1. Dependency Networks for Collaborative Filtering and Data Visualization UAI-2000 발표 : 황규백

2. Abstract Dependency networks  An alternative for the Bayesian network  A (cyclic) directed graph Basic properties of dependency networks Dependency networks for collaborative filtering Dependency networks for data visualization

3. Introduction A dependency network  A collection of regression/classification models among variables combined using Gibbs sampling  Disadvantages Not useful for encoding a causal relationships  Advantages Quite useful for encoding a predictive relationships

4. Representation of Joint Distribution In Bayesian networks In dependency networks  Via ordered Gibbs sampler Initialize each variable randomly. Resample each X i according to  Theorem 1: An ordered Gibbs sampler applied to a dependency network for X, where each X i is discrete and each local distribution p(x i |pa i ) is positive, has a unique stationary distribution for X.

5. Conditional Distribution Gibbs sampling is used.  Not so disadvantageous Learning  Not representing the causal relationships  Each local distribution can be learned without regard to acyclicity constraints. Consistency and inconsistency  Inconsistent dependency networks All conditional distributions are not obtainable from a single joint distribution p(x).  Theorem 2: If a dependency network for X is consistent with a positive distribution p(x), then the stationary distribution defined in Theorem 1 is equal to p(x).

6. Other Properties of Dependency Networks Markov networks and dependency networks  Theorem 3: The set of positive distributions consistent with a dependency network structure is equal to the set of positive distributions defined by a Markov network structure with the same adjacencies.  Defining the same distributions, however, representational forms are different. Potentials vs. Conditional probabilities Minimality of the dependency network  For every node X i, and for every parent pa i j, X i is not independent of pa i j given the remaining parents of X i.  Theorem 4: A minimal consistent dependency network for a positive distribution p(x) must be bi-directional.

7. Learning Dependency Networks Each local distribution for X i is simply a regression/classification model for x i with X \ {x i } as inputs.  Generalized linear models, neural networks, support-vector machines, … In this paper, the decision tree was used.  A simple hill-climbing approach with a Bayesian score

8. Collaborative Filtering Preferences prediction  Implicit/explicit voting  Binary/non-binary preferences Bayesian network approach In a dependency network

9. Datasets for Collaborative Filtering MS.COM(Webpages), Nielsen(TV show), MSNBC(Stories in the site)

10. Evaluation Criteria and Experimental Procedure Accuracy of the list given by a predictive model Average accuracy of a model  A case in the test set (randomly partitioned)

11. Results on Accuracy Higher score indicates better performance.

12. Results on the Prediction Time Number of predictions per second

13. Results on Computational Resources Computational resources for model learning

14. Data Visualization Predictive relationships (not causal)  Bayesian networks often interfere with the visualization of such relationships.  Dependent or independent Example  DNViewer  Media Metrix data

15. DNViewer A dependency network for Media Metrix data

16. DNViewer for Local Distribution Local probability distribution

17. Summary and Future Work The dependency network  defines a joint distribution for variables.  is easy to learn from data.  is useful for collaborative filtering and data visualization.  is for conditionals. The Bayesian network  is for joint probability distribution.