# Wednesday, March 14, 2001 - PowerPoint PPT Presentation

PPT – Wednesday, March 14, 2001 PowerPoint presentation | free to download - id: 990f1-ODQ4M The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Wednesday, March 14, 2001

Description:

### Kansas State University. Department of Computing and ... PAP. SHUNT. ANAPHYLAXIS. MINOVL. PVSAT. FIO2. PRESS. INSUFFANESTH. TPR. LVFAILURE. ERRBLOWOUTPUT ... – PowerPoint PPT presentation

Number of Views:42
Avg rating:3.0/5.0
Slides: 43
Provided by: lindajacks
Category:
Tags:
Transcript and Presenter's Notes

Title: Wednesday, March 14, 2001

1
KDD Group Presentation
Real Time Bayesian Networks Inference
Wednesday, March 14, 2001 Haipeng Guo KDD
Research Group Department of Computing and
Information Sciences Kansas State University
2
Presentation Outline
• Bayesian Networks Introduction
• Bayesian Networks Inference Algorithms Review
• Real Time Related Issues
• A Distributed Anytime Architecture for
Probabilistic reasoning from Santos paperSantos
1995
• Summary

3
Bayesian Networks Introduction
• Definition
• Why is it important?
• Examples
• Applications

4
Bayesian Networks
• Bayesian Networks, also called Bayesian Belief
networks, causal networks, or probabilistic
networks, are a network-based framework for
representing and analyzing causal models
involving uncertainty
• A BBN is a directed acyclic graph (DAG) with
conditional probabilities for each node.
• Nodes represent  random variables in a problem
domain
• Arcs  represent conditional dependence
relationship among these variables.
• Each node contains a CPT(Conditional
Probabilistic Table) that contains probabilities
of this node being specific values given the
values of its parent nodes.

5
Family-Out Example
• " Suppose when I go home at night, I want to know
if my family is home before I try the
doors.(Perhaps the most convenient door to enter
is double locked when nobody is home.) Now, often
when my wife leaves the houses, she turns on an
outdoor light. However, she sometimes turns on
the lights if she is expecting a guest. Also, we
have a dog. When nobody is home, the dog is put
in the back yard. The same is true if the dog has
bowel problems. Finally, if the dog is in the
back yard, I will probably hear her barking(or
what I think is her barking), but sometimes I can
be confused by other dogs. "

6
Asia Example from Medical Diagnostics
7
Why is BBN important?
• Offers a compact, intuitive, and efficient
graphical representation of dependence relations
between entities of a problem domain. (model the
world in a more natural way than Rule-based
systems and neural network)
• Handle uncertainty knowledge in mathematically
rigorous yet efficient and simple way
• Provides a computational architecture for
computing the impact of evidence nodes on
beliefs(probabilities) of interested query nodes
• Growing numbers of creative applications

8
Alarm Example the power of BBN
• The Alarm network
• 37 variables, 509 parameters (instead of 237)

9
Applications
• Medical diagnostic systems
• Real-time weapons scheduling
• Jet-engines fault diagnosis
• Intel processor fault diagnosis (Intel)
• Generator monitoring expert system (General
Electric)
• Software troubleshooting (Microsoft office
assistant, Win98 print troubleshooting)
• Space shuttle engines monitoring(Vista project)
• Biological sequences analysis and classification

10
Bayesian Networks Inference
• Given an observed evidence, do some computation
• An evidence e is an assignment of values to a set
of variables E in the domain, E Xk1, , Xn
• For example, E e Visit Asia True, Smoke
True
• Queries
• The posteriori belief compute the conditional
probability of a variable given the evidence,
• P(Lung Cancer Visit Asia TRUE AND Smoke
TRUE) ?
• This kind of inference tasks is called
Belief Updating
• MPE compute the Most Probable Explanation given
the evidence
• An explanation for the evidence is a complete
assignment X1 x1, , Xn xn that is
consistent with evidence. Computing a MPE is
finding an explanation such that no other
explanation has higher probability
• This kind of inference tasks is called Belief
revision

11
Belief Updating
• The problem is to compute P(XxEe) the
probability of query nodes X, given the observed
value of evidence nodes E e.
• For example Suppose that a patient arrives and
it is known for certain that he has recently
visited Asia and has dyspnea.
• - Whats the impact that this evidence has on
the probabilities of the other variables in the
network ? P(Lung Cancer) ?

Smoking
Visit to Asia
Lung Cancer
Tuberculosis
tub. or lung cancer
Bronchitis
Dyspnea
X-Ray
12
Belief Revision
Let W is the set of all nodes in our given
Bayesian network Let the evidence e be the
observation that the roses are okay. Our goal is
to now determine the assignment to all nodes
which maximizes P(we).
We only need to consider assignments where the
node roses is set to okay and maximize P(w), i.e.
the most likely state of the world given the
evidence that rose is ok in this world.
The best solution then becomes -
P(sprinklers F, rain T, street wet, lawn
wet, soil wet, roses okay) 0.2646
13
Complexity of BBN Inference
• Probabilistic Inference Using Belief Networks is
NP-hard. Cooper 1990
•  Approximating Probabilistic Inference in
Bayesian Belief Networks is NP-hard Dagum 1993
• Hardness does not mean we cannot solve inference.
It implies that
• We cannot find a general procedure that works
efficiently for all networks
• However, for particular families of networks, we
can have provably efficient algorithms either
exact or approximate
• Instead of a general exact algorithm, we seek for
special case, average case, approximate
algorithms
• Various of approximate, heuristic, hybrid and
special case algorithms should be taken into
consideration

14
BBN Inference Algorithms
• Exact algorithms
• Pearls message propagation algorithm(for single
connected networks only)
• Variable elimination
• Cutset conditioning
• Clique tree clustering
• SPI(Symbolic Probabilistic Inference)
• Approximate algorithms
• Partial evaluation methods by performing exact
inference partially
• Variational approach by exploiting averaging
phenomena in dense networks(law of large numbers)
• Search based algorithms by converting inference
problem to an optimization problem, then using
heuristic search to solve it
• Stochastic sampling also called Monte Carlo
algorithms

15
PolyTree
• Singly Connected Networks(or Polytrees)

Definition A directed acyclic graph (DAG) in
which at most one undirected path exists between
any two nodes.
Multiple parents and/or multiple children
Polytree structure satisfies definition
Do not satisfy definition
16
Propagation Algorithm Objective
Data
Data
• The algorithms purpose is fusing and
propagating the impact of new evidence and
beliefs through Bayesian networks so that each
proposition eventually will be assigned a
certainty measure consistent with the axioms of
probability theory. (Pearl, 1988, p 143)

17
PolyTree Propagation Example
The impact of each new piece of evidence is
viewed as a perturbation that propagatesthroughth
e network via message-passing betweenneighboring
variables . . . (Pearl, 1988, p 143)
? Message to Parent
? Message from Parent
Data
Data
• Exact algorithm, for Polytree only, linear in the
size of the network

18
Cutset Conditioning Algorithm
• Transfer the network into several simpler
polytrees by conditioning the cutset and then
call the Polytree propagation algorithm. Each
simple network has one or more variable
instantiated to a definite value. P(XE) is
computed as a weighted average over the values
computed by each polytree. Pearl 1988
• A cutset is a set of nodes when instantiated will
render the network single connected.
• First exact algorithm for multiple connected
networks, exponential time complexity in the
size of the cutset.
• There are exponentially many such cutset
instantiations

19
Clique Tree Clustering Algorithm
• Transform the network into a tree of cliques,
then computes probabilities for the cliques
during a two-way message passing and the
individual node probabilities P(XE) are
calculated from the probabilities of cliques
• A clique W of G is a maximal complete subset of
G, that is, there is no other complete subset of
G which properly contains W
• The most common used exact inference algorithm
for general networks
• Efficient for sparse networks, but could have a
very bad performance for more general, dense
networks
• Exact, for multiple connected networks,
exponential time complexity in the size of the
network

20
Clique tree clustering
Triangulation
Moralization
Identify Cliques
?,? Message passing
P(Clqi) and P(XE)
Form Clique Tree
21
Variable Elimination Algorithm
• General idea
• Write query in the form
• Iteratively
• Move all irrelevant terms outside of innermost
sum
• Perform innermost sum, getting a new term
• Insert the new term into the product
• Computation depends on order of elimination, a
good elimination orderings can reduce
complexity
• The size of the largest clique in the induced
graph is thus an indicator for the complexity of
variable elimination. This quantity is called the
induced width of a graph according to the
specified ordering
• Finding an ordering that minimizes the induced
width is NP-Hard
• Exact, for all networks, exponential time
complexity, inefficient

22
SPI(Symbolic Probabilistic Inference)
• General idea
• Transform BBN inference problem into a
well-defined combinatorial optimization problem -
the Optimal Factoring Problem(OFP). Thus the
problem becomes to find an optimal factoring
given a set of probability distribution. The
solution of the OFP is then used to combine the
CPT that describe the BBN and extract the desired
marginal distribution.
• OFP itself is NP-Hard.
• Exact, for all networks, exponential time
complexity, inefficient

Factoring 1 needs 72 multiplications
Factoring 2 needs only 28 multiplications
23
Approximate Algorithms
• Exact Inference for large-scale networks is
apparently infeasible.
• Real life network can be up to thousands nodes.
• For example QMR(Quick medical Reference)
consists of a combination of statistical
• and expert knowledge for approximately 600
significant diseases and 4000 findings.
• The median size of the maximal clique of the
moralized graph is 151.5 nodes. Its
• intractable for all exact inference algorithms.
• Approximate algorithms can be categorized into
• Partial evaluation methods by performing exact
inference partially
• Variational approach by exploiting averaging
phenomena in dense networks(law of large numbers)
• Search based algorithms by converting inference
problem to an optimization problem, then using
heuristic search to solve it
• Stochastic sampling also called Monte Carlo
algorithms

24
Perform Exact Algorithm Partially
• General idea reduce the complexity by reducing
the solution space
• Partial sets of nodes instantiation
• Partial sets of hypotheses
• Partial set of nodes
• Bounded conditioningCooper 1991
• Localized partial evaluationDraper 1994
• incremental SPIDAmbrosio 1993
• Probabilistic partial evaluationPoole 1997
• Mini-buckets algorithmDechter 1997
• Approximate, for all networks, complexity not
clear

25
Variational Method
• General idea exploit averaging phenomena in
dense graph
• A sum can be avoided if it contains a sufficient
number of terms such that a law of large numbers
can be invoked
• Graphically, the model is transformed into a
sub-graph of the original model in which some of
the finding nodes are delinked until its
possible to run an exact algorithm on the
resulting graph. Jaakkola Jordan 1999
• Approximate, efficient, for dense graph only

26
Search based algorithms
• General idea Convert the problem into an
optimization problem then use heuristic search
to solve it.
• Consider node instantiations across the entire
graph
• Exploiting characteristics of problem domain to
help search
• A general hop is that a relatively small fraction
of the exponentially many node instantiations
contains a majority of the probability mass, and
by exploring the high probability
instantiations(bounding the unexplored
probability mass) one can obtain reasonable
bounds on posterior probabilities.
• Cooper 1985, Peng Reggia 1987, Henrion 1991
• Best-first search(A), linear programming,
genetic algorithm
• Charniak 1994, Santos 1993, Carlos 1993
• Approximate, heuristic, maybe fail

27
Stochastic Sampling Algorithms
• General idea Run repeated simulations according
to the BBN, the probability of an event of
interest is estimated using the frequency with
which that event occurs in a set of samples.
• Logic sampling henrion 1988
• forward sampling
• backward sampling Fung 1994
• Likelihood weighting Fung Chang 1990
• Important sampling Shachter 1990
• Approximate, performance depends only on the
CPTs, can handle very large networks, but has
difficulty with extremely unlikely events.

28
Inference Algorithm Conclusions
• The general problem of exact inference is
NP-Hard.
• The general problem of approximate inference is
NP-Hard.
• Exact inference works for small, sparse networks
only.
• No single champion either exact or inference
algorithms.
• The goal of research should be that of
identifying effective approximate techniques that
work well in large classes of problems.
• Another direction is the integration of various
kinds of approximate and exact algorithms
exploiting the best characteristics of each
algorithm.

29
A Distributed Anytime Inference Architecture
• On a Distributed Anytime Architecture for
Probabilistic Reasoning
• Air Force Institute of Technology
• Eugene Santos Jr. , 1995

30
Anytime algorithms
• To meet the demand for real-time inference, an
inference algorithm must have two capibilities
• Provide a near optimal solution at any given
moment
• Improving upon solutions as more time and
resources are allocated
• Algorithms which have this property of producing
a solution at any point in time are called
anytime algorithms

31
Anywhere Algorithms
• To exploit parallelism and distributed processing
to reduce the time complexity, the tasks in the
distributed environment must be able to exploit
intermediate results produced by the other
components of the system.
• Algorithms with this property are called
anywhere algorithms.
• When different algorithms having both anytime and
anywhere properties are harnessed together into a
cooperative system, the resultant architecture
can exploit the best characteristics of each
algorithm.

32
The OVERMIND Architecture
• Part of PESKI, an online expert system for engine
diagnosis for the Space Shuttle Program
• Three components
• IRA(Intelligent Resource Allocator)
• Manages and allocates available computing
resources
• OVERSEER(Overseer task Manager)
• Initiates new tasks, directs messages/information
• LOTS(Library of Tasks)
• A set of BBN inference algorithms suitable for
performing various including an A search
algorithm, a genetic algorithm, an integer linear
programming algorithm and a hybrid stochastic
algorithm(HySS)

33
General Idea
• The best algorithm to use is problem-instance
dependent.
• In a set of anywhere algorithms, if each
particular algorithm is good at certain portion
of a problem we can then take the partial
solution of an algorithm and pass it to another
approach which itself works better on the new
portion
• This leads to an anytime anywhere solution

34
Genetic Algorithms
• A heuristic search algorithm modeled after
natural genetic evolutions
• Has anytime and anywhere property.
• No stopping criterion that guarantees an optimal
• Its ability to generate solutions early can serve
as a starting point if possible for other
deterministic algorithm.

35
Best-First Search(A)
• A heuristic algorithm searching for optimal
solution from initial state
• Provide an approximate answer when interrupted
• Allow the algorithm to accept initial guess from
another sources
• Use Best-first search to find the most probable
complete instantiation among those compatible
with the guess

36
IRA(Intelligent Resource Allocator)
• Serve to maximize processor use by coordinating
requests for resources from OVERSEER and the
• Hardware a network of workstations
• Identify resource requirements for different
• GA single CPU
• ILP multi processing

37
• Currently simple messager role
• Advance capabilities involve deliberation
scheduling employing meta-reasoning to consider
what computational tasks to execute.
• To do this, some estimate of runtime and quality
of results should be available foe each
algorithm.

38
Implementation and results
• The strengths of different methods are combined
together
• Gas produce reasonable solution immediately
• A took those solutions near some maximas
• HySS fine-tuned those maximas
• ILP finished the optimization and generated te
optimal solution
• Result
• Initial test multiple instances of GAs
• GAs 20 speed up
• HySS 35 speed up
• A and ILP 1525 speed up

39
Summary
• Exploited the anytime anywhere properties of
several inference algorithms such as Gas, ILP and
A and unified them into a single model of
parallel computation.
• The architecture can use the best characteristics
of each algorithm.

40
Future Research
• Consider more algorithms
• Study the relationship between the problem domain
and the corresponding solutions domain to help
deliberation scheduling.

41
The End
• Any Questions ?

42
Linear Programming
• The problem of finding the most probable
explanation has been transformed into an integer
linear programming problem with a set of
constraints to satisfied.
• Efficient algorithms for linear programming can
be used to compute the optimal solution