User:Mwakanosya/Optimal sequential decision making

A cognitive model is an approximation to animal cognitive processes (predominantly human) for the purposes of comprehension and prediction. Animals (and humans) are complex nonlinear systems which makes it unlikely to find simple, intuitive principles that guide their behavior. Once a model is created, rather than deriving a mathematical analytical solution, experimentation with the model is done by changing the parameters of the system in the computer, and studying the differences in the outcome of the experiments. Theories of operation of the model can be derived/deduced from these computational experiments.

Cognitive models can be developed within or without a cognitive architecture.

=History= Several early developments in the 20th century led mathematicians and scientists to conclude that human thought and behavior could be mechanized. Computing the output of functions involved manipulating mathematical symbols to transform a given input into the desired output. Alonso Church suggested "that every computable function (in the intuitive sense) is a recursive function (in the mathematical sense) (cite: Dupuy)". Alan Turing, in 1937, (cite: computability and lambda-definability) demonstrated the equivalence between recursive functions and functions computable by a Turing Machine. This allowed for the mechanization of mathematical procedures. Six years earlier, in developing his incompleteness theorem, Kurt Godel developed a technique to encode formal expressions (in particular, recursive functions) as natural numbers. This allowed Turing to demonstrate the existence of Universal Turing Machines, which could simulate any other Turing Machine (as those Turing Machines were functions which could be expressed as a number and then treated as a system input). As Turing Machines modeled human procedures (mental faculties), then Universal Turing Machines were models of the ability to model, or a model of the mind itself.


 * 1) Translating Theoretical Turing Machines into Physical Devices
 * 2) Shannon (same person as Information Theory)
 * 3) Thesis that electrical circuits of Shannon represented artificial neurons and we could construct the brain (Cyberneticists)
 * 4) McCulloch and Pitts
 * 5) Rosenblatt's Perceptron
 * 6) Ashby - Design for a Brain
 * 7) Rejection of Neural Nets and Perceptron
 * 8) Papert and Minsky's Perceptron
 * 9) von Neumann's creation of a physical device that more accurately worked as a Theoretical Turing Machine
 * 10) Jump into Cognitivism and GOFAI
 * 11) Later reaction in 80s with PDPs at UCSD
 * 12) Work in Bayesian Cognitive Science
 * 13) Work in Dynamical Cognitive Science

=Frameworks/Architectures= Cognitive architectures tend to be focused on the structural properties of the modeled system, and help constrain the development of cognitive models within the architecture. Historically, some of the most popular architectures for cognitive modeling included ACT-R and Soar.

Symbolic/Logical
Expressed in characters, usually nonnumeric, that require translation before they can be used.

Subsymbolic
A model is subsymbolic if it is made by constituent entities that are not representations in their turn, e.g., pixels, sound images as perceived by the ear, signal samples; subsymbolic units in neural networks can be considered particular cases of this category.

Dynamical Systems
Dynamicism (also known as the dynamic hypothesis, the dynamic hypothesis in cognitive science, or dynamic cognition) is a new approach in cognitive science that argues that differential equations are more suited to modelling cognition than more traditional computer models. Researchers in this area include Tim van Gelder (Mind in Motion), Esther Thelen & Linda Smith (A Dynamic Systems Approach to the Development of Cognition and Action), and Michael Spivey (The Continuity of Mind).

=Models of Cognitive Behavior= In contrast to cognitive architectures, cognitive models tend to be focused on a single cognitive phenomenon or process (e.g., list learning), how two or more processes interact (e.g., visual search and decision making), or to make behavioral predictions for a specific task or tool (e.g., how instituting a new software package will affect productivity). Model development helps to inform limitations and shortcomings of the specific architecture utilized.

AI Models
This class broadly refers to the class of algorithms that generate intelligent behavior. The aim is not to propose a mechanism for what possibly goes on inside the brain but to have working agents/algorithms that exhibit behavior that has been deemed cognitive. The examples range from classification algorithms like Latent Dirichlet Allocation (unsupervised) or Logistic regression (supervised) to computer vision algorithms employing techniques like Independent Component Analysis or Sparse coding. Broadly speaking, most of the initial endeavors toward Artificial Intelligence are encompassed by this class.

Examples

 * 1) Classification: Consider as a concrete instance the problem of determining which customers are likely to make a purchase in a given year. The customer database stores relevant information about each customer like their age, gender, family size, annual income and so on. A Logistic Regression algorithm can be employed for this task using the older database with purchase information as the training set. The final behavior of the algorithm is an intelligent classification which further aides decisions like marketing policy.
 * 2) Dimensionality Reduction: At times the data under consideration is high-dimensional (e.g. a 100x100 image represented as a 10000 dimensional data point). But for a dataset it may be so that the relevant dimensions are fewer. Consider the case when the images are of digits, only the pixels around the center carry information, the surrounding pixels just being white. In this case, dimensionality reduction techniques like Principal Component Analysis (PCA) can be used so that the further processing of the data becomes less computationally complex. PCA works by finding a lower dimensional hyperplane that describes most of the variance in the data. The result is the same dataset but with fewer dimensions and lower redundancy. Independent Component Analysis (ICA) is another dimensionality reduction technique which finds non-Gaussian and independent components instead of assuming the components are only Gaussian and uncorrelated.
 * 3) Recommender Systems: There are several applications when the feature set is impoverished. Consider as an example the task of recommending a movie to an imdb user who might have only provided minimal information during registration (like email id, date of birth, etc.). Reliable recommendations cannot be generated with this information. So the techniques like collaborative filtering are used which use the information of how the user rated other movies and how these movies were rated by other users. Using matrix decomposition like  Singular value decomposition, the algorithm extracts hidden features and uses them to predict how a given user would rate a given movie. One of the popular uses of this class of algorithm is Amazon's recommendation system.
 * 4) Multi-view Data Analysis: Using multiple views of the same data can improve the performance of dimensionality reduction techniques. For instance, if there exists a database of documents in which each document is written in two languages, one can use this information to help find meaningful linguistic structures that are also correlated across languages. Another example is learning the structure of Wikipedia (the number of distinct categories) by using each page's words and outgoing links (reference: Multi-view Clusting via CCA). One technique, Canonical Correlation Analysis (CCA), works by finding a common subspace, such that when both views of the data are projected to this subspace, they are maximally correlated. This concept has also been used to reference the human ability to correlate incoming sensory data from multiple modalities (vision, hearing, smell, etc) but from a batch processing point of view (see Multimodal integration for temporal versions).

Behavioral Models
These are mathematical models that attempt to explain a cognitive process qualitatively or quantitatively as it occurs in a living animal or human. The first step involves collecting data (e.g. decisions in a given task, response time, recall rates, etc.) from human or animal subjects. The second step involves estimating model parameters for individuals who perform the task. This data can then be used to hypothesize about the effects of varying certain experimental conditions: if new subject data aligns with model predictions, this lends support to that modeling framework.

Examples
Currently, this list of examples addresses models of cognitive tasks that assume a probabilistic and statistical framework.
 * 1) Oculomotor control: Saccades are quick, simultaneous movements of both eyes in the same direction. Our eyes move around to locate the most interesting features in the environment, so that we may foveate and obtain the highest resolution of the scene we choose to look at. Since the fovea must constantly redirected at different visual targets (cite:Harris & Wolpert 2006), it is of great importance to understand the mechanism and the dynamic of saccadic eye movement. There are two directions of modeling saccadic eye movements:
 * 2) Fixation choices (i.e. where to saccade):. There are a number of studies trying to understand saccade planning in different conditions and environment. For example, saccade as a decision in 2AFC (2 Alternative-Forced-Choice) tasks and eye fixation choices in visual-search tasks.
 * 3) Saccades in Motion-discrimination tasks: Saccades have been used as an indication of perceptual decision in random-dot motion detection tasks. (Shadlen, M. N., & Newsome, W. T, 1996). In those tasks, subjects (monkeys) need to make a left or rightward saccade to one of two locations cues, to indicate their decision of the stimuli direction, where the stimuli is a patch of random moving dots, in which a percentage (i.e. coherence) of them are moving coherently towards a pre-defined direction (either left or right). It has been found that as the task difficulty increases, subjects' reaction time will increase and accuracy will decrease. (Gold & Shadlen, 2002). It suggests that there a speed-accuracy trade-off in those tasks, which is an important effect in human decision theory.
 * 4) Saccades in Visual-Search tasks: In reality, we make sequential eye movements to locate the visual 'target'. There have been a number of studies to model saccadic eye movements in visual-search tasks where subjects are required to look for a particular 'target' embedded in a noisy environment. It has been found that saccades tended to be directed to more rewarded (Sohn & Lee, 2006), or more informative locations (Pomplun, Reingold, & Shen, 2003). Viewing saccadic eye movements as a product from top-down and bottom-up process, in visual-search tasks, it has been shown that our eye movements are both affected by our knowledge of the environment (top-down) and by the saliency of the scene (bottom-up).  Psychopysical studies of visual search (Palmer, Verghese & Pavel, 2000) showed evidence that when we process the visual information with saccadic eye movements, "information from all stimuli is combined optimally to maximize performance in the particular task. "
 * 5) Saccades trajectory: In particular, saccade duration, velocity and amplitude of saccadic eye movements (known as the 'main sequence'). Here are some major theoretical frameworks for saccadic eye movement:
 * 6) Minimum variance
 * 7) Minimum movement duration
 * 8) Minimum jerk
 * 9) Hypothesis Testing:
 * 10) Change Detection:
 * 11) Inhibitory Control:
 * 12) Sensory Discrimination: Thurstonian models attempt to explain how an intelligent agent (often humans) map continuous sensory information into discrete response categories.

=See also=

Historical Progression

 * Cybernetics
 * Perceptron / Neural Network
 * Cognitivism / GOFAI / Cognitive Psychology
 * Cognitive Science
 * Connectionism
 * Bayesian cognitive science
 * Dynamical Cognitive Science

Related Concepts

 * Artificial Intelligence
 * Intelligent Control
 * Cognitive Architecture
 * Agent Architecture

University Research Programs

 * Carnegie Mellon University
 * RPI (HCI)
 * RPI (CLARION)
 * University of Memphis
 * UMich

Category:Cognition Category:Scientific modelling