Bayesian networks
History
- created by Judea Pearl in 1985
2011 ACM Turing Award
- named after Thomas Bayes
uses Bayes' conditioning
- informal variant in 1913
Motivation
- model of the problem domain probability distribution
- probability theory provides a consistent calculus
- intuitively interpretable
- handles missing values
- flexible applicability
Conditional Independence
Two random variables X and Y are conditionally independent given a third random variable Z if and only if they are independent in their conditional probability distribution given Z.
Bayesian network
Each node is conditionally independent of its nondescendants given its parents
Chain rule
Naive bayes
Inference
- deriving logical conclusions from premises known or assumed to be true
- BNs have all necessary information
- can compute any subset of variables from any other
- generally NP-Hard
- exact inference
- Monte Carlo methods
Inference
Inference
Demo
Learning BN
- estimate parameters
- learn structure
Estimating parameters
- Maximum likelihood for complete data
- EM for incomplete data
Expectation maximization
- initialize parameters ignoring missing data
- repeat until model converges
E - calculate missing values using learned model
M - relearn model with new (computed) data
Structure learning
- state space search
- score based
- initially no connections or expert made
- penalty for each connection
- must avoid cycles
- correlation between attributes, MAP
- using ML resluts in maximum network
BNs and timeseries
- dynamic BNs
- each point in time, timeslice, is BN
- conditional dependencies between and within timeslices
BNs and timeseries
Applications of BNs
- victims identification
- oil exloration
- wireless 3G and 4G codecs
- spam filtering
- cancer risk modeling
- biomonitoring
- decision support systems
Using Bonaparte, all victims of the plane crashes in Tripoli (2010) and the Ukraine (MH17, 2014) were identified. In 2012 Bonaparte was used to solve a notorious 13 years old cold case (the Vaatstra Case). Recently Bonaparte was used to identify a serial rapist in Utrecht (2014).
Bayesian Network for Disaster Victim
Identification
Estimates the type of soil and the probability that it contains oil, gas or other valuable minerals, based on drilling measurements. The system is based on a Bayesian network where the probability computation is done using a Monte Carlo sampling method.
Used by Shell.
References
- "Machine Learning by Pedro Domingos." Coursera. University of Washington
- F. V. Jensen, T. D. Nielsen, "Bayesian Networks and Decision Graphs", 8 Feb. 2007
- "Bayesian Network." Wikipedia. Wikimedia Foundation, n.d. Web. 17 Apr. 2015
- Mihajlovic V, M Petkovic. Dynamic Bayesian Networks: A State Of The Art. 1st ed. University of Twente, 2015
Bayesian networks
By Martin Barus
Bayesian networks
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