Hierarchical Bayesian aspects of distributed neuromagnetic source models

Magnetoencephalography (MEG) enables noninvasive measurements of cerebral activity with excellent temporal resolution, but localising the neural currents generating the extracranial magnetic fields admits no unique solution. By imposing some mathematical constraints on the currents, reasonable solutions to this electromagnetic inverse problem can be obtained. In this work, we adopt the statistical formulation of the inverse problem in which the constraints are encoded as Bayesian prior probabilities. The prior is combined with a statistical MEG observation model via Bayes' theorem to yield the posterior probability of the unknown parameters, that is the currents, given the MEG data and modeling assumptions. Apart from the currents, the prior probability density may contain further parameters which are subject to uncertainty. These parameters are not related directly to the MEG observations and are called second-level parameters or hyperparameters, giving the model a hierarchical structure. The thesis considers hierarchical generalisations of the classical Minimum-Norm and Minimum-Current Estimates (MNE and MCE). The MNE and MCE are distributed source reconstruction methods from which the former is known to produce spatially diffuse distributions and the latter more focal. The here studied extensions of the MNE and MCE prior structures allow more general and flexible modeling of distributed sources with properties in between MNE and MCE. The first two studies included in this thesis involve more theoretical Bayesian analyses on the properties of the hierarchical distributed source models and the resulting inverse estimates. The latter two studies focus on validation of the models with empirical MEG data, practical analyses and interpretation of the inverse estimates.Magnetoenkefalografia (MEG) mahdollistaa pään ulkopuolelta tapahtuvan aivotoimintojen mittaamisen hyvällä ajallisella tarkkuudella, mutta nämä magneettikentät synnyttävien aivokudoksen sähkövirtojen paikallistaminen vaatii ns. sähkömagneettisen käänteisongelman ratkaisun, joka ei ole yksikäsitteinen. Jos virtakonfiguraatioille asetetaan sopivia matemaattisia rajoitteita, on kuitenkin mahdollista löytää käyttökelpoisia ratkaisuja tähän käänteisongelmaan. Tässä työssä käänteisongelmaa lähestytään tilastollisesti, ja matemaattiset rajoitteet muotoillaan Bayesilaisittain a priori todennäköisyyksinä. Tämä priorijakauma yhdistetään tilastollisen MEG-havaintomallin kanssa, jolloin saadaan Bayesin teoreeman avulla tuntemattomien parametrien eli virtakonfiguraatioiden a posteriori -jakauma, joka kertoo eri virtakonfiguraatioden todennäköisyydet, annettuna havaittu data sekä tehdyt mallioletukset. Virtojen lisäksi priorijakaumaan saattaa liittyä muita tuntemattomia suureita, jotka sisältävät epävarmuutta. Nämä parametrit eivät kytkeydy suoraan MEG-mittauksiin, joten ne ovat siis sähkövirtoihin verrattuna seuraavalla mallitasolla. Näitä priorin parametreja kutsutaan hyperparametreiksi, ja mallilla on hierarkinen rakenne. Väitöskirjassa tutkitaan klassisten miniminormi- ja minimivirtaestimaattien hierarkisia yleistyksiä. Miniminormi- ja minimivirtaestimaatit ovat lähdejakaumamalleihin liittyviä menetelmiä, joista ensimmäinen tuottaa paikallisesti varsin laajalle levineitä ja jälkimmäinen fokaalimpia käänteisongelman ratkaisuja. Näiden menetelmien tässä työssä tutkitut laajennukset mahdollistavat myös yleisempien ja joustavampien, ominaisuuksiltaan miniminormi- ja minimivirtaoletusten väliin sijoittuvien lähdejakaumien mallintamisen. Kaksi ensimmäistä osatyötä keskittyvät esitettyjen hierarkisten Bayesilaisten lähdejakaumamallien sekä niiden tuottamien käänteisongelman ratkaisujen teoreettiseen tutkimiseen. Kahdessa jälkimmäisessä osatyössä pyritään validoimaan menetelmät käyttäen mitattua MEG dataa, sekä selventämään näiden hierarkisten käänteisongelman ratkaisujen käytännön merkitystä ja tulkintaa.reviewe

Group-structured and independent subspace based dictionary learning

Thanks to the several successful applications, sparse signal representation has become one of the most actively studied research areas in mathematics. However, in the traditional sparse coding problem the dictionary used for representation is assumed to be known. In spite of the popularity of sparsity and its recently emerged structured sparse extension, interestingly, very few works focused on the learning problem of dictionaries to these codes. In the first part of the paper, we develop a dictionary learning method which is (i) online, (ii) enables overlapping group structures with (iii) non-convex sparsity-inducing regularization and (iv) handles the partially observable case. To the best of our knowledge, current methods can exhibit two of these four desirable properties at most. We also investigate several interesting special cases of our framework and demonstrate its applicability in inpainting of natural signals, structured sparse non-negative matrix factorization of faces and collaborative filtering. Complementing the sparse direction we formulate a novel component-wise acting, epsilon-sparse coding scheme in reproducing kernel Hilbert spaces and show its equivalence to a generalized class of support vector machines. Moreover, we embed support vector machines to multilayer perceptrons and show that for this novel kernel based approximation approach the backpropagation procedure of multilayer perceptrons can be generalized. In the second part of the paper, we focus on dictionary learning making use of independent subspace assumption instead of structured sparsity. The corresponding problem is called independent subspace analysis (ISA), or independent component analysis (ICA) if all the hidden, independent sources are one-dimensional. One of the most fundamental results of this research field is the ISA separation principle, which states that the ISA problem can be solved by traditional ICA up to permutation. This principle (i) forms the basis of the state-of-the-art ISA solvers and (ii) enables one to estimate the unknown number and the dimensions of the sources efficiently. We (i) extend the ISA problem to several new directions including the controlled, the partially observed, the complex valued and the nonparametric case and (ii) derive separation principle based solution techniques for the generalizations. This solution approach (i) makes it possible to apply state-of-the-art algorithms for the obtained subproblems (in the ISA example ICA and clustering) and (ii) handles the case of unknown dimensional sources. Our extensive numerical experiments demonstrate the robustness and efficiency of our approach

Emergence of collective periodic behaviour in a multi-population system of interacting neurons

We study a multi-class system of interacting neurons looking for the emergence of oscillations: we model the neuronal ensemble using Hawkes processes representing the spikes fired by each neuron in a fixed interval of time; as a result, we show that, even though the single neuron doesn’t fire its spikes periodically, a collective, intrinsic, oscillatory behaviour can be detected.We study a multi-class system of interacting neurons looking for the emergence of oscillations: we model the neuronal ensemble using Hawkes processes representing the spikes fired by each neuron in a fixed interval of time; as a result, we show that, even though the single neuron doesn’t fire its spikes periodically, a collective, intrinsic, oscillatory behaviour can be detected

Networked Data Analytics: Network Comparison And Applied Graph Signal Processing

Networked data structures has been getting big, ubiquitous, and pervasive. As our day-to-day activities become more incorporated with and influenced by the digital world, we rely more on our intuition to provide us a high-level idea and subconscious understanding of the encountered data. This thesis aims at translating the qualitative intuitions we have about networked data into quantitative and formal tools by designing rigorous yet reasonable algorithms. In a nutshell, this thesis constructs models to compare and cluster networked data, to simplify a complicated networked structure, and to formalize the notion of smoothness and variation for domain-specific signals on a network. This thesis consists of two interrelated thrusts which explore both the scenarios where networks have intrinsic value and are themselves the object of study, and where the interest is for signals defined on top of the networks, so we leverage the information in the network to analyze the signals. Our results suggest that the intuition we have in analyzing huge data can be transformed into rigorous algorithms, and often the intuition results in superior performance, new observations, better complexity, and/or bridging two commonly implemented methods. Even though different in the principles they investigate, both thrusts are constructed on what we think as a contemporary alternation in data analytics: from building an algorithm then understanding it to having an intuition then building an algorithm around it. We show that in order to formalize the intuitive idea to measure the difference between a pair of networks of arbitrary sizes, we could design two algorithms based on the intuition to find mappings between the node sets or to map one network into the subset of another network. Such methods also lead to a clustering algorithm to categorize networked data structures. Besides, we could define the notion of frequencies of a given network by ordering features in the network according to how important they are to the overall information conveyed by the network. These proposed algorithms succeed in comparing collaboration histories of researchers, clustering research communities via their publication patterns, categorizing moving objects from uncertain measurmenets, and separating networks constructed from different processes. In the context of data analytics on top of networks, we design domain-specific tools by leveraging the recent advances in graph signal processing, which formalizes the intuitive notion of smoothness and variation of signals defined on top of networked structures, and generalizes conventional Fourier analysis to the graph domain. In specific, we show how these tools can be used to better classify the cancer subtypes by considering genetic profiles as signals on top of gene-to-gene interaction networks, to gain new insights to explain the difference between human beings in learning new tasks and switching attentions by considering brain activities as signals on top of brain connectivity networks, as well as to demonstrate how common methods in rating prediction are special graph filters and to base on this observation to design novel recommendation system algorithms

Computation and representation in decision making and emotion

This thesis deals with three components of an organism’s interactions with its environment: learning, decision making, and emotions. In a series of 5 studies, I detail relationships between these processes, and investigate the representation and computations whereby they are achieved. In the first experiment I show how subjective wellbeing is influenced by one’s own rewards and expectations, but also those of other people. Furthermore, I find that parameter estimates of empathy predict decision-making in a distinct test of economic generosity. In my second study, I ask how stressful experiences modulate subsequent learning, detailing a specific impairment in action-learning under stress which also manifests itself in altered pupillary responses. In the third, I use a hierarchical model of learning to show that subjective uncertainty in aversive contexts predicts several dimensions of acute stress responses. Furthermore, I find that individuals who show greater uncertainty-tuning in their stress responses are better at predicting the presence of threat. In the final pair of studies I ask how decision variables for value-based choice are represented in the brain. I describe the combination of quality and quantity into value estimates in humans, revealing a central role for the Anterior Cingulate Cortex in value integration using functional magnetic resonance imaging. I next characterize the neural code for value in non-human primate frontal cortex, using single-neuron data from collaborators. These two studies provide convergent evidence that the value code may be more diverse and non-linear than previously reported, potentially conferring the ability to incorporate uncertainty signals directly in the activity of value coding neurons