Bayesian Decoding Research Articles

Vision and Locomotion Combine to Drive Path Integration Sequences in Mouse Retrosplenial Cortex.

The retrosplenial cortex (RSC) is involved in a broad range of cognitive functions, integrating rich sensory, motor, and spatial signals from multiple brain areas, including the hippocampal system. RSC neurons show hippocampus-dependent activity reminiscent of place cell sequences. Using cellular calcium imaging in a virtual reality (VR)-based locomotion task, we investigate how the integration of visual and locomotor inputs may give rise to such activity in RSC. A substantial population shows neural sequences that track position in the VR environment. This activity is driven by the conjunction of visual stimuli sequences and active movement, which is suggestive of path integration. The activity is anchored to a reference point and predominantly follows the VR upon manipulations of optic flow against locomotion. Thus, locomotion-gated optic flow, combined with the presence of contextual cues at the start of each trial, is sufficient to drive the sequential activity. A subpopulation shows landmark-related visual responses that are modulated by animal's position in the VR. Thus, rather than fragmenting the spatial representationinto equivalent locomotion-based ensemble versus optic-flow-based ensemble, in RSC, optic flow appears to override locomotion signals coherently in the population, when the gain betweenthe two signals is altered.

Modeling stimulus-dependent variability improves decoding of population neural responses

Objective. Neural responses to repeated presentations of an identical stimulus often show substantial trial-to-trial variability. How the mean firing rate varies in response to different stimuli or during different movements (tuning curves) has been extensively modeled in a wide variety of neural systems. However, the variability of neural responses can also have clear tuning independent of the tuning in the mean firing rate. This suggests that the variability could contain information regarding the stimulus/movement beyond what is encoded in the mean firing rate. Here we demonstrate how taking variability into account can improve neural decoding. Approach. In a typical neural coding model spike counts are assumed to be Poisson with the mean response depending on an external variable, such as a stimulus or movement. Bayesian decoding methods then use the probabilities under these Poisson tuning models (the likelihood) to estimate the probability of each stimulus given the spikes on a given trial (the posterior). However, under the Poisson model, spike count variability is always exactly equal to the mean (Fano factor = 1). Here we use two alternative models—the Conway–Maxwell–Poisson (CMP) model and negative binomial (NB) model—to more flexibly characterize how neural variability depends on external stimuli. These models both contain the Poisson distribution as a special case but have an additional parameter that allows the variance to be greater than the mean (Fano factor > 1) or, for the CMP model, less than the mean (Fano factor < 1). Main results. We find that neural responses in primary motor (M1), visual (V1), and auditory (A1) cortices have diverse tuning in both their mean firing rates and response variability. Across cortical areas, we find that Bayesian decoders using the CMP or NB models improve stimulus/movement estimation accuracy by 4%–12% compared to the Poisson model. Significance. Moreover, the uncertainty of the non-Poisson decoders more accurately reflects the magnitude of estimation errors. In addition to tuning curves that reflect average neural responses, stimulus-dependent response variability may be an important aspect of the neural code. Modeling this structure could, potentially, lead to improvements in brain machine interfaces.

Differentially synchronized spiking enables multiplexed neural coding

Multiplexing refers to the simultaneous encoding of two or more signals. Neurons have been shown to multiplex, but different stimuli require different multiplexing strategies. Whereas the frequency and amplitude of periodic stimuli can be encoded by the timing and rate of the same spikes, natural scenes, which comprise areas over which intensity varies gradually and sparse edges where intensity changes abruptly, require a different multiplexing strategy. Recording in vivo from neurons in primary somatosensory cortex during tactile stimulation, we found that stimulus onset and offset (edges) evoked highly synchronized spiking, whereas other spikes in the same neurons occurred asynchronously. Stimulus intensity modulated the rate of asynchronous spiking, but did not affect the timing of synchronous spikes. From this, we hypothesized that spikes driven by high- and low-contrast stimulus features can be distinguished on the basis of their synchronization, and that differentially synchronized spiking can thus be used to form multiplexed representations. Applying a Bayesian decoding method, we verified that information about high- and low-contrast features can be recovered from an ensemble of model neurons receiving common input. Equally good decoding was achieved by distinguishing synchronous from asynchronous spikes and applying reverse correlation methods separately to each spike type. This result, which we verified with patch clamp recordings in vitro, demonstrates that neurons receiving common input can use the rate of asynchronous spiking to encode the intensity of low-contrast features while using the timing of synchronous spikes to encode the occurrence of high-contrast features. We refer to this strategy as synchrony-division multiplexing.

In vivo Calcium Imaging Reveals That Cortisol Treatment Reduces the Number of Place Cells in Thy1-GCaMP6f Transgenic Mice.

The hippocampus, a structure essential for spatial navigation and memory undergoes anatomical and functional changes during chronic stress. Here, we investigate the effects of chronic stress on the ability of place cells to encode the neural representation of a linear track. To model physiological conditions of chronic stress on hippocampal function, transgenic mice expressing the genetically encoded calcium indicator GCaMP6f in CA1 pyramidal neurons were chronically administered with 40 μg/ml of cortisol for 8 weeks. Cortisol-treated mice exhibited symptoms typically observed during chronic stress, including diminished reward seeking behavior and reduced adrenal gland and spleen weights. In vivo imaging of hippocampal cellular activity during linear track running behavior revealed a reduced number of cells that could be recruited to encode spatial position, despite an unchanged overall number of active cells, in cortisol-treated mice. The properties of the remaining place cells that could be recruited to encode spatial information, however, was unperturbed. Bayesian decoders trained to estimate the mouse’s position on the track using single neuron activity data demonstrated reduced performance in a cue richness-dependent fashion in cortisol-treated animals. The performance of decoders utilizing data from the entire neuronal ensemble was unaffected by cortisol treatment. Finally, to test the hypothesis that an antidepressant drug could prevent the effects of cortisol, we orally administered a group of mice with 10 mg/kg citalopram during cortisol administration. Citalopram prevented the cortisol-induced decrease in single-neuron decoder performance but failed to significantly prevent anhedonia and the cortisol-induced reduction in the proportion place cells. The dysfunction observed at the single-neuron level indicates that chronic stress may impair the ability of the hippocampus to encode individual neural representations of the mouse’s spatial position, a function pivotal to forming an accurate navigational map of the mouse’s external environment; however, the hippocampal ensemble as a whole is resilient to any cortisol-induced insults to single neuronal place cell function on the linear track.

How can we play together? Temporal inconsistencies in neural coding of music.

If sensory organs encode environment, this code must be decoded to perception. The currently dominant theory of perception - predictive coding - assumes a "Bayesian decoder," a probability function, which will present (to whom?) an optimal guess, given previous encodings of the environment - old codes testing new codes. Such a process would delay perception noticeably. This is inconsistent with the perception of music, which for several reasons must be direct.

Pupil-linked arousal modulates behavior in rats performing a whisker deflection direction discrimination task.

Non-luminance-mediated changes in pupil size have been widely used to index arousal state. Recent animal studies have demonstrated correlations between behavioral state-related pupil dynamics and sensory processing. However, the relationship between pupil-linked arousal and behavior in animals performing perceptual tasks has not been fully elucidated. In the present study, we trained head-fixed rats to discriminate between directions of whisker movements using a Go/No-Go discrimination paradigm while imaging their pupils. Reaction times in this discrimination task were significantly slower than in previously reported detection tasks with similar setup, suggesting that discrimination required an increased cognitive load. We found the pupils dilated for all trials following stimulus presentation. Interestingly, in correct rejection trials, where pupil dilations solely resulted from cognitive processing, dilations were larger for more difficult stimuli. Baseline pupil size before stimulus presentation strongly correlated with behavior, as perceptual sensitivity peaked at intermediate pupil baselines and reaction time was fastest at large baselines. We further explored these relationships by investigating to what extent pupil baseline was predictive of upcoming behavior and found that a Bayesian decoder had significantly greater-than-chance probability in correctly predicting behavioral outcomes. Moreover, the outcome of the previous trial showed a strong correlation with behavior on present trials. Animals were more liberal and faster in responding following hit trials, whereas perceptual sensitivity was greatest following correct rejection trials. Taken together, these results suggest a tight correlation between pupil dynamics, perceptual performance, and reaction time in behaving rats, all of which are modulated by fluctuating arousal state. NEW & NOTEWORTHY In this study, we for the first time demonstrated that head-fixed rats were able to discriminate different directions of whisker movement. Interestingly, we found that the pupil dilated more when discriminating more difficult stimuli, a phenomenon reported in human subjects but not in animals. Baseline pupil size before stimulus presentation was found to strongly correlate with behavior, and a Bayesian decoder had significantly greater-than-chance probability in correctly predicting behavioral outcomes based on the baseline pupil size.

Space Coding Schemes for Multiple Human Localization With Fiber-Optic Sensors

This paper presents a pressure sensing system using fiber-optic sensors for multiple human localizations. The conventional fiber sensor uses complicated hardware such as optical time-domain reflectometer (OTDR) for pressure localization, while this paper aims to develop a smart floor with much simpler hardware for human localization based on binary compressive sensing and low-density parity-check (LDPC) coding. The proposed pressure sensing system includes LED emitters, plastic optical fibers, and photodetectors, as well as wireless motes. The observation space (or floor) is encoded into a set of binary codes, and multidimensional binary data are generated when targets walk on the floor. A set of Bayesian decoding algorithms are developed for the target localization using those binary data, given two types of logic operations (OR and XOR), respectively. The experimental results demonstrate the multiple human location information acquisition capability of the proposed space encoding/decoding scheme with high data efficiency and energy efficiency.

The Synaptic Properties of Cells Define the Hallmarks of Interval Timing in a Recurrent Neural Network.

Extensive research has described two key features of interval timing. The bias property is associated with accuracy and implies that time is overestimated for short intervals and underestimated for long intervals. The scalar property is linked to precision and states that the variability of interval estimates increases as a function of interval duration. The neural mechanisms behind these properties are not well understood. Here we implemented a recurrent neural network that mimics a cortical ensemble and includes cells that show paired-pulse facilitation and slow inhibitory synaptic currents. The network produces interval selective responses and reproduces both bias and scalar properties when a Bayesian decoder reads its activity. Notably, the interval-selectivity, timing accuracy, and precision of the network showed complex changes as a function of the decay time constants of the modeled synaptic properties and the level of background activity of the cells. These findings suggest that physiological values of the time constants for paired-pulse facilitation and GABAb, as well as the internal state of the network, determine the bias and scalar properties of interval timing.SIGNIFICANCE STATEMENT Timing is a fundamental element of complex behavior, including music and language. Temporal processing in a wide variety of contexts shows two primary features: time estimates exhibit a shift toward the mean (the bias property) and are more variable for longer intervals (the scalar property). We implemented a recurrent neural network that includes long-lasting synaptic currents, which cannot only produce interval-selective responses but also follow the bias and scalar properties. Interestingly, only physiological values of the time constants for paired-pulse facilitation and GABAb, as well as intermediate background activity within the network can reproduce the two key features of interval timing.

Self-Organized Attractor Dynamics in the Developing Head Direction Circuit

SummaryHead direction (HD) cells are neurons found in an extended cortical and subcortical network that signal the orientation of an animal’s head relative to its environment [1, 2, 3]. They are a fundamental component of the wider circuit of spatially responsive hippocampal formation neurons that make up the neural cognitive map of space [4]. During post-natal development, HD cells are the first among spatially modulated neurons in the hippocampal circuit to exhibit mature firing properties [5, 6], but before eye opening, HD cell responses in rat pups have low directional information and are directionally unstable [7, 8]. Using Bayesian decoding of HD cell ensemble activity recorded in the anterodorsal thalamic nucleus (ADN), we characterize this instability and identify its source: under-signaling of angular head velocity, which incompletely shifts the directional signal in proportion to head turns. We find evidence that geometric cues (the corners of a square environment) can be used to mitigate this under-signaling and, thereby, stabilize the directional signal even before eye opening. Crucially, even when directional firing cannot be stabilized, ensembles of unstable HD cells show short-timescale (1–10 s) temporal and spatial couplings consistent with an adult-like HD network. The HD network is widely modeled as a continuous attractor whose output is one coherent activity peak, updated during movement by angular head velocity signals and anchored by landmark cues [9, 10, 11]. Our findings present strong evidence for this model, and they demonstrate that the required network circuitry is in place and functional early during development, independent of reference to landmark information.

Self-organised Attractor Dynamics in the Developing Head Direction Circuit

Head direction (HD) cells signal the orientation of an animal’s head relative to its environment. During post-natal development, HD cells are the earliest spatially modulated neurons in the hippocampal circuit to emerge. However, before eye-opening, HD cell responses in rat pups carry low directional information content and are directionally unstable. Using Bayesian decoding, we characterise this instability and identify its source: despite the directional signal being internally coherent, it consistently under-signals angular head velocity (AHV), incompletely shifting in proportion to head turns. We find evidence that geometric cues (corners) can be used to mitigate this under-signalling, and stabilise the directional signal even before eye-opening. Crucially, even when directional firing cannot be stabilised, ensembles of unstable HD cells show short-timescale (1-10 sec) temporal and spatial couplings consistent with an adult-like HD network, through which activity drifts unanchored to landmark cues. The existence of fixed spatial and temporal offsets across co-recorded cells and of an AHV-responsive signal, even before HD responses become spatially stable, suggests that the HD circuit is assembled through internal, self-organising processes, without reference to external landmarks. The HD network is widely modelled as a continuous attractor whose output is one coherent activity peak, updated during movement by angular head velocity (AHV) signals, and anchored by landmark cues. Our findings present strong evidence for this model, and demonstrate that the required network circuitry is in place and functional during development, independent of reference to landmark information.

Multivariate Bayesian decoding of single-trial event-related fMRI responses for memory retrieval of voluntary actions.

This study proposes a method for classifying event-related fMRI responses in a specialized setting of many known but few unknown stimuli presented in a rapid event-related design. Compared to block design fMRI signals, classification of the response to a single or a few stimulus trial(s) is not a trivial problem due to contamination by preceding events as well as the low signal-to-noise ratio. To overcome such problems, we proposed a single trial-based classification method of rapid event-related fMRI signals utilizing sparse multivariate Bayesian decoding of spatio-temporal fMRI responses. We applied the proposed method to classification of memory retrieval processes for two different classes of episodic memories: a voluntarily conducted experience and a passive experience induced by watching a video of others’ actions. A cross-validation showed higher classification performance of the proposed method compared to that of a support vector machine or of a classifier based on the general linear model. Evaluation of classification performances for one, two, and three stimuli from the same class and a correlation analysis between classification accuracy and target stimulus positions among trials suggest that presenting two target stimuli at longer inter-stimulus intervals is optimal in the design of classification experiments to identify the target stimuli. The proposed method for decoding subject-specific memory retrieval of voluntary behavior using fMRI would be useful in forensic applications in a natural environment, where many known trials can be extracted from a simulation of everyday tasks and few target stimuli from a crime scene.

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules.

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal’s motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.

Optimizing for generalization in the decoding of internally generated activity in the hippocampus.

The decoding of a sensory or motor variable from neural activity benefits from a known ground truth against which decoding performance can be compared. In contrast, the decoding of covert, cognitive neural activity, such as occurs in memory recall or planning, typically cannot be compared to a known ground truth. As a result, it is unclear how decoders of such internally generated activity should be configured in practice. We suggest that if the true code for covert activity is unknown, decoders should be optimized for generalization performance using cross-validation. Using ensemble recording data from hippocampal place cells, we show that this cross-validation approach results in different decoding error, different optimal decoding parameters, and different distributions of error across the decoded variable space. In addition, we show that a minor modification to the commonly used Bayesian decoding procedure, which enables the use of spike density functions, results in substantially lower decoding errors. These results have implications for the interpretation of covert neural activity, and suggest easy-to-implement changes to commonly used procedures across domains, with applications to hippocampal place cells in particular. © 2017 Wiley Periodicals, Inc.

Predictive Ensemble Decoding of Acoustical Features Explains Context-Dependent Receptive Fields.

A primary goal of auditory neuroscience is to identify the sound features extracted and represented by auditory neurons. Linear encoding models, which describe neural responses as a function of the stimulus, have been primarily used for this purpose. Here, we provide theoretical arguments and experimental evidence in support of an alternative approach, based on decoding the stimulus from the neural response. We used a Bayesian normative approach to predict the responses of neurons detecting relevant auditory features, despite ambiguities and noise. We compared the model predictions to recordings from the primary auditory cortex of ferrets and found that: (1) the decoding filters of auditory neurons resemble the filters learned from the statistics of speech sounds; (2) the decoding model captures the dynamics of responses better than a linear encoding model of similar complexity; and (3) the decoding model accounts for the accuracy with which the stimulus is represented in neural activity, whereas linear encoding model performs very poorly. Most importantly, our model predicts that neuronal responses are fundamentally shaped by “explaining away,” a divisive competition between alternative interpretations of the auditory scene.SIGNIFICANCE STATEMENT Neural responses in the auditory cortex are dynamic, nonlinear, and hard to predict. Traditionally, encoding models have been used to describe neural responses as a function of the stimulus. However, in addition to external stimulation, neural activity is strongly modulated by the responses of other neurons in the network. We hypothesized that auditory neurons aim to collectively decode their stimulus. In particular, a stimulus feature that is decoded (or explained away) by one neuron is not explained by another. We demonstrated that this novel Bayesian decoding model is better at capturing the dynamic responses of cortical neurons in ferrets. Whereas the linear encoding model poorly reflects selectivity of neurons, the decoding model can account for the strong nonlinearities observed in neural data.

A Message-Passing Receiver for OFDM-Based Self-Interference-Limited Networks

In this paper, we develop a reliable bandwidth-efficient solution for coherent reception in networks prone to self-interference. Our primary focus is on orthogonal-frequency-division-multiplexing (OFDM)-based amplify-and-forward (AF) two-way relaying, where each source node suffers from reradiation of its own signal. An important issue is the superposition of the desired and interfering signals, which makes the channel estimation task difficult, particularly for varying channel coefficients. To address this challenging problem, we introduce a factor graph model of the estimation and detection problem at hand. Exploiting the conditional independence between unknown variables in the factor graph, an efficient message-passing algorithm, which performs joint Bayesian channel estimation, self-interference mitigation, and decoding, is derived. Simulation results show that the performance of the proposed method is close to that given by perfect knowledge of the channel for the target and interfering signals, even with limited training overhead.

The Bayesian Decoding of Force Stimuli from Slowly Adapting Type I Fibers in Humans.

It is well known that signals encoded by mechanoreceptors facilitate precise object manipulation in humans. It is therefore of interest to study signals encoded by the mechanoreceptors because this will contribute further towards the understanding of fundamental sensory mechanisms that are responsible for coordinating force components during object manipulation. From a practical point of view, this may suggest strategies for designing sensory-controlled biomedical devices and robotic manipulators. We use a two-stage nonlinear decoding paradigm to reconstruct the force stimulus given signals from slowly adapting type one (SA-I) tactile afferents. First, we describe a nonhomogeneous Poisson encoding model which is a function of the force stimulus and the force’s rate of change. In the decoding phase, we use a recursive nonlinear Bayesian filter to reconstruct the force profile, given the SA-I spike patterns and parameters described by the encoding model. Under the current encoding model, the mode ratio of force to its derivative is: 1.26 to 1.02. This indicates that the force derivative contributes significantly to the rate of change to the SA-I afferent spike modulation. Furthermore, using recursive Bayesian decoding algorithms is advantageous because it can incorporate past and current information in order to make predictions—consistent with neural systems—with little computational resources. This makes it suitable for interfacing with prostheses.

A Bayesian view on acoustic model-based techniques for robust speech recognition

This article provides a unifying Bayesian view on various approaches for acoustic model adaptation, missing feature, and uncertainty decoding that are well-known in the literature of robust automatic speech recognition. The representatives of these classes can often be deduced from a Bayesian network that extends the conventional hidden Markov models used in speech recognition. These extensions, in turn, can in many cases be motivated from an underlying observation model that relates clean and distorted feature vectors. By identifying and converting the observation models into a Bayesian network representation, we formulate the corresponding compensation rules. We thus summarize the various approaches as approximations or modifications of the same Bayesian decoding rule leading to a unified view on known derivations as well as to new formulations for certain approaches.

Kernel density compression for real-time Bayesian encoding/decoding of unsorted hippocampal spikes

To gain a better understanding of how neural ensembles communicate and process information, neural decoding algorithms are used to extract information encoded in their spiking activity. Bayesian decoding is one of the most used neural population decoding approaches to extract information from the ensemble spiking activity of rat hippocampal neurons. Recently it has been shown how Bayesian decoding can be implemented without the intermediate step of sorting spike waveforms into groups of single units. Here we extend the approach in order to make it suitable for online encoding/decoding scenarios that require real-time decoding such as brain-machine interfaces. We propose an online algorithm for the Bayesian decoding that reduces the time required for decoding neural populations, resulting in a real-time capable decoding framework. More specifically, we improve the speed of the probability density estimation step, which is the most essential and the most expensive computation of the spike-sorting-less decoding process, by developing a kernel density compression algorithm. In contrary to existing online kernel compression techniques, rather than optimizing for the minimum estimation error caused by kernels compression, the proposed method compresses kernels on the basis of the distance between the merging component and its most similar neighbor. Thus, without costly optimization, the proposed method has very low compression latency with a small and manageable estimation error. In addition, the proposed bandwidth matching method for Gaussian kernels merging has an interesting mathematical property whereby optimization in the estimation of the probability density function can be performed efficiently, resulting in a faster decoding speed. We successfully applied the proposed kernel compression algorithm to the Bayesian decoding framework to reconstruct positions of a freely moving rat from hippocampal unsorted spikes, with significant improvements in the decoding speed and acceptable decoding error.

Improving neural decoding in the central auditory system using bio-inspired spectro-temporal representations and a generalized bilinear model.

We study the impact of different encoding models and spectro-temporal representations on the accuracy of Bayesian decoding of neural activity recorded from the central auditory system. Two encoding models, a generalized linear model (GLM) and a generalized bilinear model (GBM), are compared along with three different spectro-temporal representations of the input stimuli: a spectrogram and two bio-inspired representations, i.e. a gammatone filter bank (GFB) and a spikegram. Signal to noise ratios between the reconstructed and original representations are used to evaluate the decoding, or reconstruction accuracy. We experimentally show that the reconstruction accuracy is best with the spikegram representation and worst with the spectrogram representation and, furthermore, that using a GBM instead of a GLM significantly increases the reconstruction accuracy. In fact, our results show that the spikegram reconstruction accuracy with a GBM fitting yields an SNR that is 3.3 dB better than when using the standard decoding approach of reconstructing a spectrogram with GLM fitting.

Estimating a dynamic state to relate neural spiking activity to behavioral signals during cognitive tasks.

An important question in neuroscience is understanding the relationship between high-dimensional electrophysiological data and complex, dynamic behavioral data. One general strategy to address this problem is to define a low-dimensional representation of essential cognitive features describing this relationship. Here we describe a general state-space method to model and fit a low-dimensional cognitive state process that allows us to relate behavioral outcomes of various tasks to simultaneously recorded neural activity across multiple brain areas. In particular, we apply this model to data recorded in the lateral prefrontal cortex (PFC) and caudate nucleus of non-human primates as they perform learning and adaptation in a rule-switching task. First, we define a model for a cognitive state process related to learning, and estimate the progression of this learning state through the experiments. Next, we formulate a point process generalized linear model to relate the spiking activity of each PFC and caudate neuron to the stimated learning state. Then, we compute the posterior densities of the cognitive state using a recursive Bayesian decoding algorithm. We demonstrate that accurate decoding of a learning state is possible with a simple point process model of population spiking. Our analyses also allow us to compare decoding accuracy across neural populations in the PFC and caudate nucleus.