582636 Probabilistic models (ohtk 25.8.2011)
| Principal theme | Prerequisite knowledge | Approaches the learning objectives | Reaches the learning objectives | Deepens the learning objectives |
|---|---|---|---|---|
|
Role of probability theory in knowledge representation and uncertain reasoning |
Basics of first-order logic and probability theory |
Can explain the basic concepts like joint probability distribution, conditional distribution, Bayes rule, and conditional independence, and by using these concepts, can formulate the basic probabilistic inference problems Can explain the meaning of a Bayesian network model as a parametric model (set of probability distributions), factorization of a joint probability distribution, and as an independence model (using d-separation, and local and global Markov properties). |
Can compute conditional distributions from a fixed discrete, Naïve Bayes classifier, finite mixture model Can implement a probabilistic inference algorithm for a fixed singly-connected graph with the parameters given |
Can implement a probabilistic inference algorithm for a discrete multi-connected graph Can justify the use of probability theory based on theoretical arguments like the Dutch book or the Cox theorem |
|
Parameter learning and Bayesian reasoning |
Introduction to Machine Learning |
Can derive the maximum likelihood parameters, the maximum posterior parameters (with conjugate prior), and the expected parameters for the Multinomial distribution Can explain the role of the parameter prior in parameter learning |
Can learn a Naïve Bayes Classifier from a set of data and use the model for predictive inference
Can learn the parameters of a Bayesian network from a set of data and use the model for predictive inference |
Can learn the parameters of continuous models In the discrete case, can implement the EM algorithm for learning the parameters of a finite mixture model |
|
Parametric model structure learning |
Introduction to Machine Learning |
Can explain the model structure learning problem and how that differs from the parameter learning problem Can explain what over-fitting is Can explain the concept of equivalence class and say whether two networks are equivalent or not |
Knows how to compute the marginal likelihood for discrete Bayesian networks and can explain how to use that for model structure selection
Can implement an algorithm for learning a discrete Bayesian network, given data |
Can derive the formula for computing the marginal likelihood Knows other model selection criteria in addition to marginal likelihood |
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