The Human Brain: Bayesic Stuff

Classification of objects is a fundamental and innate ability of our brain, which allows us to use a limited set of words to describe an almost infinite space of different objects, for instance, learning to classify food into nutritious or poisonous has been a key to the survival of organisms. The algorithmic and neuronal implementations of human classification are, however, not well understood. Why is it that a single example from a new class is sufficient to spawn a new category? Why and when do we generate new categories and how do we update them dynamically? How do our minds get so much from so little? We build rich models through which we make strong generalizations, and construct powerful abstractions, while the input data are noisy and often ambiguous. The impressive ease with which humans deal with these problems has been a major focus of the research community with many potential applications. In this talk, I will introduce recent approaches to reverse-engineering human category learning and discuss why gaining an understanding of the mechanisms that humans use to categorise data is essential for learning how the brain functions and how this knowledge can be used to create even more intelligent machines.

Transcript

1. Feryal  M  P  Behbahani     Brain  and  Behavior  Lab   Cartoon  by  Daniele  Quercia  
2. •  Cogni,ve  science:  a  process  of  reverse  engineering     •  the  only  sources  of  methods  we  have  to  reverse  engineer  any   natural    system  is  the  engineering  ideas  from  the  relevant   domains     –  Machine  learning:  provides  an  engineering  toolkit              Cogni,ve  science  draws  on  machine  learning  for  hypotheses              And  provides  machine  learning  with  interes,ng  challenges  
3. Cogni9ve  science   •  Focus  on  specific     experimental  paradigms   •  Embedded  in  psychology   •  Aiming  to  be  cogni,vely   and/or  neurally  plausible     Machine  learning   •  Focus  on  standard  learning   problems   •  Embedded  in  computer   science  and  engineering   •  Aim  for  a  working  system,   whether  mimicking  the   brain  or  not   Is  machine  learning  be=er  off  without  cogni9ve  science?!    
4. •  Computa9onal   –  What  problem  is  the  brain  solving?  What  informa,on  is   required?   •  Algorithmic   –  What  algorithms  are  computed?   •  Implementa9onal   –  How  are  those  algorithms  implemented  
6. How  do  people  represent  categories?   ? Cat   Tiger  
7. Prototype   Cat  
8. Cat   Cat   Cat   Cat   Cat   Cat   All  instances  (exemplars)     are  stored  in  memory  
9. C   C   X   X   P(C,X)   P(C|X)       "Essen9ally,  all  models  are  wrong,  but  some  are  useful"   Box  1973   P(X|C)  P(C  )      
10. •  Categoriza,on  is  a  classic  induc,ve  problem                                                  data:  s,mulus  x                          hypotheses:  category  c     •  We  can  apply  Bayes’  rule:          and  choose  c  such  that  P(c|x)  is  maximized   P(c | x) = p(x |c)P(c) p(x |c)P(c) c ∑
11. Discrimina9on  Boundary  
12. Discrimina9on  Boundary  
13. Discrimina9on  Boundary   ç Observed  shiO  in  classifica,on  boundary:   Predicted  only  by  implied  widening  of   genera,ve  representa,on  of  A  
14. Screen   Subject     •  Two  symbols  from  an  ar,ficial  language  
15. Subject   Screen     •  Two  s,ck-­‐figure  animals  
16. A   B   A   B  
17. B   A   B   A   Machine  Learner  
18. B   A   B   A   B   A   Armadilo   Horse   Machine  Learner   Human  Learner  
20. 350°   T1   T2   A   B   B   A   B   A  
21. 350°   T1   T2   A   B   B   A   B   A  
22. 22   1.    Cogni9ve  science  and  machine  learning     brain  is  the  only  intelligent  system  we  know  about  and  also  the  brain   defines  many  of  the  problems  that  machine  learning  cares  about     cogni,ve  science  depends  on  machine  learning  and  other  engineering   techniques  since  they  are  the  only  source  of  deep  insights  that  a  reverse   engineer  can  possibly  draw  on     2.    Marr’s  3  Levels  of  explana9on     3.    Human  categorisa9on  vs  machine  classifica9on    
23. Human  categorisa,on  behaviour  is  not  consistent  with  discrimina,ve  strategies;  rather,   it  can  be  best  explained  through  Bayesian  genera,ve  classifica,on.               Cartoon  by  Daniele  Quercia  
25. Ques9ons?  
26. p(x) = 1 2πσ exp{−(x − µ)2 /2σ2} Probability density p(x) (x-­‐µ)/σ   mean standard deviation variance = σ2
28. Hsu  &  Griffiths,  2010   Kalish  et  al,  2010   Bayesian  Decision  Theory  has  emerged  as  a  principled  way  to  explain  how  the  brain  has  to   act  in  the  face  of  uncertainty  and  was  very  successful  in  explaining  behavior  in  perceptual   and  motor  tasks  (Ernst  &  Banks,  2002,  Kording  &  Wolpert,  2002,  Faisal  et  al.,  2008).    
29. ILLUSTRATION: BAYESIAN COGNITIVE SCIENCE ACROSS THE LEVELS? •  Computa,onal   •  Algorithmic   •  Implementa,onal   •  Bayesian  picture  of  structure  of   reasoning   –  Consistancy   –  Bayesian  upda,ng   –  Specific  priors   •  Graphical  models,  MCMC   learning,  etc.   •  Bayesian  neural  calcula,ons   (e.g.,  Latham,  Pouget,  Shadlen   etc)