None of the above: A Bayesian account of the detection of...
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None of the above: A Bayesian account of the detection of novel categories Dan Navarro School of Psychology University of New South Wales Charles Kemp School of Psychology Carnegie Mellon University compcogscisydney.com/projects.html#noneoftheabove
Transcript of None of the above: A Bayesian account of the detection of...
None of the above: A Bayesian account of the detection
of novel categories
Dan Navarro School of Psychology
University of New South Wales
Charles Kemp School of Psychology
Carnegie Mellon University
compcogscisydney.com/projects.html#noneoftheabove
Dragon Unicorn Dragon Dragon
DragonUnicorn Unicorn Unicorn
Is this a dragon or a unicorn?
Unicycle? Segway? Roomba?
Unicycle? Segway? Roomba?
None of the above… this is the first item from a novel category
air wheels dabs dwarf planets
The “mental dictionary” of categories is extensible… how do we know when to extend it?
Structure of the talk
• Qualitative desiderata, models, a priori predictions
• Experiments with minimal cues
• Exp. 1: people satisfy the desiderata
• Exp. 2: no they don’t
• An absurd number of computational models
• Experiments with similarity structure
• Exp. 3: people integrate similarity & distribution
• Exp. 4: a better version of Exp. 3
• Conclusions
Qualitative desiderata for the discovery of new categories…
(Zabell 2011)
Any sequence of observations is
possible, so I must (a priori) assign
non-zero probability to them
= 2/5 unicorns
= 2/5 unicorns
Same number of unicorns… so my beliefs about P(unicorn) should be the same
Same number of familiar categories so the probability of a new category is the same
= 2 categories
= 2 categories
What prior beliefs must a learner have in order to satisfy those desiderata?
Bayesian category learning models use the “Chinese restaurant process” (CRP)…
P (old k) / nk“Strength” associated with an existing
category is proportional to its frequency
(Anderson 1990, Sanborn, Griffiths & Navarro 2010, etc)
Bayesian category learning models use the “Chinese restaurant process” (CRP)…
P (new) / ✓
P (old k) / nk
There is a fixed strength associated with novelty
(Anderson 1990, Sanborn, Griffiths & Navarro 2010, etc)
… but it’s a special case: the full* solution to the problem is the generalised CRP
* sort of
P (old k) / nk � ↵
P (new) / ✓ +K↵
(Zabell, 2011)
… but it’s a special case: the full* solution to the problem is the generalised CRP
* sort of
P (old k) / nk � ↵ “Strength” of old categories is slightly attenuated relative
to the CRP…
(Zabell, 2011)
… but it’s a special case: the full* solution to the problem is the generalised CRP
* sort of
P (old k) / nk � ↵
P (new) / ✓ +K↵
… because every time a new category appears, P(new) goes up
(Zabell, 2011)
What empirical predictions does the G-CRP make for human novelty
detection?
1: The familiar addition effect
1,1
2,1
3,1Adding examples from familiar
categories should decrease the probability of labelling the
next thing as “novel”
2: The novel addition effect
1,1
1,1,1
1,1,1,1
Adding an example from a novel category should
increase the probability that the next item is also “novel”
3: No effect of transfer
5,1 4,2 3,3
Nothing else about the frequency table matters except the number of exemplars N and
the number of categories K
Experiments…
Experiment 1
Stimuli were just arbitrary alphanumeric labels, to prevent similarity effects
categories
exemplars
Judge the probability that the next item will come from a new category, for every possible frequency
table with 6 or fewer exemplars
Familiar addition effect…
Novel addition effect…
No transfer effect!
Experiment 2
9,1,1,1
Experiment 2
6,2,2,2
Experiment 2
3,3,3,3
Experiment 2
12 objects in 4 categories
Experiment 2
Vary the number of categories from 2 to 10
3,3,3,39,1,1,1
Does this transfer have an effect?
3,3,3,39,1,1,1
The transfer effect exists(it’s small, so you need bigger frequency tables)
Do these results pose a serious theoretical challenge to categorisation
models?
A list of heuristic methods for estimating the probability that the
next object will be novel
They don’t work
Most existing category learning models
(SUSTAIN, simplicity, etc) also fail
What about the Bayesian models?
Expt 1 Expt 2 Expt 3 Expt 4
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Exp 1 Exp 2
Model
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x xHuman
Despite being near-universal among Bayesian models of categorisation, the CRP is terrible
Expt 1 Expt 2 Expt 3 Expt 4
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Model
Good quantitative
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xHuman
The generalised CRP does better, but misses the transfer effect
Generalised CRP
Learner observes exemplars from a subset of the categories
Unknown frequency distribution over many possible categories
(n1, n2, . . . , nK)
(p1, p2, p3, . . .)
Hierarchical generalised CRP
Learner observes exemplars from a subset of the categories
Unknown frequency distribution over many possible categories
Structure of the world that constrains the distribution
↵, ✓
(n1, n2, . . . , nK)
(p1, p2, p3, . . .)
Structure of the world that constrains the distribution
The HG-CRP model learns that this is a world with many low-frequency categories (infers a high ) and expects to see even
more low-frequency categories↵
Structure of the world that constrains the distribution
The HG-CRP model learns that this is a world with very few low-frequency
categories (infers a low ) and does not expect to see more LF categories
↵
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●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.93
●
●●
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●
r = 0.95
●
●●
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●
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
uniformC
RP
TTRG−C
RP
H−C
RP
H−TTR
HG−C
RP
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
Human
Mod
elExp 1 Exp 2
Model
Human
HG-CRP provides a good quantitative fit
●● ●
●
●●
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●●
CRP Hierarchical CRP
Types Tokens Ratio Hierarchical TTR
Generalized CRP Hierarchical Generalized CRP
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
[11]
1[1
0]2 93 84 75 66
[10]
11 822
633
552
444
9111
6222
5511
4422
3333
8111
142
222
3322
2
7111
1144
1111
3331
1122
2222
6111
111
2222
211
5111
1111
3311
1111
2222
1111
4111
1111
122
2111
111
3111
1111
1122
1111
1111
[11]
1[1
0]2 93 84 75 66
[10]
11 822
633
552
444
9111
6222
5511
4422
3333
8111
142
222
3322
2
7111
1144
1111
3331
1122
2222
6111
111
2222
211
5111
1111
3311
1111
2222
1111
4111
1111
122
2111
111
3111
1111
1122
1111
1111
Frequency Table
Prob
abilit
y of
a N
ew C
ateg
ory
It also captures the transfer effect
Is this actually a categorisation problem?(a.k.a. Do people still do this in a standard task when similarity
information exists?)
Dragon Unicorn
DragonUnicorn
In most categorisation tasks we have similarity information
Dragon Unicorn
DragonUnicorn
???
High similarity target is less likely to be novel
Dragon Unicorn
DragonUnicorn
???
Low similarity target is more likely to be novel
B A ? ?
C B A ? ?
D C B A ? ?
B B A ? ?
B B B A ? ?
C C B A ? ?
Near Far
20 40 60 80 100
11
111
1111
21
31
211
Stimulus Value
Trai
ning
Con
ditio
n
Training items vary on a single continuous stimulus dimension
B A ? ?
C B A ? ?
D C B A ? ?
B B A ? ?
B B B A ? ?
C C B A ? ?
Near Far
20 40 60 80 100
11
111
1111
21
31
211
Stimulus Value
Trai
ning
Con
ditio
n
Near test
Far test
Similarity manipulation:
B A ? ?
C B A ? ?
D C B A ? ?
B B A ? ?
B B B A ? ?
C C B A ? ?
Near Far
20 40 60 80 100
11
111
1111
21
31
211
Stimulus Value
Trai
ning
Con
ditio
nThe training items form a
2,1 frequency table
B A ? ?
C B A ? ?
D C B A ? ?
B B A ? ?
B B B A ? ?
C C B A ? ?
Near Far
20 40 60 80 100
11
111
1111
21
31
211
Stimulus Value
Trai
ning
Con
ditio
n
6 tables x 2 tests = 12 categorisation tasks
Experiment 3
Lots of stimulus sets used:
New Category Nearest Old Category Other Old Category
●
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●
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●
●
●
● ● ●● ●
●
● ● ●● ●●
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Near Test Item
Far Test Item
11 21 31 111 211 1111 11 21 31 111 211 1111 11 21 31 111 211 1111Training Condition
Res
pons
e Pr
obab
ility
New Category Nearest Old Category Other Old Category
●
● ●
● ●
●
●● ●
●
●
●
●
● ●
● ●
●
● ● ●
●
●
●
● ● ●● ●
●
● ● ●● ●●
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Near Test Item
Far Test Item
11 21 31 111 211 1111 11 21 31 111 211 1111 11 21 31 111 211 1111Training Condition
Res
pons
e Pr
obab
ility
Near test Far test
P(new)
Similarity effect
New Category Nearest Old Category Other Old Category
●
● ●
● ●
●
●● ●
●
●
●
●
● ●
● ●
●
● ● ●
●
●
●
● ● ●● ●
●
● ● ●● ●●
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Near Test Item
Far Test Item
11 21 31 111 211 1111 11 21 31 111 211 1111 11 21 31 111 211 1111Training Condition
Res
pons
e Pr
obab
ility
New Category Nearest Old Category Other Old Category
●
● ●
● ●
●
●● ●
●
●
●
●
● ●
● ●
●
● ● ●
●
●
●
● ● ●● ●
●
● ● ●● ●●
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Near Test Item
Far Test Item
11 21 31 111 211 1111 11 21 31 111 211 1111 11 21 31 111 211 1111Training Condition
Res
pons
e Pr
obab
ility
Near test Far test
P(new)
Familiar addition
New Category Nearest Old Category Other Old Category
●
● ●
● ●
●
●● ●
●
●
●
●
● ●
● ●
●
● ● ●
●
●
●
● ● ●● ●
●
● ● ●● ●●
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Near Test Item
Far Test Item
11 21 31 111 211 1111 11 21 31 111 211 1111 11 21 31 111 211 1111Training Condition
Res
pons
e Pr
obab
ility
New Category Nearest Old Category Other Old Category
●
● ●
● ●
●
●● ●
●
●
●
●
● ●
● ●
●
● ● ●
●
●
●
● ● ●● ●
●
● ● ●● ●●
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Near Test Item
Far Test Item
11 21 31 111 211 1111 11 21 31 111 211 1111 11 21 31 111 211 1111Training Condition
Res
pons
e Pr
obab
ility
Near test Far test
P(new)
Novel addition?
=
=
Experiment 4
Similarity effect
Near Far
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
New
Category
Observed
Other O
ld
[1]
[2]
[3]
[4]
1[1]
2[1]
3[1]
11[1
]
21[1
]
[1]
[2]
[3]
[4]
1[1]
2[1]
3[1]
11[1
]
21[1
]
Frequency Table
Prob
abilit
y of
Cat
egor
y
Familiar addition
Near Far
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
New
Category
Observed
Other O
ld
[1]
[2]
[3]
[4]
1[1]
2[1]
3[1]
11[1
]
21[1
]
[1]
[2]
[3]
[4]
1[1]
2[1]
3[1]
11[1
]
21[1
]
Frequency Table
Prob
abilit
y of
Cat
egor
y
Novel addition*
Near Far
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
New
Category
Observed
Other O
ld
[1]
1[1]
11[1
]
111[
1]
2[1]
21[1
]
[1]
1[1]
11[1
]
111[
1]
2[1]
21[1
]
Frequency Table
Prob
abilit
y of
Cat
egor
y
* I’m hiding the [1] condition (ask me why!)
Expt 1 Expt 2 Expt 3 Expt 4
r = 0
● ● ●●●●● ● ● ●●●● ●●● ●● ●● ●●● ● ●●● ●●
r = 0.21●
●
●
●●●
●
●
●●●
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●
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●●
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●●
●●●
●●
r = 0.98● ● ●●●●
●
●●
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●
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●
●
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●
r = 0.99●
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●
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●
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r = 0.96●
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●
r = 0.98● ● ●●●●
●
●
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●
●
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●
r = 0.98● ● ●●●
●
●
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●
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●
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●
●
r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0.99
●●●●●●
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r = 0.99
●●●●●●
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r = 0.97
●●●●●●●●●●●
●●●●●●●●
●●●●
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●●●
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●●
r = 0.99
●●●●●●
●●●●●
●●●●●
●●●
●●●●
●●
●●●
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●●
r = 0.99
●●●●●●
●●●●●
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●
●●
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●
●
●
●●●
●●
●●
r = 0.88●●●●
●●
●●●●●
●
●●● ●● ●
● ●● ●● ●
r = 0.88●●●●●●
●●●●●●
●●● ●● ●
● ●● ●● ●
r = 0.87●●●
●●
●
●
●
●
●
●
●
●●●
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●
●
●●
●
●
●
r = 0.9●●●
●●
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●
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●
●
●●●
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●
●
●●
●
●●
r = 0.94●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
r = 0.91●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
r = 0.96●●●
●●●
●●
●
●●
●
●●●
●●
●
●●
●
●
●
●
r = 0.9
● ●●●● ●● ●●●
● ●●●● ●●●●●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●●
●●
●
r = 0.58
●
●●
●
●●
●
●
●
●
●●●
●
● ●●
●
●●
●●●
●
●●●
●
●
●
●
●●
●
●●
●
●
●
●
r = 0.74
●●●
●
● ●●
●
●
●● ●●
●● ●●●●●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.76
●●●
●
● ●●
●
●
●● ●●
●● ●●●●●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.94
●
●●
●
●
●
●●
●
●
●●●
●
●●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.93
●
●●
●
●
●
●
●
●
●
●●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.95
●
●●
●
●●
●
●
●
●
●
●●
●
●●
●●●
●
●
●
●
●
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●
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●
●
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●
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
uniformC
RP
TTRG−C
RP
H−C
RP
H−TTR
HG−C
RP
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
Human
Mod
el
Exp 3 Exp 4
x
CRP performs poorly
Parameters estimated from Exp 3 and fixed for Exp 4
Expt 1 Expt 2 Expt 3 Expt 4
r = 0
● ● ●●●●● ● ● ●●●● ●●● ●● ●● ●●● ● ●●● ●●
r = 0.21●
●
●
●●●
●
●
●●●
●●
●●
●
●●
●●
●●
●●
●●●
●●
r = 0.98● ● ●●●●
●
●●
●●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
r = 0.99●
● ●●●●
●
●
●●●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
r = 0.96●
● ●●●●
●
●●
●●
●●
●
●●
●●
●
●
●
●●
●●
●●
●
●
r = 0.98● ● ●●●●
●
●
●●●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
r = 0.98● ● ●●●
●
●
●●
●●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0.99
●●●●●●
●●●●●
●●●●●
●●●
●●●●
●●
●●●
●●
●●
r = 0.99
●●●●●●
●●●●●
●●●●●
●●●
●●●●
●●
●●●
●●
●●
r = 0.97
●●●●●●●●●●●
●●●●●●●●
●●●●
●●
●●●
●●
●●
r = 0.99
●●●●●●
●●●●●
●●●●●
●●●
●●●●
●●
●●●
●●
●●
r = 0.99
●●●●●●
●●●●●
●●●●●
●
●●
●●●
●
●
●
●●●
●●
●●
r = 0.88●●●●
●●
●●●●●
●
●●● ●● ●
● ●● ●● ●
r = 0.88●●●●●●
●●●●●●
●●● ●● ●
● ●● ●● ●
r = 0.87●●●
●●
●
●
●
●
●
●
●
●●●
●●
●
●
●●
●
●
●
r = 0.9●●●
●●
●
●
●●
●
●
●
●●●
●●
●
●
●●
●
●●
r = 0.94●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
r = 0.91●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
r = 0.96●●●
●●●
●●
●
●●
●
●●●
●●
●
●●
●
●
●
●
r = 0.9
● ●●●● ●● ●●●
● ●●●● ●●●●●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●●
●●
●
r = 0.58
●
●●
●
●●
●
●
●
●
●●●
●
● ●●
●
●●
●●●
●
●●●
●
●
●
●
●●
●
●●
●
●
●
●
r = 0.74
●●●
●
● ●●
●
●
●● ●●
●● ●●●●●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.76
●●●
●
● ●●
●
●
●● ●●
●● ●●●●●
●●●
●
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r = 0.94
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r = 0.93
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0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
uniformC
RP
TTRG−C
RP
H−C
RP
H−TTR
HG−C
RP
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
Human
Mod
el
Exp 3 Exp 4
x
G-CRP model does slightly better
Parameters estimated from Exp 3 and fixed for Exp 4
Expt 1 Expt 2 Expt 3 Expt 4
r = 0
● ● ●●●●● ● ● ●●●● ●●● ●● ●● ●●● ● ●●● ●●
r = 0.21●
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r = 0.99●
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r = 0.96●
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r = 0.98● ● ●●●●
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r = 0.98● ● ●●●
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r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0.99
●●●●●●
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r = 0.99
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r = 0.97
●●●●●●●●●●●
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r = 0.99
●●●●●●
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r = 0.99
●●●●●●
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●
●●●
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●●
r = 0.88●●●●
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●
●●● ●● ●
● ●● ●● ●
r = 0.88●●●●●●
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● ●● ●● ●
r = 0.87●●●
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r = 0.9●●●
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r = 0.94●
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r = 0.91●
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r = 0.96●●●
●●●
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●●●
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●
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r = 0.9
● ●●●● ●● ●●●
● ●●●● ●●●●●
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●
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r = 0.58
●
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r = 0.74
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r = 0.76
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r = 0.94
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r = 0.93
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r = 0.95
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0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00uniform
CR
PTTR
G−C
RP
H−C
RP
H−TTR
HG−C
RP
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
Human
Mod
el
Exp 3 Exp 4
HG-CRP model is easily the best
Parameters estimated from Exp 3 and fixed for Exp 4
Summary
Expt 1 Expt 2 Expt 3 Expt 4
r = 0
● ● ●●●●● ● ● ●●●● ●●● ●● ●● ●●● ● ●●● ●●
r = 0.21●
●
●
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r = 0.98● ● ●●●●
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r = 0.99●
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r = 0.96●
● ●●●●
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r = 0.98● ● ●●●●
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●
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r = 0.98● ● ●●●
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r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0.99
●●●●●●
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r = 0.99
●●●●●●
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r = 0.97
●●●●●●●●●●●
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r = 0.99
●●●●●●
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r = 0.99
●●●●●●
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●
●●
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●
●
●
●●●
●●
●●
r = 0.88●●●●
●●
●●●●●
●
●●● ●● ●
● ●● ●● ●
r = 0.88●●●●●●
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● ●● ●● ●
r = 0.87●●●
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r = 0.9●●●
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r = 0.94●
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r = 0.91●
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r = 0.96●●●
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r = 0.9
● ●●●● ●● ●●●
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r = 0.58
●
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r = 0.74
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r = 0.76
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r = 0.94
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r = 0.93
●
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r = 0.95
●
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0.00
0.25
0.50
0.75
1.00
0.00
0.25
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0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
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1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
uniformC
RP
TTRG−C
RP
H−C
RP
H−TTR
HG−C
RP
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
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1.00
Human
Mod
el
4 experiments, 20+ models, 100+ experimental conditions,
1000+ participants later…
Expt 1 Expt 2 Expt 3 Expt 4
r = 0
● ● ●●●●● ● ● ●●●● ●●● ●● ●● ●●● ● ●●● ●●
r = 0.21●
●
●
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●
●
●●●
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r = 0.98● ● ●●●●
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r = 0.96●
● ●●●●
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r = 0.98● ● ●●●●
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r = 0.98● ● ●●●
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r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0
●●●●●● ●●●●● ●●●●● ●●● ●●●● ●● ●●● ●●●●
r = 0.99
●●●●●●
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r = 0.99
●●●●●●
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r = 0.97
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r = 0.99
●●●●●●
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r = 0.99
●●●●●●
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●●
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●
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r = 0.88●●●●
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●
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r = 0.88●●●●●●
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● ●● ●● ●
r = 0.87●●●
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r = 0.9●●●
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●●
r = 0.94●
●●
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r = 0.91●
●●
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●
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r = 0.96●●●
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●●
●
●●●
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●
●
●
r = 0.9
● ●●●● ●● ●●●
● ●●●● ●●●●●
●
●
●
●
●
●
●
●
●
●
●●●
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●●
●
r = 0.58
●
●●
●
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●
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●
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●
● ●●
●
●●
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●
●●●
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●
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●
r = 0.74
●●●
●
● ●●
●
●
●● ●●
●● ●●●●●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.76
●●●
●
● ●●
●
●
●● ●●
●● ●●●●●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.94
●
●●
●
●
●
●●
●
●
●●●
●
●●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.93
●
●●
●
●
●
●
●
●
●
●●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
r = 0.95
●
●●
●
●●
●
●
●
●
●
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●
●●
●●●
●
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●
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
uniformC
RP
TTRG−C
RP
H−C
RP
H−TTR
HG−C
RP
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
Human
Mod
el
… a model you’ve never heard of is the winner!
A better summary
How do I know this device needs a new label?
How similar is it to familiar things?
How often do I tend to run into novel categories?
How often do I encounter familiar categories?
What does the distribution of objects across categories tell me?
Similarity effects
Novel addition effectsFamiliar addition effects
Transfer effects
A theory of novelty detection needs to accommodate all these things
HG-CRP works because it also learns “what kind of world is this?” when asked
“is this novel?”
Observations
Unknown distribution over many possible categories
Structure of the world
Thanks
Individual differences (E2)
Replication check:
Why does the transfer effect exist?Learning distributional shape on the fly
0.0 0.2 0.4 0.6 0.8 1.0
Discount parameter, alpha
n = (2,2,2,2,2,2)n = (7,1,1,1,1,1)
