Reductionism and Practicality

Like most domains of science, the study of the mind has been tackled at many scales of analysis, from the behavior of large groups of people (economics and ecology), to the diffusion of ions across cellular membranes (molecular biology and biophysics).  At each of these scales, researchers often believe that the critical phenomena of interest, and the most powerful explanatory constructs and mechanisms, reside at their scale of analysis, with finer scales argued to be incapable of predicting the interesting phenomena, while coarser scales are purported to miss critical mechanistic subtleties.  Here we argue by analogy that, for better or worse, researchers at all scales are correct: phenomena at each scale of analysis are intractable from other scales; thus, while reductionism is a useful scientific goal, it will not obviate the need for macroscopic research, constructs, and formalisms

Sampling in human cognition

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 117-126).Bayesian Decision Theory describes optimal methods for combining sparse, noisy data with prior knowledge to build models of an uncertain world and to use those models to plan actions and make novel decisions. Bayesian computational models correctly predict aspects of human behavior in cognitive domains ranging from perception to motor control and language. However the predictive success of Bayesian models of cognition has highlighted long-standing challenges in bridging the computational and process levels of cognition. First, the computations required for exact Bayesian inference are incommensurate with the limited resources available to cognition (e.g., computational speed; and memory). Second, Bayesian models describe computations but not the processes that carry out these computations and fail to accurately predict human behavior under conditions of cognitive load or deficits. I suggest a resolution to both challenges: The mind approximates Bayesian inference by sampling. Experiments across a wide range of cognition demonstrate Monte-Carlo-like behavior by human observers; moreover, models of cognition based on specific Monte Carlo algorithms can describe previously elusive cognitive phenomena such as perceptual bistability and probability matching. When sampling algorithms are treated as process models of human cognition, the computational and process levels can be modeled jointly to shed light on new and old cognitive phenomena..by Edward Vul.Ph.D

A Biological Rationale for Musical Scales

Scales are collections of tones that divide octaves into specific intervals used to create music. Since humans can distinguish about 240 different pitches over an octave in the mid-range of hearing [1], in principle a very large number of tone combinations could have been used for this purpose. Nonetheless, compositions in Western classical, folk and popular music as well as in many other musical traditions are based on a relatively small number of scales that typically comprise only five to seven tones [2]–[6]. Why humans employ only a few of the enormous number of possible tone combinations to create music is not known. Here we show that the component intervals of the most widely used scales throughout history and across cultures are those with the greatest overall spectral similarity to a harmonic series. These findings suggest that humans prefer tone combinations that reflect the spectral characteristics of conspecific vocalizations. The analysis also highlights the spectral similarity among the scales used by different cultures

Perceptual multistability as Markov Chain Monte Carlo inference

While many perceptual and cognitive phenomena are well described in terms of Bayesian inference, the necessary computations are intractable at the scale of real-world tasks, and it remains unclear how the human mind approximates Bayesian computations algorithmically. We explore the proposal that for some tasks, humans use a form of Markov Chain Monte Carlo to approximate the posterior distribution over hidden variables. As a case study, we show how several phenomena of perceptual multistability can be explained as MCMC inference in simple graphical models for low-level vision

Discovering Structure in the Space of fMRI Selectivity Profiles

We present a method for discovering patterns of selectivity in fMRI data for experiments with multiple stimuli/tasks. We introduce a representation of the data as profiles of selectivity using linear regression estimates, and employ mixture model density estimation to identify functional systems with distinct types of selectivity. The method characterizes these systems by their selectivity patterns and spatial maps, both estimated simultaneously via the EM algorithm. We demonstrate a corresponding method for group analysis that avoids the need for spatial correspondence among subjects. Consistency of the selectivity profiles across subjects provides a way to assess the validity of the discovered systems. We validate this model in the context of category selectivity in visual cortex, demonstrating good agreement with the findings based on prior hypothesis-driven methods.McGovern Institute Neurotechnology (MINT) ProgramNational Institutes of Health (U.S.) (Grant NIBIB NAMIC U54-EB005149)National Institutes of Health (U.S.) (Grant NCRR NAC P41-RR13218)National Eye Institute (grant 13455)National Science Foundation (U.S.) (grant CAREER 0642971)Collaborative Research in Computational Neuroscience (IIS/CRCNS 0904625)Deshpande Center for Technological Innovation (MIT HST Catalyst grant)American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

Explaining human multiple object tracking as resource-constrained approximate inference in a dynamic probabilistic model

Multiple object tracking is a task commonly used to investigate the architecture of human visual attention. Human participants show a distinctive pattern of successes and failures in tracking experiments that is often attributed to limits on an object system, a tracking module, or other specialized cognitive structures. Here we use a computational analysis of the task of object tracking to ask which human failures arise from cognitive limitations and which are consequences of inevitable perceptual uncertainty in the tracking task. We find that many human performance phenomena, measured through novel behavioral experiments, are naturally produced by the operation of our ideal observer model (a Rao-Blackwelized particle filter). The tradeoff between the speed and number of objects being tracked, however, can only arise from the allocation of a flexible cognitive resource, which can be formalized as either memory or attention

Ensemble clustering in visual working memory biases location memories and reduces the Weber noise of relative positions

People seem to compute the ensemble statistics of objects and use this information to support the recall of individual objects in visual working memory. However, there are many different ways that hierarchical structure might be encoded. We examined the format of structured memories by asking subjects to recall the locations of objects arranged in different spatial clustering structures. Consistent with previous investigations of structured visual memory, subjects recalled objects biased toward the center of their clusters. Subjects also recalled locations more accurately when they were arranged in fewer clusters containing more objects, suggesting that subjects used the clustering structure of objects to aid recall. Furthermore, subjects had more difficulty recalling larger relative distances, consistent with subjects encoding the positions of objects relative to clusters and recalling them with magnitude-proportional (Weber) noise. Our results suggest that clustering improved the fidelity of recall by biasing the recall of locations toward cluster centers to compensate for uncertainty and by reducing the magnitude of encoded relative distances. Introduction Our visual working memory is limited in its ability to remember objects. In addition to remembering the individual elements of scenes, people may also extract the higher-order structure of an image, such as the elements' average size (e.g., In contrast to the traditional assumption that objects in visual working memory are encoded independently The structure of multiple objects may also constrain the individual constituent objects more rigidly into multiobject ''chunks'' Additionally, studies of spatial memory suggest that people encode the relative positions of objects: Rather than remember the absolute position of a paper, you may remember its position relative to your desk (e.g., the paper is one foot northwest of your desk; Here we evaluate these dimensions of visual memory structure by asking people to remember and report the locations of objects arranged in different spatial clustering structures. Subjects recalled objects more accurately when they were arranged in fewer clusters that each contained more objects separated by smaller relative distances. To directly evaluate the format of subjects' structured memories, we compared human behavior to that of three cognitive models: a hard chunking model, a hierarchical generative model, and a relative position model. The relative position model best accounted for human performance, followed closely by the hierarchical generative model, with the hard chunking model missing key aspects of human behavior. Our results demonstrate two compatible ways in which hierarchical encoding improves the fidelity of visual working memory. First, objects are biased toward their ensemble statistics to compensate for uncertainty about individual object properties. Second, objects are encoded relative to their parents in the hierarchy, and relative positions are corrupted by Weber noise, 1 such that larger relative distances yield greater errors. Experiment To distinguish different hierarchical encoding strategies that people may use, we asked subjects to report the positions of objects arranged in different clustering structures. Different encoding strategies yielded distinct patterns of errors across scenes that varied in the number of objects and the number of clusters in which they were arranged. Thus, we then examined if subjects' responses across different types of environments were consistent with different forms of structured encoding. Methods Subjects Thirty-five students from the University of California, San Diego, participated for course credit. Stimuli We generated 70 environments, each containing objects arranged into different clustering structures. We selected 440 images from Brady, Konkle, Alvarez, and Oliva Each environment had one of seven clustering structures: four clusters each containing one object (4C1), two clusters containing two objects (2C2), 1C4, 8C1, 4C2, 2C4, 1C8 Journal of Vision Results Did subjects encode objects according to their clustering structure? If subjects did encode and utilize the clustering structure of objects instead of independently encoding objects, the errors for objects in the same cluster should be more similar (in the same direction) than expected by chance. We defined the similarity of the errors (q) in reporting the locations of two objects as where x i and x j are vectors containing the spatial translational error of the two objects' reported locations. The numerator is the projection of the translational error vectors with positive values indicating vectors in the same direction and negative values indicating vectors in the opposite direction. The denominator normalizes the numerator, such that q falls between À1 and 1. Thus, if the recalled locations of two objects were both shifted in exactly the same direction, q would be 1; if they were shifted in orthogonal directions, q would be 0; and if they shifted in opposite directions, q would be À1. We calculated the translational error similarity (q) of objects in the same cluster for each environment How did clustering structure affect recall fidelity? If subjects encoded objects independently, then clustering structures should not have affected how accurately subjects recalled locations. We assessed the effect of clustering structure upon the fidelity of recall by calculating the root mean square error (RMSE 2 ) of subjects' responses ( Error model Thus far, we have demonstrated that subjects did not encode objects independently. Given that subjects appeared to use the clustering structure of objects, how did that structure constrain the locations of objects? Did subjects encode objects using hard chunking, a hierarchical generative model, and/or a relative position tree? These encoding models predict different levels of reliance on (and bias toward) objects' hierarchical structure and different patterns of noise. To determine what type(s) of structured encoding subjects' errors were consistent with, we constructed an error model that estimates the extent of errors due to misassociations, bias, and noise. First, subjects may have had difficulty remembering which objects were in which locations. We estimated the probability of correctly matching an object to its location, p T , and the probability of making a misassociation between an object and another object's location, p M ¼ 1 -p T . The probability of misassociating to a particular location then was p M nÀ1 , where n is the number of locations. To determine exactly to which location each object was misassociated, we assumed a bijective mapping of objects to locations (f), such that only one object could be paired with each location. f À1 (i) denotes the inverse mapping from locations to objects. Second, subjects may have been uncertain about objects' locations but used their memories of cluster locations to inform their responses. This would have resulted in objects being drawn toward their clusters. We accounted for two types of such ''regularization'' bias: the degree to which clusters are drawn toward the global centroid of all objects (cluster-to-global bias, b c ) and the degree to which objects are drawn toward their cluster centers (object-to-cluster bias, b o ). Here, a bias of zero indicates the object/cluster is unbiased, and a bias of one indicates the element is drawn completely toward its parent. To parameterize how the locations of objects would be shifted by these sources of bias, we decomposed the true locations of objects, t, into their relative positions and then weighted the relative positions by the bias parameters. The decomposition of the true locations yielded a relative position tree in which the locations of objects were represented relative to their clusters (x), the locations of clusters were relative to the global centroid (c), and the global centroid (g) was the mean of the true locations (t). Conditional on the mapping f À1 (i) of the true locations t to response locations s, the position of an object i's cluster relative to the global center was defined by where M() maps objects to the clusters of which they are members, and C is the absolute position of the cluster center, calculated by averaging the locations of all objects in that cluster. Similarly, the positions of objects relative to their clusters were defined by We then weighted the relative positions of clusters and objects by the cluster-to-global bias (b c ) and the object-to-cluster bias (b o ), respectively. Thus, the biased absolute positions of an object, b i , were Finally, subjects may have remembered locations with some imprecision. To account for this, the model includes three levels of spatial noise that might induce correlations in errors across objects: that which is shared globally across all object locations (r g ), for locations within the same cluster (r c ), and individual object locations (r o ). This decomposition of object positions induces an expected correlation structure on the errors in reporting individual objects, which can be parameterized with a covariance matrix, R, of the form where the three conditions reflect (in order) error covariance shared by all objects, error covariance for objects in the same cluster, and error variance for individual objects. Let H be the set of parameters {p M , b c , b o , r g , r c , r o }. Altogether, for each environment, the likelihood of a set of responses given the targets and parameters was LIKðsjt; f; HÞ ¼ ðp where s denotes the response locations, n is the number of objects, n T is the number of objects correctly mapped to their locations by f, and n M is the number of objects incorrectly mapped to their locations by f. We estimated these parameters (f, p M , b c , b o , r g , r c , r o ) for each environment across subjects using a Markov chain Monte Carlo algorithm (see Appendix C for more details concerning our Markov chain Monte Carlo algorithm and Appendix D for all parameter fits). Did subjects encode objects in addition to their hierarchical structure? Encoding objects as components of hard chunks or a hierarchical generative model should result in distinct patterns of object-to-cluster bias. If subjects encoded objects as hard chunks, they should have retained minimal information about the objects' locations and recalled the objects with a large bias toward their respective cluster centers. If subjects encoded objects in a hierarchical generative model, then they should have recalled objects with more bias toward their cluster centers when clusters contained more objects. Intuitively, subjects can more precisely estimate the centers of clusters that contain more objects and consequently should rely on those clusters more when they are uncertain about the locations of the individual objects. The bias of objects toward clusters was consistently low (b o : M ¼ .19, SEM ¼ .02, max ¼ .62), suggesting that subjects remembered the locations of individual objects within their clustering structure rather than storing chunks and discarding their internal components. Additionally, contrary to the pattern of bias we expected to find if subjects encoded objects in a hierarchical generative model, as objects were arranged in fewer clusters containing more objects, the objects tended to be recalled with less bias toward their clusters Did subjects encode objects in a relative position tree? Subjects may have encoded objects in a relative position tree, wherein object positions are coded as relative offsets from the cluster centers, and cluster centers are coded as relative offsets from the global center. At first glance, this is no different from encoding the objects according to their absolute position. However, if relative positions are recalled with Weber noise Under such a relative encoding scheme, environments that happened to contain more dispersed clusters 3 require larger relative distances to represent positions. Consequently, as the dispersion of clusters in the environment increases, subjects should recall clusters less precisely (that is, r c should increase). The dispersion of clusters in an environment was significantly correlated with the precision with which subjects recalled cluster centers (r ¼ 0.38 p , 0.01) Comparing chunking, hierarchical generative, and relative position models To directly test explicit formulations of different encoding theories, we designed three cognitive models that would encode a display and generate responses according to its biases: a hard chunking model that only remembers clusters, a hierarchical generative model that encodes absolute positions (similar to Orhan & Jacobs, 2013), and a model that encodes objects in a relative position tree and recalls relative positions with Weber noise. Each model uses a nonparametric Dirichlet process to determine the clustering of the objects Nonparametric Dirichlet process We used a nonparametric Dirichlet process to determine the clustering structure of the objects Chunking model The hard chunking model uses solely information about the clusters and which objects belong to which clusters to recall the locations of objects. Importantly, the chunking model knows nothing about the locations of the individual objects. Instead, the model recalls the location of an object by randomly sampling from the object's cluster based on the center and standard deviation of the cluster estimated by the Dirichlet process. The model has no free parameters. Hierarchical generative model The hierarchical generative model uses knowledge of clusters' locations to compensate for uncertainty in the individual objects' locations. This model is similar to the Dirichlet process mixture model used by The hierarchical generative model noisily encodes the absolute locations of all the objects as well as the properties of their clusters. Because the model pools memories of individual objects to determine the mean and dispersion of their respective clusters, each additional object in a cluster allows the model to estimate the position of that cluster more precisely. This model uses the same process to estimate the precision of the global center from the locations of the clusters. During recall, the model first recalls the locations of the clusters by averaging the positions of the clusters and global center, weighted by their precisions. The model then recalls the locations of individual objects by averaging the positions of the objects and their clusters, weighted by the precision of the encoded object locations and the posterior predictive spread of objects within a cluster, respectively. This model has one free parameter: the noise with which objects are encoded. We set the noise parameter to the average object location noise (r o ) estimated by our error model separately for the four-object and eight-object conditions. Relative position model The relative position model remembers the relative positions of objects and clusters with Weber noise and uses clustering to reduce the magnitude of relative positions. Using the clustering structure inferred by the Dirichlet process, the relative position model remembers the positions of objects relative to their clusters and the clusters relative to the global center. The model encodes relative positions via their distance and angle and recalls them with circular Gaussian noise on angle and proportional (Weber) noise on distance. The angular and distance noise are captured by two free parameters. We fit the model separately for the fourobject and eight-object conditions. Can the models predict the difficulty of environments? We tested whether the models could predict the difficulty, measured in RMSE, of each of the environments across and within clustering structures General discussion People can encode more information about multiple objects if they exploit the objects' shared statistical structure rather than encoding them independently. We considered several ways people might use this structure when encoding objects and found that in addition to using a hierarchical generative model to infer object properties, people also use the hierarchy to encode object properties as relative offsets from the central tendency of their group. Because relative positions seem to be recalled with Weber noise, hierarchical clustering reduces the number of large distances that subjects encoded and thus increases overall accuracy

Explaining human multiple object tracking as resource-constrained approximate inference in a dynamic probabilistic model

Multiple object tracking is a task commonly used to investigate the architecture of human visual attention. Human participants show a distinctive pattern of suc- cesses and failures in tracking experiments that is often attributed to limits on an object system, a tracking module, or other specialized cognitive structures. Here we use a computational analysis of the task of object tracking to ask which human failures arise from cognitive limitations and which are consequences of inevitable perceptual uncertainty in the tracking task. We find that many human perfor- mance phenomena, measured through novel behavioral experiments, are naturally produced by the operation of our ideal observer model (a Rao-Blackwelized par- ticle filter). The tradeoff between the speed and number of objects being tracked, however, can only arise from the allocation of a flexible cognitive resource, which can be formalized as either memory or attention.Psycholog

Search for patterns of functional specificity in the brain: A nonparametric hierarchical Bayesian model for group fMRI data

Functional MRI studies have uncovered a number of brain areas that demonstrate highly specific functional patterns. In the case of visual object recognition, small, focal regions have been characterized with selectivity for visual categories such as human faces. In this paper, we develop an algorithm that automatically learns patterns of functional specificity from fMRI data in a group of subjects. The method does not require spatial alignment of functional images from different subjects. The algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to learn the patterns of functional specificity shared across the group, which we call functional systems, and estimate the number of these systems. Inference based on our model enables automatic discovery and characterization of dominant and consistent functional systems. We apply the method to data from a visual fMRI study comprised of 69 distinct stimulus images. The discovered system activation profiles correspond to selectivity for a number of image categories such as faces, bodies, and scenes. Among systems found by our method, we identify new areas that are deactivated by face stimuli. In empirical comparisons with previously proposed exploratory methods, our results appear superior in capturing the structure in the space of visual categories of stimuli.McGovern Institute for Brain Research at MIT. Neurotechnology (MINT) ProgramNational Institutes of Health (U.S.) (Grant NIBIB NAMIC U54-EB005149)National Institutes of Health (U.S.) (Grant NCRR NAC P41-RR13218)National Eye Institute (Grant 13455)National Science Foundation (U.S.) (CAREER Grant 0642971)National Science Foundation (U.S.) (Grant IIS/CRCNS 0904625)Harvard University--MIT Division of Health Sciences and Technology (Catalyst Grant)American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

Different Physical Intuitions Exist Between Tasks, Not Domains

Abstract Does human behavior exploit deep and accurate knowledge about how the world works, or does it rely on shallow and often inaccurate heuristics? This fundamental question is rooted in a classic dichotomy in psychology: human intuitions about even simple scenarios can be poor, yet their behaviors can exceed the capabilities of even the most advanced machines. One domain where such a dichotomy has classically been demonstrated is intuitive physics. Here we demonstrate that this dichotomy is rooted in how physical knowledge is measured: extrapolation of ballistic motion is idiosyncratic and erroneous when people draw the trajectories but consistent with accurate physical inferences under uncertainty when people use the same trajectories to catch a ball or release it to hit a target. Our results suggest that the contrast between rich and calibrated versus poor and inaccurate patterns of physical reasoning exists as a result of using different systems of knowledge across tasks, rather than being driven solely by a universal system of knowledge that is inconsistent across physical principles