A new metric for probability distributions

We introduce a metric for probability distributions, which is bounded, information-theoretically motivated, and has a natural Bayesian interpretation. The square root of the well-known chi(2) distance is an asymptotic approximation to it. Moreover, it is a close relative of the capacitory discrimination and Jensen-Shannon divergence.Publisher PDFPeer reviewe

Probabilistic Models of Motor Production

N. Bernstein defined the ability of the central neural system (CNS) to control many degrees of freedom of a physical body with all its redundancy and flexibility as the main problem in motor control. He pointed at that man-made mechanisms usually have one, sometimes two degrees of freedom (DOF); when the number of DOF increases further, it becomes prohibitively hard to control them. The brain, however, seems to perform such control effortlessly. He suggested the way the brain might deal with it: when a motor skill is being acquired, the brain artificially limits the degrees of freedoms, leaving only one or two. As the skill level increases, the brain gradually "frees" the previously fixed DOF, applying control when needed and in directions which have to be corrected, eventually arriving to the control scheme where all the DOF are "free". This approach of reducing the dimensionality of motor control remains relevant even today. One the possibles solutions of the Bernstetin's problem is the hypothesis of motor primitives (MPs) - small building blocks that constitute complex movements and facilitite motor learnirng and task completion. Just like in the visual system, having a homogenious hierarchical architecture built of similar computational elements may be beneficial. Studying such a complicated object as brain, it is important to define at which level of details one works and which questions one aims to answer. David Marr suggested three levels of analysis: 1. computational, analysing which problem the system solves; 2. algorithmic, questioning which representation the system uses and which computations it performs; 3. implementational, finding how such computations are performed by neurons in the brain. In this thesis we stay at the first two levels, seeking for the basic representation of motor output. In this work we present a new model of motor primitives that comprises multiple interacting latent dynamical systems, and give it a full Bayesian treatment. Modelling within the Bayesian framework, in my opinion, must become the new standard in hypothesis testing in neuroscience. Only the Bayesian framework gives us guarantees when dealing with the inevitable plethora of hidden variables and uncertainty. The special type of coupling of dynamical systems we proposed, based on the Product of Experts, has many natural interpretations in the Bayesian framework. If the dynamical systems run in parallel, it yields Bayesian cue integration. If they are organized hierarchically due to serial coupling, we get hierarchical priors over the dynamics. If one of the dynamical systems represents sensory state, we arrive to the sensory-motor primitives. The compact representation that follows from the variational treatment allows learning of a motor primitives library. Learned separately, combined motion can be represented as a matrix of coupling values. We performed a set of experiments to compare different models of motor primitives. In a series of 2-alternative forced choice (2AFC) experiments participants were discriminating natural and synthesised movements, thus running a graphics Turing test. When available, Bayesian model score predicted the naturalness of the perceived movements. For simple movements, like walking, Bayesian model comparison and psychophysics tests indicate that one dynamical system is sufficient to describe the data. For more complex movements, like walking and waving, motion can be better represented as a set of coupled dynamical systems. We also experimentally confirmed that Bayesian treatment of model learning on motion data is superior to the simple point estimate of latent parameters. Experiments with non-periodic movements show that they do not benefit from more complex latent dynamics, despite having high kinematic complexity. By having a fully Bayesian models, we could quantitatively disentangle the influence of motion dynamics and pose on the perception of naturalness. We confirmed that rich and correct dynamics is more important than the kinematic representation. There are numerous further directions of research. In the models we devised, for multiple parts, even though the latent dynamics was factorized on a set of interacting systems, the kinematic parts were completely independent. Thus, interaction between the kinematic parts could be mediated only by the latent dynamics interactions. A more flexible model would allow a dense interaction on the kinematic level too. Another important problem relates to the representation of time in Markov chains. Discrete time Markov chains form an approximation to continuous dynamics. As time step is assumed to be fixed, we face with the problem of time step selection. Time is also not a explicit parameter in Markov chains. This also prohibits explicit optimization of time as parameter and reasoning (inference) about it. For example, in optimal control boundary conditions are usually set at exact time points, which is not an ecological scenario, where time is usually a parameter of optimization. Making time an explicit parameter in dynamics may alleviate this

It was (not) me: Causal Inference of Agency in goal-directed actions

Summary: 
The perception of one’s own actions depends on both sensory information and predictions derived from internal forward models [1]. The integration of these information sources depends critically on whether perceptual consequences are associated with one’s own action (sense of agency) or with changes in the external world that are not related to the action. The perceived effects of actions should thus critically depend on the consistency between the predicted and the actual sensory consequences of actions. To test this idea, we used a virtual-reality setup to manipulate the consistency between pointing movements and their visual consequences and investigated the influence of this manipulation on self-action perception. We then asked whether a Bayesian causal inference model, which assumes a latent agency variable controlling the attributed influence of the own action on perceptual consequences [2,3], would account for the empirical data: if the percept was attributed to the own action, visual and internal information should fuse in a Bayesian optimal manner, while this should not be the case if the visual stimulus was attributed to external influences. The model correctly fits the data, showing that small deviations between predicted and actual sensory information were still attributed to one’s own action, while this was not the case for large deviations when subjects relied more on internal information. We discuss the performance of this causal inference model in comparison to alternative biologically feasible statistical models applying methods for Bayesian model comparison.

Experiment: 
Participants were seated in front of a horizontal board on which their right hand was placed with the index finger on a haptic marker, representing the starting point for each trial. Participants were instructed to execute straight, fast (quasi-ballistic) pointing movements of fixed amplitude, but without an explicit visual target. The hand was obstructed from the view of the participants, and visual feedback about the peripheral part of the movement was provided by a cursor. Feedback was either veridical or rotated against the true direction of the hand movement by predefined angles. After each trial participants were asked to report the subjectively experienced direction of the executed hand movement by placing a mouse-cursor into that direction.

Model: 
We compared two probabilistic models: Both include a binary random gating variable (agency) that models the sense of ‘agency’; that is the belief that the visual feedback is influenced by the subject’s motor action. The first model assumes that both the visual feedback xv and the internal motor state estimate xe are directly caused by the (unobserved) real motor state xt (Fig. 1). The second model assumes instead that the expected visual feedback depends on the perceived direction of the own motor action xe (Fig. 2). 
Results: Both models are in good agreement with the data. Fig. A shows the model fit for Model 1 superpositioned to the data from a single subject. Fig. B shows the belief that the visual stimulus was influenced by the own action, which decreases for large deviations between predicted and real visual feedback. Bayesian model comparison shows a better fit for model 1.
Citations
[1] Wolpert D.M, Ghahramani, Z, Jordan, M. (1995) Science, 269, 1880-1882.
[2] Körding KP, Beierholm E, Ma WJ, Quartz S, Tenenbaum JB, et al (2007) PLoS ONE 2(9): e943.
[3] Shams, L., Beierholm, U. (2010) TiCS, 14: 425-432.
Acknowledgements
This work was supported by the BCCN Tübingen (FKZ: 01GQ1002), the CIN Tübingen, the European Union (FP7-ICT-215866 project SEARISE), the DFG and the Hermann and Lilly Schilling Foundation

Special issue on conceptual structures

[no abstract available

A Revised Framework for the Investigation of Expectation Update Versus Maintenance in the Context of Expectation Violations: The ViolEx 2.0 Model

Expectations are probabilistic beliefs about the future that shape and influence our perception, affect, cognition, and behavior in many contexts. This makes expectations a highly relevant concept across basic and applied psychological disciplines. When expectations are confirmed or violated, individuals can respond by either updating or maintaining their prior expectations in light of the new evidence. Moreover, proactive and reactive behavior can change the probability with which individuals encounter expectation confirmations or violations. The investigation of predictors and mechanisms underlying expectation update and maintenance has been approached from many research perspectives. However, in many instances there has been little exchange between different research fields. To further advance research on expectations and expectation violations, collaborative efforts across different disciplines in psychology, cognitive (neuro)science, and other life sciences are warranted. For fostering and facilitating such efforts, we introduce the ViolEx 2.0 model, a revised framework for interdisciplinary research on cognitive and behavioral mechanisms of expectation update and maintenance in the context of expectation violations. To support different goals and stages in interdisciplinary exchange, the ViolEx 2.0 model features three model levels with varying degrees of specificity in order to address questions about the research synopsis, central concepts, or functional processes and relationships, respectively. The framework can be applied to different research fields and has high potential for guiding collaborative research efforts in expectation research

Degeneration of Lumbar Intervertebral Discs: Characterization of Anulus Fibrosus Tissue and Cells of Different Degeneration Grades

Intervertebral disc (IVD) herniation and degeneration is a major source of back pain. In order to regenerate a herniated and degenerated disc, closure of the anulus fibrosus (AF) is of crucial importance. For molecular characterization of AF, genome-wide Affymetrix HG-U133plus2.0 microarrays of native AF and cultured cells were investigated. To evaluate if cells derived from degenerated AF are able to initiate gene expression of a regenerative pattern of extracellular matrix (ECM) molecules, cultivated cells were stimulated with bone morphogenetic protein 2 (BMP2), transforming growth factor β1 (TGFβ1) or tumor necrosis factor-α (TNFα) for 24 h. Comparative microarray analysis of native AF tissues showed 788 genes with a significantly different gene expression with 213 genes more highly expressed in mild and 575 genes in severe degenerated AF tissue. Mild degenerated native AF tissues showed a higher gene expression of common cartilage ECM genes, whereas severe degenerated AF tissues expressed genes known from degenerative processes, including matrix metalloproteinases (MMP) and bone associated genes. During monolayer cultivation, only 164 differentially expressed genes were found. The cells dedifferentiated and altered their gene expression profile. RTD-PCR analyses of BMP2- and TGFβ1-stimulated cells from mild and severe degenerated AF tissue after 24 h showed an increased expression of cartilage associated genes. TNFα stimulation increased MMP1, 3, and 13 expression. Cells derived from mild and severe degenerated tissues could be stimulated to a comparable extent. These results give hope that regeneration of mildly but also strongly degenerated disc tissue is possible

Numeričko i eksperimentalno modeliranje nosivih elemenata teške metalurške opreme

Carrying structures of heavy metallurgical equipments are during their operation often exposed to extreme loading. The short-term overloading of the structure results to high stresses in locations of their concentrations. By repeating of these phenomena is decreased the life-time of the structure and eventually this leads to local failures in their carrying elements. In the paper are on examples described advantages of using numerical and experimental methods of mechanical system modelling that is exploited for identification of overloading in carrying elements of metallurgical equipments or for detection of damage causes.Nosivi elementi teške metalurške opreme tijekom eksploatacije često su izloženi ekstremnim opterećenjima. Njihova kratkotrajna preopterećenja izazivaju visoka naprezanja na mjestima koncentracije. Ponavljanje ove pojave izaziva skraćenje životnog vijeka konstrukcije i moguća lokalna oštećenja nosivih elemenata. U ovom članku, na dva primjera su prikazane prednosti primjene numeričkih i eksperimentalnih metoda modeliranja mehaničkog sustava u otkrivanju preopterećenja ili uzroka oštećenja nosivih elemenata metalurške opreme