Loading in 2 Seconds...

Relational Markov Models and their Application to Adaptive Web Navigation

Loading in 2 Seconds...

1 Views

Download Presentation
##### Relational Markov Models and their Application to Adaptive Web Navigation

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Relational Markov Models and their Application to Adaptive**Web Navigation Corin Anderson, Pedro Domingos, Daniel Weld**Review: Hidden Markov Models**• Sequence of States • Transition distribution to next state dependant on evidence variable and current state only (in first-order case)**DBNs: A Step Up**• Multiple nodes at each state in the sequence • “Object-oriented” view**Complaint 1: Too General!**• Absolute restriction imposed on structure of state • Could individual state structure be exploited? • Adopt “Polymorphic” view**Complaint 2: Not General Enough!**• Accurate probability estimation difficult with sparse data • P(Mac_instock|mainpage) = 0 • P(apple|mainpage) = 0.375 Web log for pages linked from main_page.html**Solution: RMM**• Represent sets of states as a relation (predicate) with instantiations of the relation defining specific states • E.g. – product_page(mac, in_stock) main_page() • Transitions can now occur from sets to sets and sets to states**Going further . . .**• Using predicates defines a basic hierarchy over the state space • Why not impose further structure within each predicate argument? • Tree leaves correspond to unique arguements**Sets of sets**• Define the set of abstractions of a given state q = R( . . .) to be a set of states such that each argument to R in the abstraction is an ancestor to the corresponding argument in q. • More Formally (scientists love fancy math): R – The relation, Q – set of all possible instantiations of R d – possible arguments, D – the tree of a particular type of argument, delta – the arguments to the predicate for the given state q.**Learning with Abstractions**• Transitions between a state and an abstraction: • In practice, we can just count instances in the data. Where a is a transition matrix, q is a ground state (individual state), and alpha and beta are abstracted arguments.**Defining a mixture model**• Estimating the transition probability between ground states qs and qd: • Note that choosing lambda properly is crucial Where lambda is a mixing coefficient based on alpha and beta in the range [0,1] such that the sum of all lambdas is 1.**Choosing Lambda:**• There is a bias-variance tradeoff • Possibly high variance at lowest abstraction level • High bias at highest abstraction level • A good choice will have two properities: • Gets higher as abstraction depth increases • Gets lower as available training data decreases Where n = possible transitions from alpha to beta in the data, k is a design parameter to penalize lack of data, and rank(a) is where each d is an argument to the relation defining a.**Probability Estimation Tree**• With deep hierarchies and lots of arguments, considering every possible abstraction may not be feasible • Learn a decision tree over possible abstractions • To the left is the tree for the page Product_page(mac, in_stock)**Empirical Evaluation**• How well do the various flavors of RMM (RMM-uniform, RMM-Rank, RMM-PET) compare to traditional MMs? • Analyzed several web logs in various domains. • Tried to predict transition probabilities between pages using varied amounts of training data.**Related Work: The Cube**• Exploiting structure within RMM states (DPRM)