Hierarchical Generative Model Research Articles

A hierarchical model for integrating unsupervised generative embedding and empirical Bayes

BackgroundGenerative models of neuroimaging data, such as dynamic causal models (DCMs), are commonly used for inferring effective connectivity from individual subject data. Recently introduced “generative embedding” approaches have used DCM-based connectivity parameters for supervised classification of individual patients or to find unknown subgroups in heterogeneous groups using unsupervised clustering methods. New methodWe present a novel framework which combines DCMs with finite mixture models into a single hierarchical model. This approach unifies the inference of connectivity parameters in individual subjects with inference on population structure, i.e. the existence of subgroups defined by model parameters, and allows for empirical Bayesian estimates of a subject’s connectivity based on subgroup-specific prior distributions. We introduce a Markov chain Monte Carlo sampling method for inversion of this hierarchical generative model. ResultsThis paper formally introduces the idea behind our novel concept and demonstrates the face validity of the model in application to both simulated data as well as an empirical fMRI dataset from healthy controls and patients with schizophrenia. Comparison with existing method(s)The analysis of our empirical fMRI data demonstrates that our approach results in superior model evidence than the conventional non-hierarchical inversion of DCMs. ConclusionsIn this paper, we have presented a novel unified framework to jointly infer the effective connectivity parameters in DCMs for multiple subjects and, at the same time, discover connectivity-defined cluster structure of the whole population, using a mixture model approach.

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.

A Framework for the Strategic Management of Science & Technology Parks

Science and technology parks (STPs) have been playing an increasingly influential role in the stimulation and growth of the knowledge economy. However, the spread of STPs faces relevant challenges, such as the development of robust performance management systems, able to demonstrate results and indicate improvement opportunities. Thereby, this paper proposes a theoretical model of performance management, which combines premises of the Service-Dominant Logic (S-D Logic), the Balanced Scorecard (BSC) and the General Hierarchical Model (GHM). Based on a multiple-case exploratory and qualitative study, relevant information about the strategic planning and management of these projects were extracted and paved the way for the construction of a performance hierarchical model composed of five perspectives, according to the BSC. Considering the outcomes, it is expected that the proposed model provide useful insights for the consolidation of a framework for the strategic management of science and technology parks.

Acoustic Scene Analysis Based on Hierarchical Generative Model of Acoustic Event Sequence

Acoustic Scene Analysis Based on Hierarchical Generative Model of Acoustic Event Sequence

The felt presence of other minds: Predictive processing, counterfactual predictions, and mentalising in autism.

The mental states of other people are components of the external world that modulate the activity of our sensory epithelia. Recent probabilistic frameworks that cast perception as unconscious inference on the external causes of sensory input can thus be expanded to enfold the brain's representation of others' mental states. This paper examines this subject in the context of the debate concerning the extent to which we have perceptual awareness of other minds. In particular, we suggest that the notion of perceptual presence helps to refine this debate: are others' mental states experienced as veridical qualities of the perceptual world around us? This experiential aspect of social cognition may be central to conditions such as autism spectrum disorder, where representations of others' mental states seem to be selectively compromised. Importantly, recent work ties perceptual presence to the counterfactual predictions of hierarchical generative models that are suggested to perform unconscious inference in the brain. This enables a characterisation of mental state representations in terms of their associated counterfactual predictions, allowing a distinction between spontaneous and explicit forms of mentalising within the framework of predictive processing. This leads to a hypothesis that social cognition in autism spectrum disorder is characterised by a diminished set of counterfactual predictions and the reduced perceptual presence of others' mental states.

Uncertainty in perception and the Hierarchical Gaussian Filter.

In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder–Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient—but at the same time intuitive—framework for the resolution of perceptual uncertainty in behaving agents.

Inferring on the Intentions of Others by Hierarchical Bayesian Learning

Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition.

Shape Perception Simultaneously Up- and Downregulates Neural Activity in the Primary Visual Cortex

An essential part of visual perception is the grouping of local elements (such as edges and lines) into coherent shapes. Previous studies have shown that this grouping process modulates neural activity in the primary visual cortex (V1) that is signaling the local elements [1-4]. However, the nature of this modulation is controversial. Some studies find that shape perception reduces neural activity in V1 [2, 5, 6], while others report increased V1 activity during shape perception [1, 3, 4, 7-10]. Neurocomputational theories that cast perception as a generative process [11-13] propose that feedback connections carry predictions (i.e., the generative model), while feedforward connections signal the mismatch between top-down predictions and bottom-up inputs. Within this framework, the effect of feedback on early visual cortex may be either enhancing or suppressive, depending on whether the feedback signal is met by congruent bottom-up input. Here, we tested this hypothesis by quantifying the spatial profile of neural activity in V1 during the perception of illusory shapes using population receptive field mapping. We find that shape perception concurrently increases neural activity in regions of V1 that have a receptive field on the shape but do not receive bottom-up input and suppresses activity in regions of V1 that receive bottom-up input that is predicted by the shape. These effects were not modulated by task requirements. Together, these findings suggest that shape perception changes lower-order sensory representations in a highly specific and automatic manner, in line with theories that cast perception in terms of hierarchical generative models.

The worldly constituents of perceptual presence.

The worldly constituents of perceptual presence.

Semantic Annotation of Satellite Images Using Author–Genre–Topic Model

In this paper, we propose a novel hierarchical generative model, named author-genre-topic model (AGTM), to perform satellite image annotation. Different from the existing author-topic model in which each author and topic are associated with the multinomial distributions over topics and words, in AGTM, each genre, author, and topic are associated with the multinomial distributions over authors, topics, and words, respectively. The bias of the distribution of the authors with respect to the topics can be rectified by incorporating the distribution of the genres with respect to the authors. Therefore, the classification accuracy of documents is improved when the information of genre is introduced. By representing the images with several visual words, the AGTM can be used for satellite image annotation. The labels of classes and scenes of the images correspond to the authors and the genres of the documents, respectively. The labels of classes and scenes of test images can be estimated, and the accuracy of satellite image annotation is improved when the information of scenes is introduced in the training images. Experimental results demonstrate the good performance of the proposed method.

Bayesian assessment of electrical power transmission grid outage risk

Lack of unified risk assessment approach to electrical power transmission grid outages when taking into account uncertain data is addressed in this paper. Authors take on Bayesian approach to analyse statistical data of electric grid outages – this enables to achieve a more coherent way to express uncertainty in data and to obtain reliability related measures of the grid. The considered methodology of how to properly manage the statistical inference process is demonstrated through real outage data collected from North American transmission grid. The different cases of electrical power lines unreliability as well as cascading outages are addressed on various levels of complexity – starting from simple Bayesian assessment and then building a more general hierarchical Bayesian model. As a result, geography and environment related variability level is found to be of significant influence suggesting that unreliability of grid lines should in general be analysed having in mind specificity of each line. In addition, such variability highly influences the reliability of the whole grid or any network, as demonstrated in the paper as well. Considering the case of cascading outages, we obtained a hierarchical model, built under the basis of Borel–Tanner distribution, and demonstrated the capability to simulate large blackouts, which has a non-negligible probability of occurrence, as the history of blackouts in the last decades has already demonstrated.

Hierarchical bayesian modeling, estimation, and sampling for multigroup shape analysis.

This paper proposes a novel method for the analysis of anatomical shapes present in biomedical image data. Motivated by the natural organization of population data into multiple groups, this paper presents a novel hierarchical generative statistical model on shapes. The proposed method represents shapes using pointsets and defines a joint distribution on the population's (i) shape variables and (ii) object-boundary data. The proposed method solves for optimal (i) point locations, (ii) correspondences, and (iii) model-parameter values as a single optimization problem. The optimization uses expectation maximization relying on a novel Markov-chain Monte-Carlo algorithm for sampling in Kendall shape space. Results on clinical brain images demonstrate advantages over the state of the art.

Multiple Subcategories Parts-Based Representation for One Sample Face Identification

Small sample set, occlusion, and illumination variations are the critical obstacles for a face identification system towards practical application. In this paper, we propose a probabilistic generative model for parts-based data representation to address these difficulties. In our approach, multiple subcategories corresponding to the individual face parts, such as nose, mouth, eye, and so forth, are modeled within a probabilistic graphical model framework to mimic the process of generating a face image. The induced face representation, therefore, encodes rich discriminative information. Model training is totally unsupervised. Once the training is completed, a test sample from the face class can be recognized as a novel combination of learned parts. In summary, the main contributions of this work are threefold: 1) A novel hierarchical probabilistic generative model is proposed, which is capable of achieving an efficient parts-based representation for robust face identification. 2) A constrained variational EM algorithm is developed to learn the model parameters and infer the variables. 3) Two similarity metrics are specially designed for the novel parts-based feature representation, which are effective for matching score guided one sample face identification. The models and similarity metrics are validated on three face databases. Experimental results demonstrate the capabilities of the model to deal with small sample set, occlusions, and illumination variances.

Whatever next? Predictive brains, situated agents, and the future of cognitive science

Brains, it has recently been argued, are essentially prediction machines. They are bundles of cells that support perception and action by constantly attempting to match incoming sensory inputs with top-down expectations or predictions. This is achieved using a hierarchical generative model that aims to minimize prediction error within a bidirectional cascade of cortical processing. Such accounts offer a unifying model of perception and action, illuminate the functional role of attention, and may neatly capture the special contribution of cortical processing to adaptive success. This target article critically examines this "hierarchical prediction machine" approach, concluding that it offers the best clue yet to the shape of a unified science of mind and action. Sections 1 and 2 lay out the key elements and implications of the approach. Section 3 explores a variety of pitfalls and challenges, spanning the evidential, the methodological, and the more properly conceptual. The paper ends (sections 4 and 5) by asking how such approaches might impact our more general vision of mind, experience, and agency.

Sparse coding and challenges for Bayesian models of the brain

While the target article provides a glowing account for the excitement in the field, we stress that hierarchical predictive learning in the brain requires sparseness of the representation. We also question the relation between Bayesian cognitive processes and hierarchical generative models as discussed by the target article.

Deep Belief Networks Based Voice Activity Detection

Fusing the advantages of multiple acoustic features is important for the robustness of voice activity detection (VAD). Recently, the machine-learning-based VADs have shown a superiority to traditional VADs on multiple feature fusion tasks. However, existing machine-learning-based VADs only utilize shallow models, which cannot explore the underlying manifold of the features. In this paper, we propose to fuse multiple features via a deep model, called deep belief network (DBN). DBN is a powerful hierarchical generative model for feature extraction. It can describe highly variant functions and discover the manifold of the features. We take the multiple serially-concatenated features as the input layer of DBN, and then extract a new feature by transferring these features through multiple nonlinear hidden layers. Finally, we predict the class of the new feature by a linear classifier. We further analyze that even a single-hidden-layer-based belief network is as powerful as the state-of-the-art models in the machine-learning-based VADs. In our empirical comparison, ten common features are used for performance analysis. Extensive experimental results on the AURORA2 corpus show that the DBN-based VAD not only outperforms eleven referenced VADs, but also can meet the real-time detection demand of VAD. The results also show that the DBN-based VAD can fuse the advantages of multiple features effectively.

Minimal self-models and the free energy principle

The term “minimal phenomenal selfhood” (MPS) describes the basic, pre-reflective experience of being a self (Blanke and Metzinger, 2009). Theoretical accounts of the minimal self have long recognized the importance and the ambivalence of the body as both part of the physical world, and the enabling condition for being in this world (Gallagher, 2005a; Grafton, 2009). A recent account of MPS (Metzinger, 2004a) centers on the consideration that minimal selfhood emerges as the result of basic self-modeling mechanisms, thereby being founded on pre-reflective bodily processes. The free energy principle (FEP; Friston, 2010) is a novel unified theory of cortical function built upon the imperative that self-organizing systems entail hierarchical generative models of the causes of their sensory input, which are optimized by minimizing free energy as an approximation of the log-likelihood of the model. The implementation of the FEP via predictive coding mechanisms and in particular the active inference principle emphasizes the role of embodiment for predictive self-modeling, which has been appreciated in recent publications. In this review, we provide an overview of these conceptions and illustrate thereby the potential power of the FEP in explaining the mechanisms underlying minimal selfhood and its key constituents, multisensory integration, interoception, agency, perspective, and the experience of mineness. We conclude that the conceptualization of MPS can be well mapped onto a hierarchical generative model furnished by the FEP and may constitute the basis for higher-level, cognitive forms of self-referral, as well as the understanding of other minds.

Modeling language and cognition with deep unsupervised learning: a tutorial overview.

Deep unsupervised learning in stochastic recurrent neural networks with many layers of hidden units is a recent breakthrough in neural computation research. These networks build a hierarchy of progressively more complex distributed representations of the sensory data by fitting a hierarchical generative model. In this article we discuss the theoretical foundations of this approach and we review key issues related to training, testing and analysis of deep networks for modeling language and cognitive processing. The classic letter and word perception problem of McClelland and Rumelhart (1981) is used as a tutorial example to illustrate how structured and abstract representations may emerge from deep generative learning. We argue that the focus on deep architectures and generative (rather than discriminative) learning represents a crucial step forward for the connectionist modeling enterprise, because it offers a more plausible model of cortical learning as well as a way to bridge the gap between emergentist connectionist models and structured Bayesian models of cognition.

Deep generative learning of location-invariant visual word recognition

It is widely believed that orthographic processing implies an approximate, flexible coding of letter position, as shown by relative-position and transposition priming effects in visual word recognition. These findings have inspired alternative proposals about the representation of letter position, ranging from noisy coding across the ordinal positions to relative position coding based on open bigrams. This debate can be cast within the broader problem of learning location-invariant representations of written words, that is, a coding scheme abstracting the identity and position of letters (and combinations of letters) from their eye-centered (i.e., retinal) locations. We asked whether location-invariance would emerge from deep unsupervised learning on letter strings and what type of intermediate coding would emerge in the resulting hierarchical generative model. We trained a deep network with three hidden layers on an artificial dataset of letter strings presented at five possible retinal locations. Though word-level information (i.e., word identity) was never provided to the network during training, linear decoding from the activity of the deepest hidden layer yielded near-perfect accuracy in location-invariant word recognition. Conversely, decoding from lower layers yielded a large number of transposition errors. Analyses of emergent internal representations showed that word selectivity and location invariance increased as a function of layer depth. Word-tuning and location-invariance were found at the level of single neurons, but there was no evidence for bigram coding. Finally, the distributed internal representation of words at the deepest layer showed higher similarity to the representation elicited by the two exterior letters than by other combinations of two contiguous letters, in agreement with the hypothesis that word edges have special status. These results reveal that the efficient coding of written words—which was the model's learning objective—is largely based on letter-level information.

Deep Unsupervised Learning on a Desktop PC: A Primer for Cognitive Scientists.

Deep belief networks hold great promise for the simulation of human cognition because they show how structured and abstract representations may emerge from probabilistic unsupervised learning. These networks build a hierarchy of progressively more complex distributed representations of the sensory data by fitting a hierarchical generative model. However, learning in deep networks typically requires big datasets and it can involve millions of connection weights, which implies that simulations on standard computers are unfeasible. Developing realistic, medium-to-large-scale learning models of cognition would therefore seem to require expertise in programing parallel-computing hardware, and this might explain why the use of this promising approach is still largely confined to the machine learning community. Here we show how simulations of deep unsupervised learning can be easily performed on a desktop PC by exploiting the processors of low cost graphic cards (graphic processor units) without any specific programing effort, thanks to the use of high-level programming routines (available in MATLAB or Python). We also show that even an entry-level graphic card can outperform a small high-performance computing cluster in terms of learning time and with no loss of learning quality. We therefore conclude that graphic card implementations pave the way for a widespread use of deep learning among cognitive scientists for modeling cognition and behavior.