© Daniel S. Weld 1 Midterm Search Space Bayes Net Learning / Cross Validation Lessons for the Final...

© Daniel S. Weld 1

Midterm• Search Space• Bayes Net• Learning / Cross Validation

• Lessons for the Final I’ll hit these areas again I’ll include one midterm problem verbatim Likely others with small changes

© Daniel S. Weld 2

Bayes Nets• Since a high-stakes murder case revolves on a

DNA sample found near the murder scene, the sample is sent to two different labs.

• Each lab uses it’s own machine to determine if there is a match (events M1 and M2).

• The accuracy of each machine depends on whether it is calibrated (C1 and C2).

• The judge hires you to analyze the situation, specifically to advise on the guilt, G, of the suspect.

© Daniel S. Weld 3

Structures

• Two astronomers in Chile & Alaska measure (M1, M2) the number (N) of stars.

• Normally there is a chance of error, e, of under or over counting by 1 star.

• But sometimes, with probability f, a telescope can be out of focus (events F1 and F2) in which case the affected scientist will undercount by 3 stars

F1 F2

M1 M2

N

F1 F2

M1 M2

N

F1 F2

M1 M2

N

© Daniel S. Weld 4

Cross validation

• Partition examples into k disjoint equiv classes• Now create k training sets

Each set is union of all equiv classes except one So each set has (k-1)/k of the original training data

Train Te

st

© Daniel S. Weld 5

Cross Validation



Test

© Daniel S. Weld 6

Cross Validation



Test

© Daniel S. Weld 7

Search• You are given 12 seemingly identical coins and

a two-pan scale. • One of the coins is lighter than or heavier than

the others. • Using the scale, you must identify the bogus

coin and determine if it is lighter than or heavier than the others;

• You are allowed to do at most 3 measurements.

Describe this challenge as a search problem

© Daniel S. Weld 8

Search

• States Partial “plans” to test the coins

• Operators Plan modification operators (e.g. adding a

measurement)

© Daniel S. Weld 9

Need Two Viewpoints• Belief State of Agent

Initially 24 possible world states: Coin A … L is bogus x {heavy, light}

• Plan of Agent And / or tree

measureA vs B …AB vs CD …ABCD vs EFGH

< >=

Al Bl Cl Dl Eh Fh Gh Hh Ah Bh Ch Dh El Fl Gl Hl

Il Ih Jl Jh Kl Kh Ll Lh

© Daniel S. Weld 10

Operators

measure ABCD vs EFGH

< >=

Al Bl C

l Dl E

h Fh G

h Hh

measureA vs B …AB vs CD …ABE vs CDF

< >=


Administrivia• Reading for today’s class: ch 5

• Reading for next Tues: ch 22

• Problem Set Out soon Programming?


Activity Recognition Natural

Language

573 Core Topics

Agency

Problem Spaces

Search

Knowledge Representation

ReinforcementLearning

Inference

PlanningClassical,

MDP, POMDP SupervisedLearning

Logic-Based Probabilistic

Constraint Satisfaction

CSE 573University of Washington


OutlineProblem spaces Search

BlindInformedLocal Heuristics & Pattern DBs forConstraint satisfaction

Definition• Factoring state spaces

Backtracking policies Variable-ordering heuristics Preprocessing algorithms


Constraint Satisfaction• Kind of search in which

States are factored into sets of variables Search = assigning values to these variables Structure of space is encoded with constraints

• Backtracking-style algorithms work E.g. DFS for SAT (i.e. DPLL)

• But other techniques add speed Propagation Variable ordering Preprocessing


Chinese Food as Search? • States?

• Operators?

• Start state?

• Goal states?

• Partially specified meals

• Add, remove, change dishes

• Null meal

• Meal meeting certain conditions (rating?)


Factoring States• Rather than state = meal• Model state’s (independent) parts, e.g.

Suppose every meal for n people Has n dishes plus soup Soup = Meal 1 = Meal 2 = … Meal n =

• Or… physical state = X coordinate = Y coordinate =


Chinese Constraint Network

Soup

Total Cost< $30

ChickenDish

Vegetable

RiceSeafood

Pork Dish

Appetizer

Must beHot&Sour

No Peanuts

No Peanuts

NotChow Mein

Not BothSpicy


CSPs in the Real World

• Scheduling space shuttle repair• Airport gate assignments• Transportation Planning• Supply-chain management• Computer configuration• Diagnosis• UI optimization• Etc...

20

[Gajos & Weld, IUI-04][Gajos et al., CHI-08]

Adapting to Devices


Supple Problem Formulation

+

Hierarchy of State Vars +Methods

Screen Size,Available Widgets &Interaction Modes

Func.Interface

Spec.DeviceModel

User Trace

CustomInterface

Rendering+

Model of an IndividualUser’s Behavior(or that of a Group)

{<root, -, -> <LeftLight:Power, off, on> <Vent, 1, 3> <Projector:Input, video, computer> … }

Approaches:

•Templates•Expert System•Optimization

Functional Spec.

• Typed DAG…Not Tree Interior Nodes Container Types Leaves Simple Types

+ DeviceModel

User Trace

CustomInterface

Rendering+

Func.Interface

Spec.


Add supple


Binary Constraint Network• Set of n variables: x1 … xn• Value domains for each variable: D1 … Dn• Set of binary constraints (also “relations”)

Rij Di Dj Specifies which value pairs (xi, xj) are consistent

• V for each country• Each domain = 4

colors• Rij enforces


Binary Constraint NetworkPartial assignment of values = tuple of pairs

{...(x, a)…} means variable x gets value a...Tuple=consistent if all constraints satisfiedTuple=full solution if consistent + has all vars

Tuple {(xi, ai) … (xj, aj)} = consistent w/ a set of vars {xm … xn}

iff am … an such that {(xi, ai)…(xj, aj), (xm, am)…(xn, an)} } =

consistent


N Queens• As a CSP?

Variables? Domain? Constraints?


N Queens• Variables = board columns• Domain values = rows• Rij = {(ai, aj) : (ai aj) (|i-j| |ai-aj|)

e.g. R12 = {(1,3), (1,4), (2,4), (3,1), (4,1), (4,2)}

Q

Q

Q

• {(x1, 2), (x2, 4), (x3, 1)} consistent with (x4)?• Shorthand: “{2, 4, 1} consistent with x4”• {(x1, 2), (x2, 4), (x3, 1)} consistent with (x4) ?• Shorthand: “{2, 4, 1} consistent with x4”


Cryptarithmetic SEND+ MORE------ MONEY

• State Space Set of states Operators [and costs] Start state Goal states

• Variables?• Domains (variable values)?• Constraints?


Classroom Scheduling• Variables?

• Domains (possible values for variables)?

• Constraints?


CSP as a search problem?• What are states?

(nodes in graph)• What are the operators?

(arcs between nodes)• Initial state?• Goal test?

Q

Q

Q


Chronological Backtracking (BT) (e.g., depth first

search)

Q

Q

Q

Q

Q

Q

Q

Q

Q

Q

Q

1

2

34

5

6

Consistency check performed in the order in which vars were instantiatedIf c-check fails, try next value of current varIf no more values, backtrack to most recent var


Backjumping (BJ)• Similar to BT, but

more efficient when no consistent instantiation can be found for the current var

• Instead of backtracking to most recent var… BJ reverts to deepest var which was c-checked

against the current var

BJ Discovers (2, 5, 3, 6) inconsistent with x6

No sense trying other values of x5

Q

Q

Q

Q

Q


5

Conflict-Directed Backjumping (CBJ)• More sophisticated backjumping behavior

• Each variable has conflict set CS Set of vars that failed c-checks w/ current val Update this set on every failed c-check

• When no more values to try for xi Backtrack to deepest var, xd, in CS(xi) And update CS(xd):=CS(xd)CS(xi)-{xd}

CBJ Discovers(2, 5, 3) inconsistent with {x5, x6 }

Q

Q

Q

Q

Q

1 13

23

3 3

2123456

x1 x2 x3 x4 x5 x6

CS(x5)1,2,3

CS(x6)1,2,3,5

Too complex to explain

(Animation may be incorrect)


BT

{vs. BJ vs. CBJ

Consistent node

Inconsistent node


Forward Checking (FC)• Perform Consistency Check Forward• Whenever a var is assigned a value

Prune inconsistent values from As-yet unvisited variables Backtrack if domain of any var ever collapses

Q

Q

Q

Q

Q

FC only visits consistent nodes but not all such nodes skips (2, 5, 3, 4) which CBJ visitsBut FC can’t detect that (2, 5, 3) inconsistent with {x5, x6 }


Number of Nodes ExploredBT=BM

BJ=BMJ=BMJ2

CBJ=BM-CBJ

FC-CBJ

FC

More

Fewer=BM-CBJ2


Number of Consistency Checks

BMJ2

BT

BJ

BMJ

BM-CBJ

CBJFC-CBJ

BM

BM-CBJ2

FC

More

Fewer


Crosswords

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