Bayesian regression explains how human participants handle parameter uncertainty

Author summary How do humans make prediction when the critical factor that influences the quality of the prediction is hidden? Here, we address this question by conducting a simple psychophysical experiment in which participants had to extrapolate a parabola with an unknown quadratic parameter. We show that in this task, humans perform in a manner consistent with the mathematically optimal model, i.e., Bayesian regression. Accumulating evidence indicates that the human brain copes with sensory uncertainty in accordance with Bayes' rule. However, it is unknown how humans make predictions when the generative model of the task at hand is described by uncertain parameters. Here, we tested whether and how humans take parameter uncertainty into account in a regression task. Participants extrapolated a parabola from a limited number of noisy points, shown on a computer screen. The quadratic parameter was drawn from a bimodal prior distribution. We tested whether human observers take full advantage of the given information, including the likelihood of the quadratic parameter value given the observed points and the quadratic parameter's prior distribution. We compared human performance with Bayesian regression, which is the (Bayes) optimal solution to this problem, and three sub-optimal models, which are simpler to compute. Our results show that, under our specific experimental conditions, humans behave in a way that is consistent with Bayesian regression. Moreover, our results support the hypothesis that humans generate responses in a manner consistent with probability matching rather than Bayesian decision theory.

Bayesian modeling of brain function and behavior

Maya Anna Jastrzebowska

The application of Bayesian modeling techniques is increasingly common in neuroscience due to the coherent and principled way in which the paradigm deals with uncertainty. The Bayesian framework is particularly valuable in the context of complex, ill-posed generative problems, in which case the incorporation of prior knowledge is optimal and practical. If one wants to take full advantage of joint imaging and behavioral data, the need for comprehensive generative models is evident. Here, I exploited the versatility afforded by Bayesian modeling approaches to investigate a series of questions from clinical, systems, and cognitive neuroscience. First, I investigated the lateralization of the cortical motor network in Parkinson's disease patients on and off dopaminergic medication with fMRI and dynamic causal modeling (DCM). Group-level model comparison revealed that disease and medication effects differentially involve homotopic cortical motor connections, but medication does not appear to have a restorative effect at the systems level. Our findings suggest the presence of maladaptive mechanisms, resulting from disease progression and long-term dopamine replacement. In a second project, I considered the way in which humans handle uncertainty in the parameters of the generative model of a task at hand. Using a novel psychophysics paradigm, participants' responses to fitting a parabola to a set of noisy points were compared to the predictions of a set of regression models, including Bayesian regression and several sub-optimal models. Only Bayesian regression could explain participants' response distributions across various levels of sensory uncertainty, suggesting that humans process parameter uncertainty in accordance with Bayesian regression. This finding deepens our understanding of the way in which humans learn and generalize from sparse, ambiguous data. The topic investigated in the greatest depth in this thesis was visual crowding - the deterioration of target discrimination due to the presence of flanking objects. Traditionally, vision is modeled as a feedforward, hierarchical network. Thus, crowding is explained as a pooling of neighboring elements' features, leading to a "bottleneck" at the earliest stages of vision. However, additional flankers can paradoxically improve performance (uncrowding). First, I used DCM and fMRI to show that recurrent processing is crucial for crowding and un-crowding alike. Higher visual areas modulate the lower areas, suggesting that explicit object representation plays a key role. I then used population receptive field (pRF) mapping to investigate the effects of context on pRF size. In accordance with pooling model predictions, the pRF size in crowding is larger than in the case of no crowding. However, in uncrowding, the pRF size is smaller than in crowding and no crowding, providing further evidence against purely feedforward models. Overall, my findings provide strong empirical evidence of context-dependent feedback modulation in vision. I propose a possible implementation which integrates the observed findings into a generative model of crowding: context-agnostic feedforward mechanisms transmit the information about the target and flankers retinotopically to higher visual areas; a subsequent context-dependent feedback pRF determines whether the target will be enhanced - by decreasing the pRF size - or suppressed - by enlarging the pRF size to encompass flankers.

EPFL2020

Stress, noradrenaline, and realistic prediction of mouse behaviour using reinforcement learning

Wulfram Gerstner, Gediminas Luksys, Maria del Carmen Sandi Perez

Suppose we train an animal in a conditioning experiment. Can one predict how a given animal, under given experimental conditions, would perform the task? Since various factors such as stress, motivation, genetic background, and previous errors in task performance can influence animal behavior, this appears to be a very challenging aim. Reinforcement learning (RL) models have been successful in modeling animal (and human) behavior, but their success has been limited because of uncertainty as to how to set meta-parameters (such as learning rate, exploitation-exploration balance and future reward discount factor) that strongly influence model performance. We show that a simple RL model whose meta- parameters are controlled by an artificial neural network, fed with inputs such as stress, affective phenotype, previous task performance, and even neuromodulatory manipulations, can successfully predict mouse behavior in the "hole-box" - a simple conditioning task. Our results also provide important insights on how stress and anxiety affect animal learning, performance accuracy, and discounting of future rewards, and on how noradrenergic systems can interact with these processes

Curran Associates, Inc.2009

High-Dimensional Inference on Dense Graphs with Applications to Coding Theory and Machine Learning

Mohamad Baker Dia

We are living in the era of "Big Data", an era characterized by a voluminous amount of available data. Such amount is mainly due to the continuing advances in the computational capabilities for capturing, storing, transmitting and processing data. However, it is not always the volume of data that matters, but rather the "relevant" information that resides in it. Exactly 70 years ago, Claude Shannon, the father of information theory, was able to quantify the amount of information in a communication scenario based on a probabilistic model of the data. It turns out that Shannon's theory can be adapted to various probability-based information processing fields, ranging from coding theory to machine learning. The computation of some information theoretic quantities, such as the mutual information, can help in setting fundamental limits and devising more efficient algorithms for many inference problems. This thesis deals with two different, yet intimately related, inference problems in the fields of coding theory and machine learning. We use Bayesian probabilistic formulations for both problems, and we analyse them in the asymptotic high-dimensional regime. The goal of our analysis is to assess the algorithmic performance on the first hand and to predict the Bayes-optimal performance on the second hand, using an information theoretic approach. To this end, we employ powerful analytical tools from statistical physics. The first problem is a recent forward-error-correction code called sparse superposition code. We consider the extension of such code to a large class of noisy channels by exploiting the similarity with the compressed sensing paradigm. Moreover, we show the amenability of sparse superposition codes to perform joint distribution matching and channel coding. In the second problem, we study symmetric rank-one matrix factorization, a prominent model in machine learning and statistics with many applications ranging from community detection to sparse principal component analysis. We provide an explicit expression for the normalized mutual information and the minimum mean-square error of this model in the asymptotic limit. This allows us to prove the optimality of a certain iterative algorithm on a large set of parameters. A common feature of the two problems stems from the fact that both of them are represented on dense graphical models. Hence, similar message-passing algorithms and analysis tools can be adopted. Furthermore, spatial coupling, a new technique introduced in the context of low-density parity-check (LDPC) codes, can be applied to both problems. Spatial coupling is used in this thesis as a "construction technique" to boost the algorithmic performance and as a "proof technique" to compute some information theoretic quantities. Moreover, both of our problems retain close connections with spin glass models studied in statistical mechanics of disordered systems. This allows us to use sophisticated techniques developed in statistical physics. In this thesis, we use the potential function predicted by the replica method in order to prove the threshold saturation phenomenon associated with spatially coupled models. Moreover, one of the main contributions of this thesis is proving that the predictions given by the "heuristic" replica method are exact. Hence, our results could be of great interest for the statistical physics community as well, as they help to set a rigorous mathematical foundation of the replica predictions.