Attentive monitoring of multiple video streams driven by a Bayesian foraging strategy

In this paper we shall consider the problem of deploying attention to subsets of the video streams for collating the most relevant data and information of interest related to a given task. We formalize this monitoring problem as a foraging problem. We propose a probabilistic framework to model observer's attentive behavior as the behavior of a forager. The forager, moment to moment, focuses its attention on the most informative stream/camera, detects interesting objects or activities, or switches to a more profitable stream. The approach proposed here is suitable to be exploited for multi-stream video summarization. Meanwhile, it can serve as a preliminary step for more sophisticated video surveillance, e.g. activity and behavior analysis. Experimental results achieved on the UCR Videoweb Activities Dataset, a publicly available dataset, are presented to illustrate the utility of the proposed technique.Comment: Accepted to IEEE Transactions on Image Processin

Decision Making Under Uncertainty: A Neural Model Based on Partially Observable Markov Decision Processes

A fundamental problem faced by animals is learning to select actions based on noisy sensory information and incomplete knowledge of the world. It has been suggested that the brain engages in Bayesian inference during perception but how such probabilistic representations are used to select actions has remained unclear. Here we propose a neural model of action selection and decision making based on the theory of partially observable Markov decision processes (POMDPs). Actions are selected based not on a single “optimal” estimate of state but on the posterior distribution over states (the “belief” state). We show how such a model provides a unified framework for explaining experimental results in decision making that involve both information gathering and overt actions. The model utilizes temporal difference (TD) learning for maximizing expected reward. The resulting neural architecture posits an active role for the neocortex in belief computation while ascribing a role to the basal ganglia in belief representation, value computation, and action selection. When applied to the random dots motion discrimination task, model neurons representing belief exhibit responses similar to those of LIP neurons in primate neocortex. The appropriate threshold for switching from information gathering to overt actions emerges naturally during reward maximization. Additionally, the time course of reward prediction error in the model shares similarities with dopaminergic responses in the basal ganglia during the random dots task. For tasks with a deadline, the model learns a decision making strategy that changes with elapsed time, predicting a collapsing decision threshold consistent with some experimental studies. The model provides a new framework for understanding neural decision making and suggests an important role for interactions between the neocortex and the basal ganglia in learning the mapping between probabilistic sensory representations and actions that maximize rewards

Mismatch responses: Probing probabilistic inference in the brain

Sensory signals are governed by statistical regularities and carry valuable information about the unfolding of environmental events. The brain is thought to capitalize on the probabilistic nature of sequential inputs to infer on the underlying (hidden) dynamics driving sensory stimulation. Mis-match responses (MMRs) such as the mismatch negativity (MMN) and the P3 constitute prominent neuronal signatures which are increasingly interpreted as reflecting a mismatch between the current sensory input and the brain’s generative model of incoming stimuli. As such, MMRs might be viewed as signatures of probabilistic inference in the brain and their response dynamics can provide insights into the underlying computational principles. However, given the dominance of the auditory modality in MMR research, the specifics of brain responses to probabilistic sequences across sensory modalities and especially in the somatosensory domain are not well characterized. The work presented here investigates MMRs across the auditory, visual and somatosensory modality by means of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). We designed probabilistic stimulus sequences to elicit and characterize MMRs and employed computational modeling of response dynamics to inspect different aspects of the brain’s generative model of the sensory environment. In the first study, we used a volatile roving stimulus paradigm to elicit somatosensory MMRs and performed single-trial modeling of EEG signals in sensor and source space. Model comparison suggested that responses reflect Bayesian inference based on the estimation of transition probability and limited information integration of the recent past in order to adapt to a changing environment. The results indicated that somatosensory MMRs reflect an initial mismatch between sensory input and model beliefs represented by confidence-corrected surprise (CS) followed by model adjustment dynamics represented by Bayesian surprise (BS). For the second and third study we designed a tri-modal roving stimulus paradigm to delineate modality specific and modality general features of mismatch processing. Computational modeling of EEG signals in study 2 suggested that single-trial dynamics reflect Bayesian inference based on estimation of uni-modal transition probabilities as well as cross-modal conditional dependencies. While early mismatch processing around the MMN tended to reflect CS, later MMRs around the P3 rather reflect BS, in correspondence to the somatosensory study. Finally, the fMRI results of study 3 showed that MMRs are generated by an interaction of modality specific regions in higher order sensory cortices and a modality general fronto-parietal network. Inferior parietal regions in particular were sensitive to expectation violations with respect to the cross-modal contingencies in the stimulus sequences. Overall, our results indicate that MMRs across the senses reflect processes of probabilistic inference in a complex and inherently multi-modal environment.Sensorische Signale sind durch statistische Regularitäten bestimmt und beinhalten wertvolle Informationen über die Entwicklung von Umweltereignissen. Es wird angenommen, dass das Gehirn die Wahrscheinlichkeitseigenschaften sequenzieller Reize nutzt um auf die zugrundeliegenden (verborgenen) Dynamiken zu schließen, welche sensorische Stimulation verursachen. Diskrepanz-Reaktionen ("Mismatch responses"; MMRs) wie die "mismatch negativity" (MMN) und die P3 sind bekannte neuronale Signaturen die vermehrt als Signale einer Diskrepanz zwischen der momentanen sensorischen Einspeisung und dem generativen Modell, welches das Gehirn von den eingehenden Reizen erstellt angesehen werden. Als solche können MMRs als Signaturen von wahrscheinlichkeitsbasierter Inferenz im Gehirn betrachtet werden und ihre Reaktionsdynamiken können Einblicke in die zugrundeliegenden komputationalen Prinzipien geben. Angesichts der Dominanz der auditorischen Modalität in der MMR-Forschung, sind allerdings die spezifischen Eigenschaften von Hirn-Reaktionen auf Wahrscheinlichkeitssequenzen über sensorische Modalitäten hinweg und vor allem in der somatosensorischen Modalität nicht gut charakterisiert. Die hier vorgestellte Arbeit untersucht MMRs über die auditorische, visuelle und somatosensorische Modalität hinweg anhand von Elektroenzephalographie (EEG) und funktioneller Magnetresonanztomographie (fMRT). Wir gestalteten wahrscheinlichkeitsbasierte Reizsequenzen, um MMRs auszulösen und zu charakterisieren und verwendeten komputationale Modellierung der Reaktionsdynamiken, um verschiedene Aspekte des generativen Modells des Gehirns von der sensorischen Umwelt zu untersuchen. In der ersten Studie verwendeten wir ein volatiles "Roving-Stimulus"-Paradigma, um somatosensorische MMRs auszulösen und modellierten die Einzel-Proben der EEG-Signale im sensorischen und Quell-Raum. Modellvergleiche legten nahe, dass die Reaktionen Bayes’sche Inferenz abbilden, basierend auf der Schätzung von Transitionswahrscheinlichkeiten und limitierter Integration von Information der jüngsten Vergangenheit, welche eine Anpassung an Umweltänderungen ermöglicht. Die Ergebnisse legen nahe, dass somatosen-sorische MMRs eine initiale Diskrepanz zwischen sensorischer Einspeisung und Modellüberzeugung reflektieren welche durch "confidence-corrected surprise" (CS) repräsentiert ist, gefolgt von Modelanpassungsdynamiken repräsentiert von "Bayesian surprise" (BS). Für die zweite und dritte Studie haben wir ein Tri-Modales "Roving-Stimulus"-Paradigma gestaltet, um modalitätsspezifische und modalitätsübergreifende Eigenschaften von Diskrepanzprozessierung zu umreißen. Komputationale Modellierung von EEG-Signalen in Studie 2 legte nahe, dass Einzel-Proben Dynamiken Bayes’sche Inferenz abbilden, basierend auf der Schätzung von unimodalen Transitionswahrscheinlichkeiten sowie modalitätsübergreifenden bedingten Abhängigkeiten. Während frühe Diskrepanzprozessierung um die MMN dazu tendierten CS zu reflektieren, so reflektierten spätere MMRs um die P3 eher BS, in Übereinstimmung mit der somatosensorischen Studie. Abschließend zeigten die fMRT-Ergebnisse der Studie 3 dass MMRs durch eine Interaktion von modalitätsspezifischen Regionen in sensorischen Kortizes höherer Ordnung mit einem modalitätsübergreifenden fronto-parietalen Netzwerk generiert werden. Inferior parietale Regionen im Speziellen waren sensitiv gegenüber Erwartungsverstoß in Bezug auf die modalitätsübergreifenden Wahrscheinlichkeiten in den Reizsequenzen. Insgesamt weisen unsere Ergebnisse darauf hin, dass MMRs über die Sinne hinweg Prozesse von wahrscheinlichkeitsbasierter Inferenz in einer komplexen und inhärent multi-modalen Umwelt darstellen

Neural surprise in somatosensory Bayesian learning

Tracking statistical regularities of the environment is important for shaping human behavior and perception. Evidence suggests that the brain learns environmental dependencies using Bayesian principles. However, much remains unknown about the employed algorithms, for somesthesis in particular. Here, we describe the cortical dynamics of the somatosensory learning system to investigate both the form of the generative model as well as its neural surprise signatures. Specifically, we recorded EEG data from 40 participants subjected to a somatosensory roving-stimulus paradigm and performed single-trial modeling across peri-stimulus time in both sensor and source space. Our Bayesian model selection procedure indicates that evoked potentials are best described by a non-hierarchical learning model that tracks transitions between observations using leaky integration. From around 70ms post-stimulus onset, secondary somatosensory cortices are found to represent confidence-corrected surprise as a measure of model inadequacy. Indications of Bayesian surprise encoding, reflecting model updating, are found in primary somatosensory cortex from around 140ms. This dissociation is compatible with the idea that early surprise signals may control subsequent model update rates. In sum, our findings support the hypothesis that early somatosensory processing reflects Bayesian perceptual learning and contribute to an understanding of its underlying mechanisms

The brain as a generative model: information-theoretic surprise in learning and action

Our environment is rich with statistical regularities, such as a sudden cold gust of wind indicating a potential change in weather. A combination of theoretical work and empirical evidence suggests that humans embed this information in an internal representation of the world. This generative model is used to perform probabilistic inference, which may be approximated through surprise minimization. This process rests on current beliefs enabling predictions, with expectation violation amounting to surprise. Through repeated interaction with the world, beliefs become more accurate and grow more certain over time. Perception and learning may be accounted for by minimizing surprise of current observations, while action is proposed to minimize expected surprise of future events. This framework thus shows promise as a common formulation for different brain functions. The work presented here adopts information-theoretic quantities of surprise to investigate both perceptual learning and action. We recorded electroencephalography (EEG) of participants in a somatosensory roving-stimulus paradigm and performed trial-by-trial modeling of cortical dynamics. Bayesian model selection suggests early processing in somatosensory cortices to encode confidence-corrected surprise and subsequently Bayesian surprise. This suggests the somatosensory system to signal surprise of observations and update a probabilistic model learning transition probabilities. We also extended this framework to include audition and vision in a multi-modal roving-stimulus study. Next, we studied action by investigating a sensitivity to expected Bayesian surprise. Interestingly, this quantity is also known as information gain and arises as an incentive to reduce uncertainty in the active inference framework, which can correspond to surprise minimization. In comparing active inference to a classical reinforcement learning model on the two-step decision-making task, we provided initial evidence for active inference to better account for human model-based behaviour. This appeared to relate to participants’ sensitivity to expected Bayesian surprise and contributed to explaining exploration behaviour not accounted for by the reinforcement learning model. Overall, our findings provide evidence for information-theoretic surprise as a model for perceptual learning signals while also guiding human action.Unsere Umwelt ist reich an statistischen Regelmäßigkeiten, wie z. B. ein plötzlicher kalter Windstoß, der einen möglichen Wetterumschwung ankündigt. Eine Kombination aus theoretischen Arbeiten und empirischen Erkenntnissen legt nahe, dass der Mensch diese Informationen in eine interne Darstellung der Welt einbettet. Dieses generative Modell wird verwendet, um probabilistische Inferenz durchzuführen, die durch Minimierung von Überraschungen angenähert werden kann. Der Prozess beruht auf aktuellen Annahmen, die Vorhersagen ermöglichen, wobei eine Verletzung der Erwartungen einer Überraschung gleichkommt. Durch wiederholte Interaktion mit der Welt nehmen die Annahmen mit der Zeit an Genauigkeit und Gewissheit zu. Es wird angenommen, dass Wahrnehmung und Lernen durch die Minimierung von Überraschungen bei aktuellen Beobachtungen erklärt werden können, während Handlung erwartete Überraschungen für zukünftige Beobachtungen minimiert. Dieser Rahmen ist daher als gemeinsame Bezeichnung für verschiedene Gehirnfunktionen vielversprechend. In der hier vorgestellten Arbeit werden informationstheoretische Größen der Überraschung verwendet, um sowohl Wahrnehmungslernen als auch Handeln zu untersuchen. Wir haben die Elektroenzephalographie (EEG) von Teilnehmern in einem somatosensorischen Paradigma aufgezeichnet und eine trial-by-trial Modellierung der kortikalen Dynamik durchgeführt. Die Bayes'sche Modellauswahl deutet darauf hin, dass frühe Verarbeitung in den somatosensorischen Kortizes confidence corrected surprise und Bayesian surprise kodiert. Dies legt nahe, dass das somatosensorische System die Überraschung über Beobachtungen signalisiert und ein probabilistisches Modell aktualisiert, welches wiederum Wahrscheinlichkeiten in Bezug auf Übergänge zwischen Reizen lernt. In einer weiteren multimodalen Roving-Stimulus-Studie haben wir diesen Rahmen auch auf die auditorische und visuelle Modalität ausgeweitet. Als Nächstes untersuchten wir Handlungen, indem wir die Empfindlichkeit gegenüber der erwarteten Bayesian surprise betrachteten. Interessanterweise ist diese informationstheoretische Größe auch als Informationsgewinn bekannt und stellt, im Rahmen von active inference, einen Anreiz dar, Unsicherheit zu reduzieren. Dies wiederum kann einer Minimierung der Überraschung entsprechen. Durch den Vergleich von active inference mit einem klassischen Modell des Verstärkungslernens (reinforcement learning) bei der zweistufigen Entscheidungsaufgabe konnten wir erste Belege dafür liefern, dass active inference menschliches modellbasiertes Verhalten besser abbildet. Dies scheint mit der Sensibilität der Teilnehmer gegenüber der erwarteten Bayesian surprise zusammenzuhängen und trägt zur Erklärung des Explorationsverhaltens bei, das jedoch nicht vom reinforcement learning-Modell erklärt werden kann. Insgesamt liefern unsere Ergebnisse Hinweise für Formulierungen der informationstheoretischen Überraschung als Modell für Signale wahrnehmungsbasierten Lernens, die auch menschliches Handeln steuern

Predictive Coding Theories of Cortical Function

Predictive coding is a unifying framework for understanding perception, action and neocortical organization. In predictive coding, different areas of the neocortex implement a hierarchical generative model of the world that is learned from sensory inputs. Cortical circuits are hypothesized to perform Bayesian inference based on this generative model. Specifically, the Rao-Ballard hierarchical predictive coding model assumes that the top-down feedback connections from higher to lower order cortical areas convey predictions of lower-level activities. The bottom-up, feedforward connections in turn convey the errors between top-down predictions and actual activities. These errors are used to correct current estimates of the state of the world and generate new predictions. Through the objective of minimizing prediction errors, predictive coding provides a functional explanation for a wide range of neural responses and many aspects of brain organization

Spike-Based Bayesian-Hebbian Learning of Temporal Sequences

Many cognitive and motor functions are enabled by the temporal representation and processing of stimuli, but it remains an open issue how neocortical microcircuits can reliably encode and replay such sequences of information. To better understand this, a modular attractor memory network is proposed in which meta-stable sequential attractor transitions are learned through changes to synaptic weights and intrinsic excitabilities via the spike-based Bayesian Confidence Propagation Neural Network (BCPNN) learning rule. We find that the formation of distributed memories, embodied by increased periods of firing in pools of excitatory neurons, together with asymmetrical associations between these distinct network states, can be acquired through plasticity. The model's feasibility is demonstrated using simulations of adaptive exponential integrate-and-fire model neurons (AdEx). We show that the learning and speed of sequence replay depends on a confluence of biophysically relevant parameters including stimulus duration, level of background noise, ratio of synaptic currents, and strengths of short-term depression and adaptation. Moreover, sequence elements are shown to flexibly participate multiple times in the sequence, suggesting that spiking attractor networks of this type can support an efficient combinatorial code. The model provides a principled approach towards understanding how multiple interacting plasticity mechanisms can coordinate hetero-associative learning in unison

The Neural Particle Filter

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals based on the history of observations, provides a mathematical framework for dynamic perception in real time. Since the general, nonlinear filtering problem is analytically intractable, particle filters are considered among the most powerful approaches to approximating the solution numerically. Yet, these algorithms prevalently rely on importance weights, and thus it remains an unresolved question how the brain could implement such an inference strategy with a neuronal population. Here, we propose the Neural Particle Filter (NPF), a weight-less particle filter that can be interpreted as the neuronal dynamics of a recurrently connected neural network that receives feed-forward input from sensory neurons and represents the posterior probability distribution in terms of samples. Specifically, this algorithm bridges the gap between the computational task of online state estimation and an implementation that allows networks of neurons in the brain to perform nonlinear Bayesian filtering. The model captures not only the properties of temporal and multisensory integration according to Bayesian statistics, but also allows online learning with a maximum likelihood approach. With an example from multisensory integration, we demonstrate that the numerical performance of the model is adequate to account for both filtering and identification problems. Due to the weightless approach, our algorithm alleviates the 'curse of dimensionality' and thus outperforms conventional, weighted particle filters in higher dimensions for a limited number of particles

Control flow in active inference systems Part I: Classical and quantum formulations of active inference

Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. In this Part I, we introduce the free-energy principle (FEP) and the idea of active inference as Bayesian prediction-error minimization, and show how the control problem arises in active inference systems. We then review classical and quantum formulations of the FEP, with the former being the classical limit of the latter. In the accompanying Part II, we show that when systems are described as executing active inference driven by the FEP, their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implemented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales

Action and behavior: a free-energy formulation

We have previously tried to explain perceptual inference and learning under a free-energy principle that pursues Helmholtz’s agenda to understand the brain in terms of energy minimization. It is fairly easy to show that making inferences about the causes of sensory data can be cast as the minimization of a free-energy bound on the likelihood of sensory inputs, given an internal model of how they were caused. In this article, we consider what would happen if the data themselves were sampled to minimize this bound. It transpires that the ensuing active sampling or inference is mandated by ergodic arguments based on the very existence of adaptive agents. Furthermore, it accounts for many aspects of motor behavior; from retinal stabilization to goal-seeking. In particular, it suggests that motor control can be understood as fulfilling prior expectations about proprioceptive sensations. This formulation can explain why adaptive behavior emerges in biological agents and suggests a simple alternative to optimal control theory. We illustrate these points using simulations of oculomotor control and then apply to same principles to cued and goal-directed movements. In short, the free-energy formulation may provide an alternative perspective on the motor control that places it in an intimate relationship with perception