Co-Clustering with Generative Models

In this paper, we present a generative model for co-clustering and develop algorithms based on the mean field approximation for the corresponding modeling problem. These algorithms can be viewed as generalizations of the traditional model-based clustering; they extend hard co-clustering algorithms such as Bregman co-clustering to include soft assignments. We show empirically that these model-based algorithms offer better performance than their hard-assignment counterparts, especially with increasing problem complexity

Nonparametric measurement of long-run growth in consumer welfare

How should we measure long-run changes in consumer welfare? This paper proposes a nonparametric approach that is valid under arbitrary preferences that depend on observable consumer characteristics, e.g. when expenditure shares vary with income. Our approach only requires data on the consumption baskets of a cross section of consumers facing a common set of prices. Using nominal expenditures under a constant set of prices as our money-metric for real consumption (welfare), we derive a consistent measure of its growth in terms of a correction to the conventional measures based on price index formulas. Our correction ac-counts for the cross-sectional dependence of the measured price indices on consumer income and other characteristics. We use nonparametric methods to approximate these corrections and provide bounds on the resulting approximation errors. Applying the approach to the measurement of growth in US real consumption per capita, we find a sizable correction to the standard measures of growth in the post-war era, a period of fast growth combined with substantial inflation gaps across income groups

Generative models for group fMRI data

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 151-174).In this thesis, we develop an exploratory framework for design and analysis of fMRI studies. In our framework, the experimenter presents subjects with a broad set of stimuli/tasks relevant to the domain under study. The analysis method then automatically searches for likely patterns of functional specificity in the resulting data. This is in contrast to the traditional confirmatory approaches that require the experimenter to specify a narrow hypothesis a priori and aims to localize areas of the brain whose activation pattern agrees with the hypothesized response. To validate the hypothesis, it is usually assumed that detected areas should appear in consistent anatomical locations across subjects. Our approach relaxes the conventional anatomical consistency constraint to discover networks of functionally homogeneous but anatomically variable areas. Our analysis method relies on generative models that explain fMRI data across the group as collections of brain locations with similar profiles of functional specificity. We refer to each such collection as a functional system and model it as a component of a mixture model for the data. The search for patterns of specificity corresponds to inference on the hidden variables of the model based on the observed fMRI data. We also develop a nonparametric hierarchical Bayesian model for group fMRI data that integrates the mixture model prior over activations with a model for fMRI signals. We apply the algorithms in a study of high level vision where we consider a large space of patterns of category selectivity over 69 distinct images. The analysis successfully discovers previously characterized face, scene, and body selective areas, among a few others, as the most dominant patterns in the data. This finding suggests that our approach can be employed to search for novel patterns of functional specificity in high level perception and cognition.by Danial Lashkari.Ph.D

Categories and functional units: An infinite hierarchical model for brain activations

We present a model that describes the structure in the responses of different brain areas to a set of stimuli in terms of stimulus categories (clusters of stimuli) and functional units (clusters of voxels). We assume that voxels within a unit respond similarly to all stimuli from the same category, and design a nonparametric hierarchical model to capture inter-subject variability among the units. The model explicitly encodes the relationship between brain activations and fMRI time courses. A variational inference algorithm derived based on the model learns categories, units, and a set of unit-category activation probabilities from data. When applied to data from an fMRI study of object recognition, the method finds meaningful and consistent clusterings of stimuli into categories and voxels into units.National Science Foundation (U.S.) (Grant IIS/CRCNS 0904625)National Science Foundation (U.S.) (CAREER Grant 0642971)McGovern Institute for Brain Research at MIT (Neurotechnology Program Grant)National Institutes of Health (U.S.) (Grant NIBIB NAMIC U54-EB005149)National Institutes of Health (U.S.) (Grant NCRR NAC P41-RR13218

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

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

Decoupling function and anatomy in atlases of functional connectivity patterns: Language mapping in tumor patients

In this paper we construct an atlas that summarizes functional connectivity characteristics of a cognitive process from a population of individuals. The atlas encodes functional connectivity structure in a low-dimensional embedding space that is derived from a diffusion process on a graph that represents correlations of fMRI time courses. The functional atlas is decoupled from the anatomical space, and thus can represent functional networks with variable spatial distribution in a population. In practice the atlas is represented by a common prior distribution for the embedded fMRI signals of all subjects. We derive an algorithm for fitting this generative model to the observed data in a population. Our results in a language fMRI study demonstrate that the method identifies coherent and functionally equivalent regions across subjects. The method also successfully maps functional networks from a healthy population used as a training set to individuals whose language networks are affected by tumors.National Science Foundation (U.S.). Division of Information & Intelligent Systems (Collaborative Research in Computational Neuroscience Grant 0904625)National Science Foundation (U.S.) (CAREER Grant 0642971)National Institutes of Health (U.S.) (National Center for Research Resources (U.S.)/Neuroimaging Analysis Center (U.S.) P41-RR13218)National Institutes of Health (U.S.) (National Institute for Biomedical Imaging and Bioengineering (U.S.)/Neuroimaging Analysis Center (U.S.) P41-EB-015902)National Institutes of Health (U.S.) (National Institute for Biomedical Imaging and Bioengineering (U.S.)/National Alliance for Medical Image Computing (U.S.) U54-EB005149)National Institutes of Health (U.S.) (U41RR019703)National Institutes of Health (U.S.) (Eunice Kennedy Shriver National Institute of Child Health and Human Development (U.S.) R01HD067312)National Institutes of Health (U.S.) (P01CA067165)Brain Science FoundationKlarman Family FoundationEuropean Commission (FP7/2007–2013) n°257528 (KHRESMOI))European Commission (330003 (FABRIC))Austrian Science Fund (P 22578-B19 (PULMARCH)