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Sensory Cue Integration Sensory Cue Integration Multisensory Predictive Learning, Fall, 2011 Summary by Byoung-Hee Kim Computer Science and Engineering (CSE) http://bi.snu.ac.kr/ Presentation Guideline ¥ Quiz on the gist of the chapter (5 min) ¥ Presenters: prepare one main question ¥ Students: read the material before the class ¥ Presentation (30 min) ¥ Include all equations and figures ¥ Limit of slides: maximum 20 pages + appendix (unlimited) ¥ Discussion (30 min) ¥ Understanding the contents ¥ Pros and cons / benefits and pitfalls ¥ Implications of the results ¥ Extensions or applications Multisensory Predictive Learning, Fall, 2011 2 Quiz (5 min) ¥ Q. (question on the gist of the chapter) List and explain briefly ideal observer models of cue integration Multisensory Predictive Learning, Fall, 2011 3 Contents ¥ Motivations and arguments ¥ Problems and experiments ¥ Ideal-observer models ¥ Linear models for maximum reliability ¥ Bayesian estimation and decision making ¥ Nonlinear models: generative models and hidden variables ¥ Issues and concerns ¥ Appendix Multisensory Predictive Learning, Fall, 2011 4 Estimation from Various Information Environment 3D orientation size location depth Vision cues Sensory information Texture / Linear perspective shading binocular disparity, stereopsis auditory cues Cue integration haptic cues Estimation and decision/action Motion planning Motor planning Multisensory Predictive Learning, Fall, 2011 5 Uncertain relationship btw cues and environmental properties Is this optimal? - Variability in the mapping btw the cue and a property - Errors in the nervous system’s measurement of the cue - Measured cue values vary unpredictably across viewing conditions and scenes - Estimates may be based on assumptions about the scene and will be flawed if those assumptions are invalid Multisensory Predictive Learning, Fall, 2011 6 Motivations ¥ Studying perceptual computations ¥ Modeling cue combination ¥ General introduction to the fiend of cue combination from the perspective of optimal cue integration Multisensory Predictive Learning, Fall, 2011 7 Arguments ¥ The organism can make more accurate estimates of environmental properties or more beneficial decisions by integrating multiple sources of information ¥ Observers should be more likely to approach optimal behavior in tasks that are important for survival ¥ “ideal-observer” analysis is a critical step in the iterative scientific process of studying perceptual computations Multisensory Predictive Learning, Fall, 2011 8 Problems and experiments Estimation Cues ExperimentalTask Target Surface orientation Visual / Haptic Walk blindfolded toward Distance to a drop-off Visual / auditory the drop-off / Movement planning Size Visual / Haptic Checking JND, PSE Seeing ridges as real Depth Visual (texture, shading) objects or as computer- graphic image Multisensory Predictive Learning, Fall, 2011 9 Ideal-observer models ¥ Cue combinations from the perspective of optimal cue integration ¥ Building ideal observers helps formulate the scientific questions that need to be answered before we can understand how the brain solves these problems ¥ Models ¥ Linear models for maximum reliability ¥ Bayesian estimation and decision making ¥ Nonlinear models: generative models and hidden variables Multisensory Predictive Learning, Fall, 2011 10 Linear models for maximum reliability ¥ Assumptions ¥ An observer has access to unbiased estimates of a particular world property from each cue ¥ The cues are Gaussian distributed (Gaussian noise) and conditionally independent (n cues è n independent, Gaussian random variables) ¥ The minimum-variance unbiased estimator is a weighted average of the individual estimates from each cue (eq. 1.1) ri: cue’s reliability (inverse variance ) Multisensory Predictive Learning, Fall, 2011 11 BAYESIAN ESTIMATION AND DECISION MAKING Multisensory Predictive Learning, Fall, 2011 12 Bayesian decision theory as a more general framework ¥ Pitfalls of the linear model ¥ Providing important insights into human perceptual and sensorimotor processing ¥ Only provides a “local” approximation to the ideal observer ¥ Bayes’ Rule s: scene properties d: data likelihood prior posterior Normalizing term Multisensory Predictive Learning, Fall, 2011 13 Bayesian decision theory as a more general framework ¥ Bayesian decision maker ¥ Compute the posterior distribution ¥ Choose an estimate, a course of ‘optimal’ action, based on the loss function ¥ An optimal choice of action is one that maximizes expected gain Special cases - ML estimation - MAP estimation - Mean of the posterior ¥ P(s): A model of the environment. Prior distribution on the scenes ¥ P(d|s): Noisy sensory data d conditioned on a particular state of the world ¥ a(d): optimal action ¥ t: outcome of the decision or action plan. For estimation, ¥ g(t,s): negative of loss, or gain Multisensory Predictive Learning, Fall, 2011 14 Bayesian decision theory and cue integration ¥ Cue integration ¥ Assumption: sensory data associated with each cue are conditionally independent ¥ Likelihood and posterior ¥ Special cases ¥ For Gaussian, the MAP (maximum a posteriori) estimate and the mean of the posterior both yield a linear estimation procedure ¥ Flat prior yield the posterior as the product of cue likelihoods ¥ Conditional independence does not hold è weights should cover the covariance structure of the data Multisensory Predictive Learning, Fall, 2011 15 Bayesian integration of sensory cues ¥ Examples of two simple cases • A: Two cues to object size, visual and haptic, each have Gaussian likelihoods • B: Two visual cues to surface orientation are provided: skew symmetry (a figural cue) and stereo disparity Multisensory Predictive Learning, Fall, 2011 16 NONLINEAR MODELS: GENERATIVE MODELS AND HIDDEN VARIABLES Multisensory Predictive Learning, Fall, 2011 17 Problems and models in nonlinear cases ¥ Conditions under which optimal cue integration is not linear (cues interact) ¥ Cue disambiguation ¥ Raw sensory data from different cues are often incommensurate ¥ Mixture priors (Ch. 9) ¥ The true prior is a mixture of distributions ¥ Causal inference (Chs. 2, 3, 4, 13) ¥ Cues may derive from different sources ¥ The observer should infer the structure of the scene before estimation Multisensory Predictive Learning, Fall, 2011 18 Cue Disambiguation Viewing distance: hidden variable Estimation Relative Disparity Cues target depth Velocity * Promotion: preliminary conversion of cue values into common units Multisensory Predictive Learning, Fall, 2011 19 Use case of a mixture prior: Bayesian model of slant from texture ¥ Discrepant cue: cues may suggest very different values for some scene property Estimation Disparity slant Cues target Texture ¥ A: compression cue. mixture of likelihood Long-tail has long tail ¥ B: small cue conflicts. Disparities (red) suggest a slant which is slightly differ from the compression cue (blue) ¥ C: large cue conflicts. Model selection / model switching Multisensory Predictive Learning, Fall, 2011 20 Causal inference ¥ Cues may be derived from different sources location ¥ The observer need to infer the structure of the scene, not just to estimate ¥ Location estimation from auditory and visual cues ¥ When two stimuli are presented in nearby locations, subjects’ estimates of the auditory stimulus are pulled toward the visual stimulus (the ventriloquist effect) ¥ When they are presented far apart, they appear to be separate sources and do not affect one another ¥ Model: Bayesian inference of structural models ¥ Probabilistic description of a generative model of the scene (two step process in Fig. 1.4) ¥ An observer has to invert the generative model and infer the locations of the visual and auditory sources Multisensory Predictive Learning, Fall, 2011 21 Take home messages ¥ Bayesian decision theory provides a completely general normative framework for cue integration ¥ The representational framework used to model specific problems depends critically on the structure of the information available and the observer’s task Multisensory Predictive Learning, Fall, 2011 22 THEORY MEETS DATA Multisensory Predictive Learning, Fall, 2011 23 Methodology ¥ A variety of experimental techniques has been used to test theories of cue integration ¥ Example: combination of visual and haptic cues to size ¥ Four kinds of stimuli: visual-only; haptic-only; two-cue, consistent stimuli; two-cue inconsistent stimuli ¥ Threshold value (just-noticeable difference, JND) is used to estimate the underlying single-cue noise ¥ To find the point of subjective equality (PSE) Multisensory Predictive Learning, Fall, 2011 24 Overview of results ¥ Experimental supports optimality of human perception ¥ Optimal linear cue integration ¥ Cue promotion is an issue for many cue- integration problems ¥ Evidence for robustness in intrasensory cue combination ¥ Human performance appears to be consistent with the predictions of mixture-prior model Multisensory Predictive Learning, Fall, 2011 25 ISSUES AND CONCERNS Multisensory Predictive Learning, Fall, 2011 26 Issues and Concerns ¥ Realism and unmodeled cues ¥ The lack of realism and the dearth of sensory cues in the laboratory may place the perceiver in situations for which the nervous systems is ill suited and therefore may perform suboptimally ¥ Considering unmodeled cues seems to be important (Buckley and Frisby, 1993) ¥ Estimation of uncertainty ¥ Measurement of the reliability of individual cues ¥ For intramodal cue integration, difficulties arise in isolating a cue ¥ Single-cue discrimination experiments
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