is a Random Variable
Answer: Function from sample space to R or a subset of R
●● What is the Multinomial Distribution
Answer: Multiple categories of N trials with each outcome having a
different probability
●● What is a Dirichlet Distribution
Answer: Continuous multivariate probability distributions parameterized
by a vector of alphas
●● What is a Multivariate Gaussian Distribution
Answer: Random vector with many gaussian variables and covariance
matrix
●● What is the Wishart Distribution
Answer: Made up of random matrices instead of vectors
●● What is Conditioning
Answer: Finding the denominator of Bayes theorem using the sum rule.
Treating an event as being known to have occurred.
●● What is a Noninformative Prior
, Answer: Approach taken when we dont know much about whats going
on
●● What is a Conjugate Prior
Answer: Approach that is very fast and effective where the posterior has
exactly the same distribution as the prior. It is a convenient use way to
pick a prior as well as a closed form analytical solution that is fast for
computation and prediction.
●● What are disadvantages of Conjugate Priors
Answer: 1. Minimize importance of the data
2. Restrictive to the distributions available
3. May get good answer to the wrong problem
●● What are some univariate Conjugate Priors
Answer: Beta-Binomial, Gaussian Gaussian, Gaussian t-distribution
●● What are some multivariate Conjugate Priors
Answer: Dirchilet-Multinomial, Multivariate Gaussian Gaussian
●● Laplace Principle for Insufficient Reason
Answer: Without further knowledge assume a uniform distribution.
Problems are improper, not coherent, and not invariant under
transformation
OPTIMIZATION PERSPECTIVE UPDATED
ACTUAL QUESTIONS AND CORRECT
ANSWERS COMPLETE STUDY GUIDE FULL
SOLUTION
●● What is the Sample Subspace
Answer: Set out Outcomes
●● What is an Event
Answer: Subset of the sample space
●● What is the Conditional Probability
Answer:
●● What is the Sum Rule
Answer: P(A) = Sum P(A, B)
●● What is Bayes Rule
Answer:
,●● What is a Random Variable
Answer: Function from sample space to R or a subset of R
●● What is the Multinomial Distribution
Answer: Multiple categories of N trials with each outcome having a
different probability
●● What is a Dirichlet Distribution
Answer: Continuous multivariate probability distributions parameterized
by a vector of alphas
●● What is a Multivariate Gaussian Distribution
Answer: Random vector with many gaussian variables and covariance
matrix
●● What is the Wishart Distribution
Answer: Made up of random matrices instead of vectors
●● What is Conditioning
Answer: Finding the denominator of Bayes theorem using the sum rule.
Treating an event as being known to have occurred.
●● What is a Noninformative Prior
, Answer: Approach taken when we dont know much about whats going
on
●● What is a Conjugate Prior
Answer: Approach that is very fast and effective where the posterior has
exactly the same distribution as the prior. It is a convenient use way to
pick a prior as well as a closed form analytical solution that is fast for
computation and prediction.
●● What are disadvantages of Conjugate Priors
Answer: 1. Minimize importance of the data
2. Restrictive to the distributions available
3. May get good answer to the wrong problem
●● What are some univariate Conjugate Priors
Answer: Beta-Binomial, Gaussian Gaussian, Gaussian t-distribution
●● What are some multivariate Conjugate Priors
Answer: Dirchilet-Multinomial, Multivariate Gaussian Gaussian
●● Laplace Principle for Insufficient Reason
Answer: Without further knowledge assume a uniform distribution.
Problems are improper, not coherent, and not invariant under
transformation
