Hierarchical Generative Model Research Articles

Top-Down Feedback in an HMAX-Like Cortical Model of Object Perception Based on Hierarchical Bayesian Networks and Belief Propagation

Hierarchical generative models, such as Bayesian networks, and belief propagation have been shown to provide a theoretical framework that can account for perceptual processes, including feedforward recognition and feedback modulation. The framework explains both psychophysical and physiological experimental data and maps well onto the hierarchical distributed cortical anatomy. However, the complexity required to model cortical processes makes inference, even using approximate methods, very computationally expensive. Thus, existing object perception models based on this approach are typically limited to tree-structured networks with no loops, use small toy examples or fail to account for certain perceptual aspects such as invariance to transformations or feedback reconstruction. In this study we develop a Bayesian network with an architecture similar to that of HMAX, a biologically-inspired hierarchical model of object recognition, and use loopy belief propagation to approximate the model operations (selectivity and invariance). Crucially, the resulting Bayesian network extends the functionality of HMAX by including top-down recursive feedback. Thus, the proposed model not only achieves successful feedforward recognition invariant to noise, occlusions, and changes in position and size, but is also able to reproduce modulatory effects such as illusory contour completion and attention. Our novel and rigorous methodology covers key aspects such as learning using a layerwise greedy algorithm, combining feedback information from multiple parents and reducing the number of operations required. Overall, this work extends an established model of object recognition to include high-level feedback modulation, based on state-of-the-art probabilistic approaches. The methodology employed, consistent with evidence from the visual cortex, can be potentially generalized to build models of hierarchical perceptual organization that include top-down and bottom-up interactions, for example, in other sensory modalities.

Sasaki Metrics for Analysis of Longitudinal Data on Manifolds.

Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. In this paper, we present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling T 2 statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.

MGMR: leveraging RNA-Seq population data to optimize expression estimation

BackgroundRNA-Seq is a technique that uses Next Generation Sequencing to identify transcripts and estimate transcription levels. When applying this technique for quantification, one must contend with reads that align to multiple positions in the genome (multireads). Previous efforts to resolve multireads have shown that RNA-Seq expression estimation can be improved using probabilistic allocation of reads to genes. These methods use a probabilistic generative model for data generation and resolve ambiguity using likelihood-based approaches. In many instances, RNA-seq experiments are performed in the context of a population. The generative models of current methods do not take into account such population information, and it is an open question whether this information can improve quantification of the individual samplesResultsIn order to explore the contribution of population level information in RNA-seq quantification, we apply a hierarchical probabilistic generative model, which assumes that expression levels of different individuals are sampled from a Dirichlet distribution with parameters specific to the population, and reads are sampled from the distribution of expression levels. We introduce an optimization procedure for the estimation of the model parameters, and use HapMap data and simulated data to demonstrate that the model yields a significant improvement in the accuracy of expression levels of paralogous genes.ConclusionsWe provide a proof of principal of the benefit of drawing on population commonalities to estimate expression. The results of our experiments demonstrate this approach can be beneficial, primarily for estimation at the gene level.

Number, texture and crowding

A recent study shows that selectivity for numerosity emerges as a natural property in deep networks of hierarchical generative models of visual perception. These results, together with recent conceptualizations of crowding and texture, suggest that the 'sense of number' is a fundamental visual property, independent of texture and seemingly related attributes.

Bayesian models with dominance effects for genomic evaluation of quantitative traits

Genomic selection refers to the use of dense, genome-wide markers for the prediction of breeding values (BV) and subsequent selection of breeding individuals. It has become a standard tool in livestock and plant breeding for accelerating genetic gain. The core of genomic selection is the prediction of a large number of marker effects from a limited number of observations. Various Bayesian methods that successfully cope with this challenge are known. Until now, the main research emphasis has been on additive genetic effects. Dominance coefficients of quantitative trait loci (QTLs), however, can also be large, even if dominance variance and inbreeding depression are relatively small. Considering dominance might contribute to the accuracy of genomic selection and serve as a guide for choosing mating pairs with good combining abilities. A general hierarchical Bayesian model for genomic selection that can realistically account for dominance is introduced. Several submodels are proposed and compared with respect to their ability to predict genomic BV, dominance deviations and genotypic values (GV) by stochastic simulation. These submodels differ in the way the dependency between additive and dominance effects is modelled. Depending on the marker panel, the inclusion of dominance effects increased the accuracy of GV by about 17% and the accuracy of genomic BV by 2% in the offspring. Furthermore, it slowed down the decrease of the accuracies in subsequent generations. It was possible to obtain accurate estimates of GV, which enables mate selection programmes.

Emergence of a 'visual number sense' in hierarchical generative models

Numerosity estimation is phylogenetically ancient and foundational to human mathematical learning, but its computational bases remain controversial. Here we show that visual numerosity emerges as a statistical property of images in 'deep networks' that learn a hierarchical generative model of the sensory input. Emergent numerosity detectors had response profiles resembling those of monkey parietal neurons and supported numerosity estimation with the same behavioral signature shown by humans and animals.

Dopamine, Affordance and Active Inference

The role of dopamine in behaviour and decision-making is often cast in terms of reinforcement learning and optimal decision theory. Here, we present an alternative view that frames the physiology of dopamine in terms of Bayes-optimal behaviour. In this account, dopamine controls the precision or salience of (external or internal) cues that engender action. In other words, dopamine balances bottom-up sensory information and top-down prior beliefs when making hierarchical inferences (predictions) about cues that have affordance. In this paper, we focus on the consequences of changing tonic levels of dopamine firing using simulations of cued sequential movements. Crucially, the predictions driving movements are based upon a hierarchical generative model that infers the context in which movements are made. This means that we can confuse agents by changing the context (order) in which cues are presented. These simulations provide a (Bayes-optimal) model of contextual uncertainty and set switching that can be quantified in terms of behavioural and electrophysiological responses. Furthermore, one can simulate dopaminergic lesions (by changing the precision of prediction errors) to produce pathological behaviours that are reminiscent of those seen in neurological disorders such as Parkinson's disease. We use these simulations to demonstrate how a single functional role for dopamine at the synaptic level can manifest in different ways at the behavioural level.

Beyond “Error-Correction”

Beyond “Error-Correction”

Brain Oscillations and Predictive Processing

Brain Oscillations and Predictive Processing

Emotion and Anticipation in an Enactive Framework for Cognition (Response to Andy Clark)

Undeniably, anticipation plays a crucial role in cognition. By what means, to what extent, and what it achieves remain open questions. In a recent BBS target article, Clark (in press) depicts an integrative model of the brain that builds on hierarchical Bayesian models of neural processing (Rao and Ballard, 1999; Friston, 2005; Brown et al., 2011), and their most recent formulation using the free-energy principle borrowed from thermodynamics (Feldman and Friston, 2010; Friston, 2010; Friston et al., 2010). Hierarchical generative models of cognition, such as those described by Clark, presuppose the manipulation of representations and internal models of the world, in as much detail as is perceptually available. Perhaps surprisingly, Clark acknowledges the existence of a “virtual version of the sensory data” (p. 4), but with no reference to some of the historical debates that shaped cognitive science, related to the storage, manipulation, and retrieval of representations in a cognitive system (Shanahan, 1997), or accounting for the emergence of intentionality within such a system (Searle, 1980; Preston and Bishop, 2002). Instead of demonstrating how this Bayesian framework responds to these foundational questions, Clark describes the structure and the functional properties of an action-oriented, multi-level system that is meant to combine perception, learning, and experience (Niedenthal, 2007).

Unsupervised learning of hierarchical representations with convolutional deep belief networks

There has been much interest in unsupervised learning of hierarchical generative models such as deep belief networks (DBNs); however, scaling such models to full-sized, high-dimensional images remains a difficult problem. To address this problem, we present the convolutional deep belief network , a hierarchical generative model that scales to realistic image sizes. This model is translation-invariant and supports efficient bottom-up and top-down probabilistic inference. Key to our approach is probabilistic max-pooling , a novel technique that shrinks the representations of higher layers in a probabilistically sound way. Our experiments show that the algorithm learns useful high-level visual features, such as object parts, from unlabeled images of objects and natural scenes. We demonstrate excellent performance on several visual recognition tasks and show that our model can perform hierarchical (bottom-up and top-down) inference over full-sized images.

Bayesian Learning of Generalized Board Positions for Improved Move Prediction in Computer Go

Computer Go presents a challenging problem for machine learning agents. With the number of possible board states estimated to be larger than the number of hydrogen atoms in the universe, learning effective policies or board evaluation functions is extremely difficult. In this paper we describe Cortigo, a system that efficiently and autonomously learns useful generalizations for large state-space classification problems such as Go. Cortigo uses a hierarchical generative model loosely related to the human visual cortex to recognize Go board positions well enough to suggest promising next moves. We begin by briefly describing and providing motivation for research in the computer Go domain. We describe Cortigo’s ability to learn predictive models based on large subsets of the Go board and demonstrate how using Cortigo’s learned models as additive knowledge in a state-of-the-art computer Go player (Fuego) significantly improves its playing strength.

Adaptive object recognition model using incremental feature representation and hierarchical classification

This paper presents an adaptive object recognition model based on incremental feature representation and a hierarchical feature classifier that offers plasticity to accommodate additional input data and reduces the problem of forgetting previously learned information. The incremental feature representation method applies adaptive prototype generation with a cortex-like mechanism to conventional feature representation to enable an incremental reflection of various object characteristics, such as feature dimensions in the learning process. A feature classifier based on using a hierarchical generative model recognizes various objects with variant feature dimensions during the learning process. Experimental results show that the adaptive object recognition model successfully recognizes single and multiple-object classes with enhanced stability and flexibility.

Kernels for Longitudinal Data with Variable Sequence Length and Sampling Intervals

We develop several kernel methods for classification of longitudinal data and apply them to detect cognitive decline in the elderly. We first develop mixed-effects models, a type of hierarchical empirical Bayes generative models, for the time series. After demonstrating their utility in likelihood ratio classifiers (and the improvement over standard regression models for such classifiers), we develop novel Fisher kernels based on mixture of mixed-effects models and use them in support vector machine classifiers. The hierarchical generative model allows us to handle variations in sequence length and sampling interval gracefully. We also give nonparametric kernels not based on generative models, but rather on the reproducing kernel Hilbert space. We apply the methods to detecting cognitive decline from longitudinal clinical data on motor and neuropsychological tests. The likelihood ratio classifiers based on the neuropsychological tests perform better than than classifiers based on the motor behavior. Discriminant classifiers performed better than likelihood ratio classifiers for the motor behavior tests.

Learning Features of Simple and Complex Cells: A Generative Approach via Multiplicative Interactions

AbstractWe develop a hierarchical generative model to learn features of simple and complex cells in the primary visual cortex via multiplicative interactions and address the problem of learning invariant visual representation from natural image sequences. Generally, the overall objective of a generative sparse coding model (Olshausen and Field, Nature, 1996) is to reconstruct the input *x* via a linear combination of feature bases *A = [A~1~,A~2~,...,A~M~]*, such that *x = As*, where s is the latent representation with a sparse constraint.In the proposed model, we added another hidden layer with complex cells to modulate the latent representation *s*, such that *s* is generated via an element-wise product of bottom-up representation *y = A^T^x* and top-down representation *z = Bc*, i.e., *s = y.*z* . Here *c* represents the top layer with complex cells, and *B* is the feature matrix connecting from the simple cell layer to the complex cell layer. Similar to the well known bilinear models (Tenenbaum and Freeman, Neural Computation, 2000) for invariant representation, the complex cell layer here represents the content variables and the simple cell layer represents the style variables. However, instead of using three-order tensor weight parameters as in the bilinear models, our model provides a factorized approach by the product of two two-order tensor weight parameters *A* and *B*, and thus makes learning simpler and more efficient. Moreover, while bilinear models dealt with two latent variables, our model contains only one latent variable *c* for invariant representation.The penalties of sparseness and slowness priors are integrated into this model as well. In addition, non-negativity constraints of the latent variable c and weight matrices *A* and *B* are enforced to fit the known neurophysiology better. We utilize the gradient descent algorithm to train our model from natural image sequences. A dictionary of Gabor-like orientation selective features is developed in the simple cell layer, where topography of receptive fields is automatically generated. In this way, similar simple cell receptive fields are pooled together to produce locally-invariant representation in complex cells.

Balancing generalization and lexical conservatism: An artificial language study with child learners

Successful language acquisition involves generalization, but learners must balance this against the acquisition of lexical constraints. Such learning has been considered problematic for theories of acquisition: if learners generalize abstract patterns to new words, how do they learn lexically-based exceptions? One approach claims that learners use distributional statistics to make inferences about when generalization is appropriate, a hypothesis which has recently received support from Artificial Language Learning experiments with adult learners (Wonnacott, Newport, & Tanenhaus, 2008). Since adult and child language learning may be different (Hudson Kam & Newport, 2005), it is essential to extend these results to child learners. In the current work, four groups of children (6years) were each exposed to one of four semi-artificial languages. The results demonstrate that children are sensitive to linguistic distributions at and above the level of particular lexical items, and that these statistics influence the balance between generalization and lexical conservatism. The data are in line with an approach which models generalization as rational inference and in particular with the predictions of the domain general hierarchical Bayesian model developed in Kemp, Perfors & Tenenbaum, 2006. This suggests that such models have relevance for theories of language acquisition.

Integrated image representation based natural scene classification

Natural scene classification (NSC) is a challenging pattern classification problem. As one of state-of-the-art techniques, the bag-of-feature (BOF) model has received extensive considerations in characterizing the image. To boost the flexibility during visterm construction in BOF model, an integrated scheme for image representation is proposed by adaptive analysis on the local visual complexity of image itself. First, the flatness of each scene category is determined by the total flatness of all images belonging to this category. Then the new integrated image representation of the scene category is built by weighting the two representations (based on a pixels gray value descriptor and a dense SIFT descriptor) through the normalized coefficients computed by the flatness of the category. Finally, a hierarchical generative model is exploited to learn natural scene categories. Experimental results demonstrate that the satisfactory classification accuracy achieves about 83.67% on a large set of 15 categories of complex scenes.

How cognitive modeling can benefit from hierarchical Bayesian models

Hierarchical Bayesian modeling provides a flexible and interpretable way of extending simple models of cognitive processes. To introduce this special issue, we discuss four of the most important potential hierarchical Bayesian contributions. The first involves the development of more complete theories, including accounting for variation coming from sources like individual differences in cognition. The second involves the capability to account for observed behavior in terms of the combination of multiple different cognitive processes. The third involves using a few key psychological variables to explain behavior on a wide range of cognitive tasks. The fourth involves the conceptual unification and integration of disparate cognitive models. For all of these potential contributions, we outline an appropriate general hierarchical Bayesian modeling structure. We also highlight current models that already use the hierarchical Bayesian approach, as well as identifying research areas that could benefit from its adoption.

Neural Decoding with Hierarchical Generative Models

Recent research has shown that reconstruction of perceived images based on hemodynamic response as measured with functional magnetic resonance imaging (fMRI) is starting to become feasible. In this letter, we explore reconstruction based on a learned hierarchy of features by employing a hierarchical generative model that consists of conditional restricted Boltzmann machines. In an unsupervised phase, we learn a hierarchy of features from data, and in a supervised phase, we learn how brain activity predicts the states of those features. Reconstruction is achieved by sampling from the model, conditioned on brain activity. We show that by using the hierarchical generative model, we can obtain good-quality reconstructions of visual images of handwritten digits presented during an fMRI scanning session.

Perturbation method for determining the group of invariance of hierarchical models

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342–358]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof by Aoki and Takemura which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.