Text Classification with
Belief Augmented Frames
Colin Tan
Department of Computer Science,
School of Computing,
National University of Singapore.
Outline
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What are Belief Augmented Frames?
Motivation behind Belief Augmented Frames
Representing Beliefs in BAFs
Some Definitions
Belief Augmented Frame Logic (BAF-Logic)
Applying BAF-Logic to Text Classification
Experiment Protocol and Results
Conclusions
What are Belief Augmented
Frames?
• Belief Augmented Frames (BAF) combine
classical AI frames with belief measures.
– Frame-based system to structure knowledge
and relations between entities.
– Belief measures provide uncertain reasoning on
existence of entities and the relationships
between them.
Motivation behind Belief
Augmented Frames
• Why Belief Measures?
– Statistical Measures
• Standard tool for modeling uncertainty.
• Essentially, if the probability that a proposition E is true is p,
then the probability of that E is false is 1-p.
– P(E) = p
– P(not E) = 1-p
• This relationship essentially leaves no room for ignorance.
Either the proposition is true with a probability of p, or it is
false with a probability of 1-p.
• This can be counter-intuitive at times.
Motivation behind Belief
Augmented Frames
• Why Belief Measures?
– [Shortliffe75] cites a study in which, given a set
of symptoms, doctors were willing to declare
with certainty x that a patient was suffering
from a disease D, yet were unwilling to declare
with certainty 1-x that the patient was not
suffering from D.
Motivation behind Belief
Augmented Frames
• Why Belief Measures?
– To allow for ignorance our research focuses on
belief measures.
– The ability to model ignorance is inherent in
belief systems.
• E.g. in Dempster-Shafer Theory [Dempster67], if
our belief in E1 and E2 are 0.1 and 0.3 respectively,
then the ignorance is (1 – (0.1 + 0.3)) = 0.6.
Motivation behind Belief
Augmented Frames
• Why Frames?
– Frames are a powerful form of representation.
• Intuitively represents relationships between objects
using slot-filler pairs.
– Simple to perform reasoning based on relationships.
• Hierarchical
– Can perform generalizations to create general models
derived from a set of frames.
Example BAF
Donkey
0.6, 0.3
color
1.0, 0.0
Grey,
1.0, 0.0
owns
0.7, 0.2
Alice,
1.0, 0.0
walks
0.9, 0.1
Blue,
1.0, 0.0
color
1.0, 0.0
Dog
0.9, 0.0
location
1.0, 0.0
Bay,
1.0, 0.0
Belief Representation in Belief
Augmented Frames
• Beliefs are represented by two masses:
– φT: Belief mass supporting a proposition.
– φF: Belief mass refuting a proposition.
– In general φT + φF  1
• Room to model ignorance of the facts.
• Separate belief masses allow us to:
– Draw φT and φF from different sources.
– Have different chains of reasoning for φT and φF.
Belief Representation in Belief
Augmented Frames
• This ability to derive the refuting masses
from different sources and chains of
reasoning is unique to BAF.
– In Probabilistic Argumentation Systems (the
closest competitor to BAF) for example, p(not
E) = 1 – p(E).
Some Definitions
• Degree of Inclination
– The Degree of Inclination is defined as:
• DI = T - F
– DI is in the range of [-1, 1].
– One possible interpretation of DI:
-1
False
-0.75
Most
Probably
False
-0.5
Probably
False
-0.25
Likely
False
0
Ignorant
0.25
Likely
True
0.5
Probably
True
0.75
Most
Probably
True
1
True
Some Definitions
• Utility Value
– The Degree of Inclination DI can be re-mapped
to the range [0, 1] through the Utility function:
• U = (DI + 1) / 2
• By normalizing U across all relevant propositions it
becomes possible to use U as a statistical measure.
Belief Augmented Frame Logic
(BAF-Logic)
• Belief Augmented Frame Logic, or BAFLogic, is used for reasoning with BAFs.
• Throughout the remainder of this
presentation, we will consider two
propositions A and B, with supporting and
refuting masses TA, FA, TB, and FB.
Belief Augmented Frame Logic
(BAF-Logic)
• A  B:
– TA B = min(TA, TB)
– FA B = max(FA, FB)
• A  B:
– TA  B = max(TA, TB)
– FA  B = min(FA, FB)
•  A:
– T A = F A
– F A = T A
Belief Augmented Frame Logic
(BAF-Logic)
• BAF-Logic properties that are identical to
Propositional Logic:
– Associativity, Commutativity, Distributivity,
Idempotency, Absorption, De-Morgan’s Theorem, elimination.
• Other properties of Propositional Logic work
slightly differently in BAF-Logic.
– In particular, some of the properties hold true only if the
constituent propositions are at least “probably true” or
“probably false”
• I.e. |DIP |  0.5
Belief Augmented Frame Logic
(BAF-Logic)
• An Example:
– Given the following propositions in your
knowledge base:
• KB = {(A, 0.7, 0.2), (B, 0.9, 0.1), (C, 0.2, 0.7), (A
B R, TONE , FONE,), (A  B R, TONE ,
FONE)}
• We want to derive TR, FR.
Belief Augmented Frame Logic
(BAF-Logic)
• Combining our clauses regarding R, we
obtain:
– R = (A  B)   (A   B)
• = A  B  ( A  B)
• With De-Morgan’s Theorem we can derive
 R:
–  R= A   B  (A   B)
Belief Augmented Frame Logic
(BAF-Logic)
• TR = min(TA , TB , max(FA , TB ))
= min(0.7, 0.9, max(0.2, 0.9))
= min(0.7, 0.9, 0.9)
= 0.7
• FR = max(FA , FB , min(TA , FB ))
= max(0.2, 0.1, min(0.7, 0.1))
= max(0.2, 0.1, 0.1)
= 0.2
Belief Augmented Frame Logic
(BAF-Logic)
• DIR
= TR - FR
= 0.7 – 0.2
= 0.5
• UR
= (1 + 0.5) / 2.0
= 0.75
• Suppose now it is known that B C R
Belief Augmented Frame Logic
(BAF-Logic)
• Combining our clauses regarding R, we
obtain:
– R = (A  B)  (B  C)  (A   B)
= A  B  C  ( A  B)
• With De-Morgan’s Theorem we can derive
 R:
–  R= A   B   C  (A   B)
Belief Augmented Frame Logic
(BAF-Logic)
•  TR = min(TA , TB , TC , max(FA , TB ))
= min(0.7, 0.9, 0.2, max(0.2, 0.9))
= min(0.7, 0.9, 0.2, 0.9)
= 0.2
• FR = max(FA , FB , FC , min(TA , FB ))
= max(0.2, 0.1, 0.7, min(0.7, 0.1))
= max(0.2, 0.1, 0.7, 0.1)
= 0.7
Belief Augmented Frame Logic
(BAF-Logic)
• DIR
= TR - FR
= 0.2 – 0.7
= -0.5
• UR
= (1 - 0.5) / 2.0
= 0.25
• Here the new evidence that B C R fails
to support R, because C is not true (DIC = 0.5)
Text Classification
First Approach
• First Formulation:
– Using Individual Word Scores
– Assuming that a document di belongs to a class
ck, then for every term tij the following relation
holds:
di  ck  (ti0  ck  ti1  ck  ti2  ck … 
ti,n-1  ck)
Text Classification
First Approach
• Likewise, for a document di not belonging
to a class ck, we can derive:
di  ck  m, mk (ti0  cm  ti1  cm  ti2 
cm …  ti,n-1  cm)
• These can be formulated in BAF-Logic:
Tdi  ck = min(p(ck | ti0), p(ck | ti1), …, p(ck | ti, n-1))
Fdi  ck = max(min(p(cm | ti0), p(cm | ti1), …,
p(cm | ti, n-1)), min(p(cn|ti0),
p(cn|ti1),…,p(cn|ti,n-1)), …)), m, n etc  k
Text Classification
First Approach
• The final score of a document di belong to
class cj is given by:
U d i ck 
1.0  DI d i ck
2
• Where:
DI d i ck   dTi ck   dFi ck
Text Classification
First Approach
• Individual term probabilities are derived
using Bayesian probabilities:
p(ck | tij ) 
p(tij | ck ) p(ck )
p(tij )
Text Classification
Second Approach
• We classify the entire document using
Naïve Bayes assumption:
p( ck | d i )   p( ck | tij )
j
• Trivial to derive the supporting score that di
 ck.
– It is simply p(ck | di)
Text Classification
Second Approach
• Formulating the Refuting Score is
straightforward too:
di  ck  di cm  di  cn di  cp…, m, n, p, etc  k
• We can formulate both supporting and
refuting scores in BAF-Logic:
T
d i ck  p(ck | di )
dF c  max( p(cm | di ), p(cn | di ), p(c p | di ),...)
i
k
Text Classification
Second Approach
• We retain the definitions of DI and U from
the first approach.
Experiment Protocol
• Using Andrew McCallum’s “Bag of Words”
or BOW library.
– Extended “rainbow”, the text-classification
front-end, with two BAF classification
methods.
• Methods are called BAF1 and BAF2
– Also extended with two PAS methods (see
paper for more details)
• Methods are called PAS1 and PAS2
Experiment Protocol
• Corpus:
– 20 Newsgroups
– 80% (16,000) documents used to generate
statistics.
– 20% (4,000) documents used for testing
– Choice of documents for training/testing
handled by BOW
– Headers removed from all documents
Experiment Protocol
• Trials
– 10 trials were performed using each
classification method.
• Naïve Bayes, tf.idf, kNN, EMM, Max entropy,
Probabilistic Indexing, BAF1, BAF2, PAS1, PAS2
– The average was taken from the 10 trials for
each method.
Experiment Results
Text Classification Accuray
100
90
82.09 79.88
82.01 81.15
80
68.98
70
65.87 67.46
60
50
35.17
40
30
20
10
Method
PA
S2
PA
S1
BA
F2
BA
F1
AX
EN
T
PR
IN
D
M
EM
kN
N
id
f
tf.
Ba
ye
s
0
Na
ïv
e
Accuracy (%)
82.36
77.73
Analysis
• BAF1 performs poorly.
– Using individual word scores appears to be a poor idea.
• BAF2 performs very well.
– Better than the other methods attempted.
• BAF2 Performance slightly better than Naïve
Bayers
– Appears that considering a document to belong to
another class has a positive effect on classification
scores.
Conclusion
• Experiment results show that the use of BAFLogic to classify documents might be a good idea.
• In addition there are features of BAFs (e.g.
daemons attached to slots) that might enhance
classification performance further.
• More work should be done on this.
– Understanding better why BAF-Logic works for text
classification.
– Improving classification performance.