Overview

1. Overview PSYC 575 Computational Modeling

2. Goals Introduce enough concepts so that you will recognize these building blocks in articles that you might read that use modeling Expose you to a variety of modeling approaches so that you know what tools are available The goal is not to teach you how to use all of these tools or the entire palette of possible tools There are simply too many The goal is also not to teach you how to program You will learn how the models behave and why Programmers will learn enough in the course to program models themselves

3. General approach in class Start with a historical overview Discuss the linear statistical approaches as baseline of comparison Then progress through families of architectures/algorithms Move from simplest to most complex We will often look at a specific application of the technique.

4. Modeling is all about the formal specification of relationships These relationships are either: Observed - your model summarizes historical relationships, Inferred - your model goes beyond historical relationships to posit unobserved ones. Model used to generate predictions.

5. Approaches discussed in class Modeling linear relationships to predict y Regression (GLM � general and generalized) Modeling nonlinear relationships to predict y Pattern association (inferring one set of variables from another) Linear, nonlinear, backprop, nearest neighbor, RBF. Temporal relations (using nn approaches) MLM (new topic � repeated measures modeling) Finding patterns - Unsupervised learning.

6. Nonlinear vs. Linear techniques The goal is to model or describe a relationship Linear approximates are common Nonlinear relationships are superior in situations where behavior must meet certain requirements. For example, dv must exceed 0, is constrained to a range, or subject to known properties of time/physics/mathematics. Many nonlinear approaches are theory-free (e.g., splines, neural networks) Many neural networks are similar or identical to statistical methods (Sarle, 1994).

7. Finding a solution Most nonlinear approaches provide an iterative method to converge on a solution � data is given a bit at a time and solutions are approached, not solved for. Take a guess at right answer and then adjust ad infinitum Statistical methods are sometimes iterative, but often can find a solution (e.g., LSM) in a single step given all of the data

8. Classes of relationships to be learned - I Predicting continuous variables from others Regression Associative learning Problem � most people know how to do simple and multiple regression, but few have the tools and knowledge to do nonlinear regression or multivariate regression.

9. Classes of relationships to be learned - II Predicting continuous variables from categorical ones ANOVA, MANOVA Associative learning Issue � how many are comfortable with MANOVA?

10. Classes of relationships to be learned - III Predicting categorical from categorical Chi-squared, loglinear analysis Associative learning w/response mapping Issue � do you even know what loglinear analysis is?

11. Classes of relationships to be learned - IV Cluster analysis Various cluster analysis techniques Competitive learning Dimensionality reduction Factor analysis & principal component analysis Unsupervised Hebbian learning, autoassociative models

12. Specific mappings between some neural net and statistical techniques Feedforward nets with no hidden layer are basically generalized linear models. Feedforward nets with one hidden layer are closely related to projection pursuit regression. Kohonen nets for adaptive vector quantization are very similar to k-means cluster analysis. Hebbian learning is closely related to principal component analysis. Some neural network areas appear to have no close relatives in the existing statistical literature Reinforcement learning, backpropagation

13. Bottom line Most statistical techniques assume a particular functional relationship between the independent and dependent variables. Some stat techniques and most neural net algorithms are universal function approximators If your problem conforms to a standard statistical technique that you are familiar with and it can answer your questions, use it! Don�t just use neural network or nonlinear models just because you can. Statistical models can tell us a lot. e.g., what is the relative weight of various factors e.g., does the variability across many behaviors boil down to a handful of underlying factors.

14. Modeling issues Many of the issues you face with statistical analyses also arise in modeling. Examples � Too little data on which to base model. Too many predictors can create a model with too many dfs�. Overfitting. Use of an intercept = use of bias nodes. Multicollinearity in predictors produces unstable estimates of the relative importance of each predictor

15. Different modeling philosophies Models for theory testing Strong inference method � comparing two models/theories quantitatively. Example: Lots� Young & Wasserman, 2007 Models of the brain Neurophysiology drives the architecture and computational methods used. Simplification is inevitable. Examples (next�)

16. Atallah et al. (2004)

17. Modeling philosophies, cont Models as evidence proofs Common � method of weak inference? Example: Look! A simple associative system can do it without positing complex symbolic structures Rationale based on law of parsimony but doesn�t disprove a more complex theory. Models as thought experiments Provides a different way of thinking about psychological processes and representation. Common in philosophy (Dennett, Churchlands, Clark). Models for data analysis Uses it like a statistical tool. Often to solve applied problems (e.g., diagnosis, prediction).

18. Your philosophy will drive the input and output representations What are your goals? e.g., Veridical input vs. preprocessed input An example, text comprehension Must you solve the problem of converting bitmaps to letters and then to words before you can start worrying about the extraction of meaning? Evidence proof vs. theory testing Evidence proof � sufficient to show that one type of network with one set of parameters will solve the task. Theory testing � need to compare the best fitting parameters for two models that are being compared.

19. Next class An informal introduction to �R� Discussion of Platt article on strong inference Discussion of Luce article on modeling