VE generalizes Resolution Resolution A or B B or C A or C A B C AC Variable Elimination There is still an important difference, though.
Story so far Logic uses absolute rules; Probabilistic models can deal with noise, and generalize logic; But...
Logical reasoning ends early office meeting office talk office pick_book... Given evidence meeting, we are done after considering first rule alone.
Ending early in deterministic graphical model Variable Elimination uses all nodes to calculate P(office | meeting) officemeeting talk pick_book
Ending early in deterministic graphical model But if meeting is observed, we dont need to look beyond it office talk pick_book
Ending early in deterministic graphical model We can use smarter algorithms to end early here as well office talk pick_book
Ending early in non-deterministic graphical models Calculating P(noisy_office | meeting) noisy_officemeeting talk pick_book
Ending early in non-deterministic graphical models P(noisy_office | meeting) depends on all nodes noisy_office talk pick_book
Ending early in non-deterministic graphical models noisy_office talk pick_book But we already know P(noisy_office | meeting) [0.99, 0.9992] Can we take advantage of this?
Goal A graphical model inference algorithm that derives a bound on solution so far; Ends as soon as bound is good enough; An anytime algorithm.
Probabilistic Resolution Resolution A or B B or C A or C A B C AC Variable Elimination Variable Elimination generalizes Resolution, but neither provides intermediate results nor ends early. Probabilistic Resolution = VE + ending early
Story so far Logic uses absolute rules; Probabilistic models can deal with noise, and generalize logic; Logic ends as soon as possible, graphical models do not; They can if we are willing to use bounds; But how to calculate bounds?
Algorithm Same as Variable Elimination, but update bounds every time a neighbor is eliminated; Bounds always improve at each neighbor elimination; Trade-off between granularity of bound updates (explain granularity) and ordering efficiency.
Complexity Issues Calculating bound is exponential on the size of neighborhood component, so complexity is exponential on largest neighborhood component during execution; This can be larger than tree-width; But finding tree-width is hard anyway.
Your consent to our cookies if you continue to use this website.