Post on 19-Dec-2015
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Incorporating ReliabilityIncorporating Reliabilityin a TV Recommenderin a TV RecommenderIncorporating ReliabilityIncorporating Reliabilityin a TV Recommenderin a TV Recommender
Verus PronkVerus Pronk
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Context
• Increasing availability of TV programs• Availability of electronic program guides
(EPGs)
How about a personal TV recommender?
Applications• Highlights in EPG• Auto-recording/deletion on HD recorders• Creation of personalized channels
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Summary
Introduction Naive Bayesian classificationAn exampleReliable classificationResultsConcluding remarks
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Introduction
Thousands of programs offered each day
People tend to browse only a limited number of channels
EPGs provide easier access
Low percentage of interesting programs
More advanced solutions required
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Introduction
Programs are described by metadata (EPG)User rates a number of programs as or User profile describes relation between them
TV programrecommender
TV program
trainingset
user
userprofile
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Introduction
Example of metadata
An Officer and a Gentleman: ( date : Tuesday, Nov. 23, 2004;
time : 20:30 h.;station : SBS 6;genre : drama;cast : Richard Gere;credit : Taylor Hackford;...
)
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Naive Bayesian classification
Given : a training set X: i-th feature value of x
known class of xGiven : an instance t
Asked : c(t)
Approach: estimatebased on the user profile calculated from X
Xx
Cjjtc ),)(Pr(
Cxc )(ii Vx
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Naive Bayesian classification
Problem issues
• Cold start• Changing preferences• Feature selection• Accuracy• Reliability• ...
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Naive Bayesian classification
))(Pr( jtc
)Pr(
))(|Pr())(Pr(
)Pr(
))(|Pr())(Pr(
)|)(Pr(
tx
jxctxjxc
tx
jxctxjxc
txjxc
iii
prior probabilities
conditional probabilities
posterior probabilities
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Naive Bayesian classification
Conditional independence violation
• The BBC news is always broadcast on the BBC
• Clint Eastwood generally plays in action movies
NBC is nevertheless successfully applied in many application areas
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Naive Bayesian classification
Priors set to pj
Conditionals estimated using training set
Denominator irrelevant
)Pr(
))(|Pr())(Pr())(Pr(
tx
jxctxjxcjtc iii
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Naive Bayesian classification
User profile
)(
),,( ~ ))(Pr(
jN
jtiNpjtc i
ij
)0( |})(|{| )(
|})(|{| ),,(
jxcXxjN
vxjxcXxjviN i
)(
),,( argmax)(ˆ
jN
jtiNptc i
ijCj
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Naive Bayesian classification
Classification error
E is a convex combination of the Ejs
))(|)(ˆPr(
))()(ˆPr(
jxcjxcE
xcxcE
j
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Naive Bayesian classification
On the prior probabilities
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An examplefeature value day Monday 31 7 Tuesday 12 43 ... (57) (50) time 20:30 21 7 20:35 22 10 ... (57) (83) genre romance 8 12 drama 17 4 ... (75) (84) cast Richard Gere 23 1 Sandra Bullock 3 6 ... (74) (93) credit Steven Spielberg 11 2 Taylor Hackford 18 4 ... (71) (94)
1
1
1
1
1
16
feature value day Monday 31 7 Tuesday 12 43 ... (57) (50) time 20:30 21 7 20:35 22 10 ... (57) (83) genre romance 8 12 drama 17 4 ... (75) (84) cast Richard Gere 23 1 Sandra Bullock 3 6 ... (74) (93) credit Steven Spielberg 11 2 Taylor Hackford 18 4 ... (71) (94)
100
12
100
43100
21
100
7100
17
100
4100
23
100
1100
18
100
4
2.0
8.0
51055.3
71085.3
Training set:
100 TV programs
100 TV programs
Program: Tue. 20:30 Drama R. Gere T. Hackford
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Reliable classification
X random N(i, v, j) and N( j) randomand dependent
X uniform both binomially distributed
)0( |})(|{| )(
|})(|{| ),,(
jxcXxjN
vxjxcXxjviN iX
X
)(
),,( argmax)(ˆ
jN
jtiNptc i
ijCj
statisticalanalysis
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Reliable classification
Theorem 1
Let Z ~ Bin(N, p), 0 < p < 1, Yn ~ Bin(n, q)
Z0 :
Then ...
)0|Pr()Pr( 0 ZnZnZ
0
0
Z
YR Z
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Reliable classification
where
,)1()1()1(1
)1()1( NNN
N
HpHp
pqqR
qRE
.)(1
N
n
n
N nH
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Reliable classification
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Reliable classification
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Reliable classification
Theorem 2
Let Ri, i = 1, 2, ..., f, independent
r constant
Then
(Ris not actually independent)
22222 iiiiiii RERERrRr
iiii RErRrE
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Reliable classification
)(
),,(
)(
jN
jviNq
X
jNp
XN
Back to the original problem
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Reliable classification
Standard deviation of can be estimated by
),( jt
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1 )(
),,(
)(
),,(1
)(1
)(11
)(1
)(
),,(1
)(
),,(
jN
jtiN
jN
jtiN
n
XjN
XjN
XjN
jN
jtiN
jN
jtiNp i
ii
X
n
n
X
X
iiij
)(
),,(
jN
jtiNp i
ij
),( jtP
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Reliable classification
Confidence intervals for
),(),( jtjtP
),( jtP
Two approaches
A: Fix and don’t classify if
intervals overlap: coverage
B: Choose such that intervals
just do not overlap: explicitnotion of confidence
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Results
Simulation TV recommenderTraining sets Briarcliff data
Prior probabilities Set such that E E
EConfidence levels = 0, 0.1, 0.2, ..., 1Training set sizes 100, 400
Approach Aoffset classification error against coverage
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Results
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Results
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Concluding remarks
• Reliability adds another dimension to classification
• Our approach is explicit and robust• Separates difficult from easy instances• Also applicable to other domains
– medical diagnosis– biometrics (e.g. face recognition)
AcknowledgementsSrinivas Gutta, Wim Verhaegh, Dee Denteneer