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Computational Cognitive Science

Computational Cognitive Science 9
Introduction Types of Models Course Overview Computational Cognitive Science Lecture 1: Introduction Frank Keller School of Informatics University of Edinburgh kellerinf.ed.ac.uk September 20, 2016 Frank Keller Computational Cognitive Science 1Introduction Types of Models Course Overview 1 Introduction Models and Theories Models in Cognitive Science 2 Types of Models Data Description Process Characterization Process Explanation 3 Course Overview Reading: Lewandowsky and Farrell (2011: Ch. 1). Frank Keller Computational Cognitive Science 2Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Models and Theories The aim of cognitive science is to understand how the mind works. This involves describing, predicting, and ultimately, explaining human behavior. To achieve this, analyzing data and forming verbal theories is not sucient, we need quantitative mathematical models. Example from physics: planets in the night sky move back and forth in loops. Frank Keller Computational Cognitive Science 3Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Models and Theories Frank Keller Computational Cognitive Science 4Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Models and Theories Observation: retrograde motion of planets: this observation is hard to explain (or even to describe) without a model; the model itself (even though it may explain the data) is an unobservable, abstract device; there are always several possible models that explain the data. Competing models of planetary motion: Ptolemaic: planets move around the earth in deferents and epicycles; Copernican: planets move around the sun in circles. Frank Keller Computational Cognitive Science 5Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Ptolemaic Model of Planetary Motion center of epicycle planet retrograde motion epicycle center of deferent Earth deferent trajectory of epicycle Frank Keller Computational Cognitive Science 6Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Deciding between Models Ptolemaic (geocentric) vs. Copernican (heliocentric) model:  both predict the position of the planets to within 1 accuracy; Copernican model predicts latitude slightly better; but its main advantage is elegance and simplicity, not goodness of t to the data. Does that mean that goodness of t is irrelevant Then why do we need quantitative models Kepler's laws of planetary motion replace the circles in the Copernican model with ellipses (of di erent eccentricities); this small modi cation achieves nearperfect t with the data. For discussion of model comparison, see lecture 6. Frank Keller Computational Cognitive Science 7Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Models in Cognitive Science Categorization experiment (Nosofsky 1991): training: participants classify cartoon faces into two categories; transfer: participants see a larger set, both faces they've seen before and new ones; they need to classify the face, say how con dent they are, and whether they've seen it before. Moderate correlation between classi cation con dence and recognition probability. Frank Keller Computational Cognitive Science 8Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Models in Cognitive Science 33 1.0 18 34 3 4 32 28 30 1 0.8 15 2 5 24 27 9 23 14 7 6 8 16 20 0.6 10 11 25 26 0.4 21 31 22 29 1913 17 12 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Classification “Confidence” Frank Keller Computational Cognitive Science 9 Recognition ProbabilityIntroduction Models and Theories Types of Models Models in Cognitive Science Course Overview Models in Cognitive Science No strong relationship between classi cation and recognition. Can we conclude that whether you con dently classify a face doesn't depend on whether you remember it No, there is a cognitive model (the GCM, details below), which relates classi cation and recognition and predicts both accurately. The data don't speak for themselves, but require a quantitative model to be described and explained. Frank Keller Computational Cognitive Science 10Introduction Models and Theories Types of Models Models in Cognitive Science Course Overview Models in Cognitive Science Categorization Recognition 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Predicted Probability Predicted Probability Frank Keller Computational Cognitive Science 11 Observed Probability Observed ProbabilityIntroduction Data Description Types of Models Process Characterization Course Overview Process Explanation Types of Models A model is supposed to describe existing data, predict new observations, and provide an explanation for the relevant behavior. Lewandowsky and Farrell (2011) propose three types of models: data descriptions: summarize the data in mathematical form, typically involving parameters estimated from the data; process characterizations: postulate distinct cognitive components that generate the data, but remain neutral with respect to their implementation. process explanations: provide detailed speci cation of the components underlying a cognitive process. Frank Keller Computational Cognitive Science 12Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Data Description Example: The relationship between the amount of practice and the response time in a learning task can be described by power law: RT = N An alternative model is in terms of an exponential function: N RT = e where RT is the response time, N is the number of trials, and and are learning rates. Frank Keller Computational Cognitive Science 13Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Data Description 7000 7000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000 0 100 150 50 Trial Number Frank Keller Computational Cognitive Science 14 Response Time (ms)Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Data Description Both models provide a good t to the data (dashed line: power law; solid line: exponential function). Ways to decide between them: goodness of t: recent work shows that the exponential function provides a better t to the data on learning; empirical predictions: the mathematical form of the power law implies that the learning rate decreases with increasing practice; the exponential function implies it stays constant. Ideally, however, we want to tie the parameters in the model to psychological processes. Frank Keller Computational Cognitive Science 15Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Process Characterization A process characterization postulates distinct cognitive components, but remains neutral as to how these are implemented. Example: multinomial processing tree model of memory recall: information is recalled intact with probability I ; information that is not recalled intact is redintegrated (reconstructed) with probability R. The model predicts C , the probability of a correct response, and E , the probability of an error, as: C = I + (1 I )R E = (1 I )(1 R) Frank Keller Computational Cognitive Science 16Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Process Characterization This model therefore assumed to independent processing stages, each associated with a characteristic parameter: 1 I I C 1 R R E C For parameter estimation, see lectures 3, 4, and 8. Frank Keller Computational Cognitive Science 17Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Process Explanation A process explanation not only identi es the components of a cognitive process, but also speci es them in detail. Example: Generalized Context Model (GCM; Nosofsky 1986), an exemplar model of categorization: during training, the model stores every instance of a category; during testing, a new instance activates all stored exemplars depending on similarity; response probability depends on the sum of the similarity with each member of the category. Frank Keller Computational Cognitive Science 18Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Generalized Context Model Example instances (Nosofsky 1991): Features: eye height, eye separation, nose length, and mouth height. Frank Keller Computational Cognitive Science 19Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation Generalized Context Model The distance d between two instances i and j, where each has K ij features with values x and x , is: ik jk 1 K 2 X 2 d = jx x j ij ik jk k=1 The similarity between i and j is (where c is a parameter): s = exp(c d ) ij ij Then the probability of classifying instance i into category A (rather than category B) is: P s ij j2A P P P(R = Aji) = i s + s ij ij j2A j2B Frank Keller Computational Cognitive Science 20Introduction Data Description Types of Models Process Characterization Course Overview Process Explanation The Power of Models Models are useful because they can: help classify phenomena (e.g., by relating seemingly unrelated data, see categorization vs. recognition); provide new understanding (e.g., show that an architecture can generate a phenomenon, see single route vs. dual route); help explore the implications of a theory (e.g., lesioning a model, scaling to larger data sets, exploring learning). Frank Keller Computational Cognitive Science 21Introduction Types of Models Course Overview Course Overview This course provides an introduction to computational cognitive modeling. There are two main parts: introduction to modeling methodology; discussion of speci c implemented models. We will cover three broad areas of cognition: memory; language; vision. The textbook is Lewandowsky and Farrell: Computational Modeling in Cognition. The university has an electronic subscription. This is complemented by papers, see reading list on course web page. Frank Keller Computational Cognitive Science 22Introduction Types of Models Course Overview Required Background This course requires programming skills. We will use Matlab for the assignment. Some Matlab will be covered in the tutorials, but you may need a text book such as McMahon: MATLAB Demysti ed. The second requirement is maths background: probability theory: random variables, distributions, expectations, Bayes theorem, etc.; linear algebra: basic vector and matrix operations. If you need a refresher, use Sharon Goldwater's maths tutorial: http://homepages.inf.ed.ac.uk/sgwater/mathtutorials.html Frank Keller Computational Cognitive Science 23Introduction Types of Models Course Overview Communication When you sign up for the course, you will have access to: the course mailing list: used for all essential communication; the Learn page of the course: used for quizzes, assignment, lecture recordings; all other material will appear on the course web page. On Learn, there will also be a discussion forum for the course: you can use it to post questions about the course content, including tutorials and assignment; the main purpose is peer support: students discuss course material and help each other; lecturer and TA moderate the discussion and contribute. Frank Keller Computational Cognitive Science 24Introduction Types of Models Course Overview Assessment, Tutorials, Lectures The assessment on this course will consist of: an assessed assignment, worth 25 of the overall mark; a nal exam (120 minutes), worth 75 of the overall mark. See the course web page for: date of assignment and how to submit it; plagiarism policy; lecture slides, lecture recordings, old exams. There are weekly tutorials for this course: tutorials are both practical (use Matlab) and theoretical; they start in Week 3; you will be automatically assigned a tutorial group; if you have a timetable clash, contact the ITO. Frank Keller Computational Cognitive Science 25Introduction Types of Models Course Overview Feedback Feedback students will receive in this course: some lectures will feature short, nonassessed quizzes; tutorials will be based on nonassessed exercises; you should try to solve these before the tutorials sample solutions will be released for tutorials; tutorials include a feedforward session for the assignment; the assignment will be returned to students within two weeks; individual, written comments will be provided by the marker; a sample solutions for the assignment will be provided. Frank Keller Computational Cognitive Science 26Introduction Types of Models Course Overview References Lewandowsky, Stephan and Simon Farrell. 2011. Computational Modeling in Cognition: Principles and Practice. Sage, Thousand Oaks, CA. Nosofsky, Robert M. 1986. Attention, similarity, and the identi cationcategorization relationship. Journal of Experimental Psychology: General 115(1):3957. Nosofsky, Robert M. 1991. Tests of an exemplar model for relating perceptual classi cation and recognition memory. Journal of Experimental Psychology: Human Perception and Performance 17(1):327. Frank Keller Computational Cognitive Science 27