cognitive modeling

Cognitive modeling

Bram Zandbelt

[email protected]

@bbzandbelt

https://www.bramzandbelt.com

Download at: http://www.slideshare.net/bramzandbelt/cognitive-modeling

http://www.slideshare.net/bramzandbelt/cognitive-modeling

Preview

Cognitive modeling

1. What is a model?

1.1. Why ask this question in the first place?

1.2. Examples of models

1.3. Definition of a model

2. Why use models?

2.1. Why use models in general?

2.2. Why use models in cognitive neuroscience?

2.3. Formal models come in di erent flavors

3. How to use models?

3.1. How to formulate a model?

3.2. How to estimate a model?

3.3. How to evaluate a model?

Bram Zandbelt

1.1 Why ask the question in the first place?

Source: Google

Bram Zandbelt

Source: http://www.scientificamerican.com/article/just-a-theory-7-misused-science-words/

1.1 Why ask the question in the first place?

Bram Zandbelt

http://www.scientificamerican.com/article/just-a-theory-7-misused-science-words/

1.2 Examples of models

Models

Schematic PhysicalSymbolic

Verbal Formal

Bram Zandbelt

1.3 Definition of a model

Fum et al. (2007) Cog Sys Res 8:135

“A model is a simpler and more abstract version of a system that keeps its essential features

while omitting unnecessary details”

–Howard Skipper

“A model is a lie that helps you see the truth”

Bram Zandbelt

Preview

Cognitive modeling

1. What is a model?




2. Why use models?








Bram Zandbelt

2.1 Why use models?

Data never speak for themselvesA framework, theory, causal model, logical construct, perception of the world, etc. is necessary to make sense of data

Models address scientific questions Models are tools serving various purposes, including description, prediction, and explanation

… lead to new experiments […] leading to new hypotheses, guiding experiments, and findings

… and are often complex Abstractions help to see the big picture

… promote a scientific habit Formulating models forces you to think logically and clearly about what you know and don’t know

Bram Zandbelt

Same data, different conclusions

Optimist: glass half full

Pessimist: glass half empty


2.1 Why use models?

Bram Zandbelt

Sources: fieltriptoolbox.org



2.1 Why use models?

Bram Zandbelt

http://www.fieldtriptoolbox.org/_media/tutorial/natmeg_temp/natmeg_databrowser2.png?w=650

http://fieltriptoolbox.org

Sources: Van Belle et al. (2014) Neuroimage; fieltriptoolbox.org



2.1 Why use models?

Bram Zandbelt

http://www.fieldtriptoolbox.org/_media/tutorial/natmeg_temp/natmeg_databrowser2.png?w=650

http://www.fieldtriptoolbox.org/_media/tutorial/eventrelatedaveraging/singleplot_mlc24_3feb09_erf.png?w=400

http://fieltriptoolbox.org




2.1 Why use models?

Bram Zandbelt



… lead to new experiments They suggest novel hypotheses, predicting future findings, and guide experimental design



2.1 Why use models?

Bram Zandbelt

2.2 Why use (formal) models in cognitive neuroscience?

The brain is a complex system Complex systems need to be understood at multiple levels

Bram Zandbelt

Marr’s level Question

1 Computational/Functional

What is the function? Why is it performed?

input i output o

Sources: Marr (1982)


Bram Zandbelt




2 Algorithm What algorithm achieves this function? How are inputs and outputs represented?

f(i)input i output o



Bram Zandbelt




2 Algorithm What algorithm achieves this function? How are inputs and outputs represented?

3 Implementation How are algorithm and representation realized physically?


input i output o


Bram Zandbelt



Models can help to bridge the gap between brain and behavior Understanding computation guides research in the underlying circuits and provides a language for theories of behavior

Bram Zandbelt

Implementation Algorithm Function

Sources: Carandini (2012) Nat Neurosci


Bram Zandbelt


Models can take different forms Verbal: words or box-and-arrow diagrams Formal: axioms, equations, computer code


Models can help to bridge the gap between brain and behavior Understanding computation guides research in the underlying circuits and provides a language for theories of behavior

Bram Zandbelt

Cognitive process

input i output o = f(i)


Bram Zandbelt

Cognitive processBrain… …

Model inputs Predicted behavior

Unobserved neural/mental

process N

Brainsignal detection … …response

preparationresponse execution

qualitative fit

RTData/Reality


Verbal model

Observed neural

process 1


process i

qualitative constraints

Bram Zandbelt

BrainObserved

neural process

1… …

Model inputs Predicted behavior


process i


process N

Brain… …∫dt

qualitative and

quantitative fit

Model parameters

RT

qualitative and

quantitative constraints

RT

signal detection

response preparation

response execution


Formal model

Data/Reality

Bram Zandbelt

Potential problems ofverbal models

Solutions from formal models

Flawed reasoning(inconsistencies, contradictions, gaps)

e.g. belief bias

Formal system (clarity, coherence, completeness)

Sources: Farrell, S., & Lewandowsky, S. (2010). Curr Dir Psych Sci; Fum et al. (2007) Cog Sys Res; Hintzman (1991)


Bram Zandbelt

Does the conclusion logically follow from the premises?

Premise 1 No police dogs are vicious

No nutritional things are inexpensive

No addictive things are inexpensive

No millionaires are hard workers

Premise 2 Some highly trained dogs are vicious

Some vitamin tablets are inexpensive

Some cigarettes are inexpensive

Some rich people are hard works

ConclusionTherefore, some highly trained dogs are not police dogs

Therefore, some vitamin tablets are not nutritional

Therefore, some addictive things are not cigarettes

Therefore, some millionaires are not rich people

Valid Believable

Valid Unbelievable

Invalid Believable

Invalid Unbelievable

Sources: Evans et al. (1983) Mem Cogn


Bram Zandbelt





e.g. belief bias


Limits of human thinking(imagination, working memory)

e.g. reasoning about complex systems

Computational power(in-depth exploration, no memory issues)


Bram Zandbelt

Sources: Marder (2014) Ann Rev Neurosci


Bram Zandbelt





e.g. belief bias


Limits of human thinking(imagination, working memory)

e.g. reasoning about complex systems

Computational power(in-depth exploration, no memory issues)

Misunderstanding(hidden assumptions, vague definitions)

e.g. concept of inhibition

Computer code and equations(explicit assumptions, precise definitions)


Bram Zandbelt

Sources: Aron (2007) Neuroscientist; see also MacLeod et al. (2003) in Psychology of learning and motivation, B. Ross, Ed., vol. 43, pp. 163–214.


Bram Zandbelt

Sources: Lewandowsky, S. (1993) Psych Sci; Jacobs, A. M., & Grainger, J. (1994). J Exp Psychol um Percept Perform; Ulrich (2009) in: Rösler, Ranganath, Röder, Kluwe (Eds.), Neuroimaging of human memory:linking cognitive processes to neural systems. New York: Oxford University Press

… overspecification of irrelevant details Obscures the discovery of general principles

… less suitable for new research fields Sometimes we only have vague ideas

… overparameterizationGood fits can be bad; simpler models may exist

… realism comes at a costBonini’s paradox: as a model becomes more realistic, it becomes increasingly difficult to understand


Formal models have limitations, too:

Bram Zandbelt

Psychophysical models Relate physical stimuli to sensation/perception

2.3 Formal models come in different flavors

Bram Zandbelt

Expected Utility

Axiomatic models Replace the phenomenon to be modeled with logical propositions from which behavior can be derived



Source: von Neumann & Morgenstern (1944)

Bram Zandbelt



Algebraic modelsSimple equations that describe how input stimuli and model parameters are combined to produce behavior


Source: Logan (1988) Psych Rev; Logan (2002) Psych Rev

Bram Zandbelt

Algorithmic models Defined in terms of a computer simulation that describes how processes interact to produce behavior





Bram Zandbelt





Connectionist models Describe behavior with multilayer networks of interconnected units


Bram Zandbelt

http://www.mind.ilstu.edu/curriculum/connectionism_intro/imgs/PDP_3LFFN_1.GIF

Schizophrenia is not a rare disorder. It has a lifetime risk of ~0.7%1 (similar to that of rheumatoid arthritis). It has a genetic basis, but the importance of social fac-tors in its emergence is also recognized. Schizophrenia is devastating for both sufferers and their carers. Patients are likely to be unemployed or fail to fulfil their original potential. Contact with the police result-ing from socially unacceptable behaviour is common, and the risk of suicide is high. The first episode typi-cally occurs when patients are in their mid 20s, and most sufferers never fully recover. Although drug treat-ment and, more recently, cognitive behavioural therapy can reduce suffering, there is as yet no cure for this disorder. Furthermore, although schizophrenia clearly has a strong biological component (BOX 1), no diagnos-tic physiological markers have been found. Diagnosis, therefore, is made on the basis of symptoms described by the patient, signs observed by the clinician and the history of the disorder (BOX 2).

The most striking and characteristic features of the disorder are hallucinations and delusions. Hallucinations are false perceptions, such as patients hearing people talking about them or hearing their thoughts spoken aloud (TABLE 1). Delusions are per-sistent bizarre or irrational beliefs that are not easily understood in terms of an individual’s social or cul-tural background. For example, patients may believe

that other people can hear their thoughts or that the government is monitoring their every action. Hallucinations and delusions are examples of positive symptoms, which are so called because the abnormal-ity lies in their presence. Positive symptoms contrast with negative symptoms (also known as signs), which are defined by the absence of normal functions, as is the case with reduced speech output (alogia) or loss of motivation (avolition). There is evidence that posi-tive and negative symptoms reflect different under lying physiological disorders2,3. Although an important chal-lenge for future work will be to find an explanation for both positive and negative symptoms, we believe that the current state of the field and the fact that these symptoms seem to dissociate across groups of patients make it sensible to confine our ideas in this Review to the positive symptoms. Our aim is to consider how abnormal physiological responses in the brains of peo-ple with schizophrenia might be linked to the positive symptoms that they experience. We show that a com-mon mechanism, involving minimization of predic-tion error, may underlie perception and inference, and that a disruption in this mechanism may cause both abnormal perceptions (hallucinations) and abnormal beliefs (delusions). We are not concerned with the ulti-mate causes of the disorder, in which both genetic and environmental factors play a part.

*University of Cambridge, Department of Psychiatry, Addenbrooke’s Hospital, Hills Road, Cambridge, CB2 2QQ, UK. ‡Centre for Functionally Integrative Neuroscience, Aarhus University Hospital, 8000 Aarhus C, Denmark. §Wellcome Trust Centre for Neuroimaging, Functional Imaging Laboratory, University College London, London, WC1N 3BG, UK.Correspondence to C.D.F.e-mail: [email protected]:10.1038/nrn2536Published online 3 December 2008

Cognitive behavioural therapyA form of psychotherapy in which the patient is encouraged to examine the cognitive processes by which they arrive at a particular state of mind, and to change these processes together with the accompanying behaviours that may reinforce them.

Perceiving is believing: a Bayesian approach to explaining the positive symptoms of schizophreniaPaul C. Fletcher* and Chris D. Frith‡§

Abstract | Advances in cognitive neuroscience offer us new ways to understand the symptoms of mental illness by uniting basic neurochemical and neurophysiological observations with the conscious experiences that characterize these symptoms. Cognitive theories about the positive symptoms of schizophrenia — hallucinations and delusions — have tended to treat perception and belief formation as distinct processes. However, recent advances in computational neuroscience have led us to consider the unusual perceptual experiences of patients and their sometimes bizarre beliefs as part of the same core abnormality — a disturbance in error-dependent updating of inferences and beliefs about the world. We suggest that it is possible to understand these symptoms in terms of a disturbed hierarchical Bayesian framework, without recourse to separate considerations of experience and belief.

REVIEWS

48 | JANUARY 2009 | VOLUME 10 www.nature.com/reviews/neuro

Source: Fletcher & Frith (2009) Nat Rev Neurosci





Connectionist models Describe behavior with multilayer networks of interconnected units

Bayesian modelsAssume that we make inferences using Bayesian statistics


Bram Zandbelt

Preview

Cognitive modeling

1. What is a model?




2. Why use models?








Bram Zandbelt

Steps in cognitive modeling

Formulation

EstimationEv

aluation

Bram Zandbelt

3.1 How to formulate a model?

Core assumptions (A)Based on conceptual theory of underlying mechanismAuxilliary assumptions Conceptual theories often lack important detailsDefinitions Of dependent variables, such as RT

Theorems (T)Combine assumptions & definitions to derive abstract predictions

Predictions (P) Add parameters for concrete predictions that can be compared with data

ParametersTuning knobs of the model

Sources: Ulrich (2009) in: Rösler, Ranganath, Röder, Kluwe (Eds.), Neuroimaging of human memory:linking cognitive processes to neural systems. New York: Oxford University Press

Bram Zandbelt

Sources: Ulrich (2009) in: Rösler, Ranganath, Röder, Kluwe (Eds.), Neuroimaging of human memory:linking cognitive processes to neural systems. New York: Oxford University Press

Model of cross modal temporal discrimination


Bram Zandbelt


Bram Zandbelt

3.2 How to estimate a model?

Main estimation methods: LSE & MLE LSE: finds parameters that most accurately describe the data MLE: finds parameters that most likely have generated the data

Least-squares estimation (LSE)

Maximum likelihood estimation (LSE)

Bram Zandbelt

3.2 How to estimate a model?

Source: Lewandowsky, S., & Farrell, S. (2010). Computational modeling in cognition: Principles and practice. Sage.

Main estimation methods: LSE & MLE LSE: finds parameters that most accurately describe the data MLE: finds parameters that most likely have generated the data

Various approaches to find best fit Grid search - easy but laborious

Simplex - efficient but risk ending in local minimum

Simulated annealing, genetic algorithm - likely to end in global minimum but time-consumingparam X

param Y

cost fun

Bram Zandbelt

3.3 How to evaluate a model?

Source: Cavagnaro, Myung, Pitt (2010) in: Oxford Handbook of Quantitative Methods, Volume 1: Foundations, Ed. T. Little; see also Jacobs & Grainger (1994) J Exp Psychol Hum Percept Perform

Bram Zandbelt

Goodness of fit can be quantified with likelihood or root mean squared error

Source: Cavagnaro, Myung, Pitt (2010) in: Oxford Handbook of Quantitative Methods, Volume 1: Foundations, Ed. T. Little


Bram Zandbelt

Complexity can be quantified with Akaike and Bayesian Information Criterion (AIC,BIC)

Goodness of fitPenalty for

free parameters



Bram Zandbelt

Generalizability can be quantified with cross validation


Same model, new data


Bram Zandbelt

Further reading

Lewandowsky, S., & Farrell, S. (2010). Computational modeling in cognition: Principles and practice. Sage.

Cavagnaro, D. R., Myung, J. I., & Pitt, M. A. (2010). Mathematical modeling. In T. D. Little (Ed.), The Oxford Handbook of Quantitative Methods (Vol. 1, pp. 438–453). New York, NY: Oxford University Press.

C H A P T E R

21 Mathematical Modeling

Daniel R. Cavagnaro, Jay I. Myung, and Mark A. Pitt

Abstract

Explanations of human behavior are most often presented in a verbal form as theories. Psychologistscan also harness the power and precision of mathematics by explaining behavior quantitatively. Thischapter introduces the reader to how this is done and the advantages of doing so. It begins bycontrasting mathematical modeling with hypothesis testing to highlight how the two methods ofknowledge acquisition differ. The many styles of modeling are then surveyed, along with theiradvantages and disadvantages. This is followed by an in-depth example of how to create amathematical model and fit it to experimental data. Issues in evaluating models are discussed, includinga survey of quantitative methods of model selection. Particular attention is paid to the concept ofgeneralizability and the trade-off of model fit with model complexity. The chapter closes by describingsome of the challenges for the discipline in the years ahead.

Key Words: Cognitive modeling, model testing, model evaluation, model comparison

IntroductionPsychologists study behavior. Data, acquired

through experimentation, are used to build theo-ries that explain behavior, which in turn providemeaning and understanding. Because behavior iscomplex, a complete theory of any behavior (e.g.,depression, reasoning, motivation) is likely to becomplex as well, having many variables and condi-tions that influence it.

Mathematical models are tools that assist in the-ory development and testing. Models are theories, orparts of theories, formalized mathematically. Theycomplement theorizing in many ways, as discussedin the following pages, but their ultimate goalis to promote understanding of the theory, andthus behavior, by taking advantage of the precisionoffered by mathematics. Although they have beenpart of psychology since its inception, their popu-larity began to rise in the 1950s and has increasedsubstantially since the 1980s, in part because of the

introduction of personal computers. This interest isnot an accident or fad. Every style of model thathas been introduced has had a significant impactin its discipline, and sometimes far beyond that.After reading this chapter, the reader should beginto understand why.

This chapter is written as a first introduction tomathematical modeling in psychology for those withlittle or no prior experience with the topic. Our aimis to provide a good conceptual understanding ofthe topic and make the reader aware of some ofthe fundamental issues in mathematical modelingbut not necessarily to provide an in-depth step-by-step tutorial on how to actually build and evaluate amathematical model from scratch. In doing so, weassume no more of the reader than a year-long coursein graduate-level statistics. For related publicationson the topic, the reader is directed to Busemeyer andDiederich (2010), Fum, Del Missier, and Stocco(2007), and Myung and Pitt (2002). In particular,

437

Bram Zandbelt

Feel free to distribute, remix, tweak, and build upon these slides.

Please attribute Bram Zandbelt with a link to http://www.slideshare.net/bramzandbelt/cognitive-modeling

Except where otherwise noted, this work is licensed under http://creativecommons.org/licenses/by/4.0/

Bram Zandbelt

http://www.slideshare.net/bramzandbelt/cognitive-modeling

http://creativecommons.org/licenses/by/4.0/

cognitive modeling

Presentations & Public Speaking

use models

formal models

examples of models

sense of data models

causal model

model fum

scientific questions

truth bram zandbelt