Bayesian Decoding Research Articles

Calibrating Bayesian Decoders of Neural Spiking Activity.

Accurately decoding external variables from observations of neural activity is a major challenge in systems neuroscience. Bayesian decoders, which provide probabilistic estimates, are some of the most widely used. Here we show how, in many common settings, the probabilistic predictions made by traditional Bayesian decoders are overconfident. That is, the estimates for the decoded stimulus or movement variables are more certain than they should be. We then show how Bayesian decoding with latent variables, taking account of low-dimensional shared variability in the observations, can improve calibration, although additional correction for overconfidence is still needed. Using data from males, we examine (1) decoding the direction of grating stimuli from spike recordings in the primary visual cortex in monkeys, (2) decoding movement direction from recordings in the primary motor cortex in monkeys, (3) decoding natural images from multiregion recordings in mice, and (4) decoding position from hippocampal recordings in rats. For each setting, we characterize the overconfidence, and we describe a possible method to correct miscalibration post hoc. Properly calibrated Bayesian decoders may alter theoretical results on probabilistic population coding and lead to brain-machine interfaces that more accurately reflect confidence levels when identifying external variables.

Older adults preserve audiovisual integration through enhanced cortical activations, not by recruiting new regions.

Effective interactions with the environment rely on the integration of multisensory signals: Our brains must efficiently combine signals that share a common source, and segregate those that do not. Healthy ageing can change or impair this process. This functional magnetic resonance imaging study assessed the neural mechanisms underlying age differences in the integration of auditory and visual spatial cues. Participants were presented with synchronous audiovisual signals at various degrees of spatial disparity and indicated their perceived sound location. Behaviourally, older adults were able to maintain localisation accuracy. At the neural level, they integrated auditory and visual cues into spatial representations along dorsal auditory and visual processing pathways similarly to their younger counterparts but showed greater activations in a widespread system of frontal, temporal, and parietal areas. According to multivariate Bayesian decoding, these areas encoded critical stimulus information beyond that which was encoded in the brain areas commonly activated by both groups. Surprisingly, however, the boost in information provided by these areas with age-related activation increases was comparable across the 2 age groups. This dissociation-between comparable information encoded in brain activation patterns across the 2 age groups, but age-related increases in regional blood-oxygen-level-dependent responses-contradicts the widespread notion that older adults recruit new regions as a compensatory mechanism to encode task-relevant information. Instead, our findings suggest that activation increases in older adults reflect nonspecific or modulatory mechanisms related to less efficient or slower processing, or greater demands on attentional resources.

Efficient Decoding of Large-Scale Neural Population Responses With Gaussian-Process Multiclass Regression.

Neural decoding methods provide a powerful tool for quantifying the information content of neural population codes and the limits imposed by correlations in neural activity. However, standard decoding methods are prone to overfitting and scale poorly to high-dimensional settings. Here, we introduce a novel decoding method to overcome these limitations. Our approach, the gaussian process multiclass decoder (GPMD), is well suited to decoding a continuous low-dimensional variable from high-dimensional population activity and provides a platform for assessing the importance of correlations in neural population codes. The GPMD is a multinomial logistic regression model with a gaussian process prior over the decoding weights. The prior includes hyperparameters that govern the smoothness of each neuron's decoding weights, allowing automatic pruning of uninformative neurons during inference. We provide a variational inference method for fitting the GPMD to data, which scales to hundreds or thousands of neurons and performs well even in data sets with more neurons than trials. We apply the GPMD to recordings from primary visual cortex in three species: monkey, ferret, and mouse. Our decoder achieves state-of-the-art accuracy on all three data sets and substantially outperforms independent Bayesian decoding, showing that knowledge of the correlation structure is essential for optimal decoding in all three species.

Bayesian encoding and decoding as distinct perspectives on neural coding.

The Bayesian brain hypothesis is one of the most influential ideas in neuroscience. However, unstated differences in how Bayesian ideas are operationalized make it difficult to draw general conclusions about how Bayesian computations map onto neural circuits. Here, we identify one such unstated difference: some theories ask how neural circuits could recover information about the world from sensory neural activity (Bayesian decoding), whereas others ask how neural circuits could implement inference in an internal model (Bayesian encoding). These two approaches require profoundly different assumptions and lead to different interpretations of empirical data. We contrast them in terms of motivations, empirical support and relationship to neural data. We also use a simple model to argue that encoding and decoding models are complementary rather than competing. Appreciating the distinction between Bayesian encoding and Bayesian decoding will help to organize future work and enable stronger empirical tests about the nature of inference in the brain.

A Bayesian Decoder Representing Single-Directional Connectivity between Neurons in Brain-Machine Interface.

Directional neural connectivity is essential to understanding how neurons encode and transmit information in the neural network. The previous studies on single neuronal encoding models illustrate how the neurons modulate the stimulus, underlying movement, and interactions with other neurons. And these encoding models have been used in the Bayesian decoders of the brain-machine interface (BMI) to explain how the neural population represents the movement intentions. However, the existing methods only consider rough correlations between neurons without directional connections, while the synapses between real neurons have explicit directions. Therefore, in these models, we cannot specify the proper functional neural connectivity and how the neurons cooperate to represent the movement intentions in truth. Therefore, we propose representing the directional neural connectivity in the Bayesian decoder in BMI. Our method derives a chain-likelihood based on Bayes' rule to form the single-directional influence between neurons. According to the derived structure, the prior causality relationship can be used to build more precise neural encoding models. Therefore, our method can represent the functional neural circuit more precisely and benefit the decoding in the BMI. We validate the proposed method in synthetic data simulating the rat's two-lever discrimination task. The results demonstrate that our method outperforms the existing methods by representing directional-neural connectivity. Besides, our method is more efficient in training because it employs fewer parameters. Consequently, our method can be used to evaluate the causality between neurons at the behavior level.Clinical Relevance-This paper proposes a decoder that can represent single-directional neural connectivity, which is potential to validate the causality relationship between neurons at behavior level.

Constant Weight Codes With Gabor Dictionaries and Bayesian Decoding for Massive Random Access

This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on Gabor frames. The decoder applies an extension of approximate message passing (AMP) by iteratively exchanging soft information between an AMP module that accounts for the dictionary structure, and a second inference module that utilizes the structure of the involved constant-weight code. We apply the encoding structure to (i) the unsourced random access setting, where all users employ a common dictionary, and (ii) to the “sourced” random access setting with user-specific dictionaries. When applied to a fading scenario, the communication scheme essentially operates non-coherently, as channel state information is required neither at the transmitter nor at the receiver. We observe that in regimes of practical interest, the proposed scheme compares favorably with state-of-the art schemes, in terms of the (per-user) energy-per-bit requirement, as well as the number of active users that can be simultaneously accommodated in the system. Importantly, this is achieved with a considerably smaller size of the transmitted codewords, potentially yielding lower latency and bandwidth occupancy, as well as lower implementation complexity.

Information Bottleneck-Inspired Type Based Multiple Access for Remote Estimation in IoT Systems

Type-based multiple access (TBMA) is a semantics-aware multiple access protocol for remote inference. In TBMA, codewords are reused across transmitting sensors, with each codeword being assigned to a different observation value. Existing TBMA protocols are based on fixed shared codebooks and on conventional maximum-likelihood or Bayesian decoders, which require knowledge of the distributions of observations and channels. In this letter, we propose a novel design principle for TBMA based on the information bottleneck (IB). In the proposed IB-TBMA protocol, the shared codebook is jointly optimized with a decoder based on artificial neural networks (ANNs), so as to adapt to source, observations, and channel statistics based on data only. We also introduce the Compressed IB-TBMA (CIB-TBMA) protocol, which improves IB-TBMA by enabling a reduction in the number of codewords via an IB-inspired clustering phase. Numerical results demonstrate the importance of a joint design of codebook and neural decoder, and validate the benefits of codebook compression.

Decoding trajectories of imagined hand movement using electrocorticograms for brain–machine interface

Objective. Reaching hand movement is an important motor skill actively examined in the brain–computer interface (BCI). Among the various components of movement analyzed is the hand’s trajectory, which describes the hand’s continuous positions in three-dimensional space. While a large body of studies have investigated the decoding of real movements and the reconstruction of real hand movement trajectories from neural signals, fewer studies have attempted to decode the trajectory of the imagined hand movement. To develop BCI systems for patients with hand motor dysfunctions, the systems essentially have to achieve movement-free control of external devices, which is only possible through successful decoding of purely imagined hand movement. Approach. To achieve this goal, this study used a machine learning technique (i.e. the variational Bayesian least square) to analyze the electrocorticogram (ECoG) of 18 epilepsy patients obtained from when they performed movement execution (ME) and kinesthetic movement imagination (KMI) of the reach-and-grasp hand action. Main results. The variational Bayesian decoding model was able to successfully predict the imagined trajectories of the hand movement significantly above the chance level. The Pearson’s correlation coefficient between the imagined and predicted trajectories was 0.3393 and 0.4936 for the KMI (KMI trials only) and MEKMI paradigm (alternating trials of ME and KMI), respectively. Significance. This study demonstrated a high accuracy of prediction for the trajectories of imagined hand movement, and more importantly, a higher decoding accuracy of the imagined trajectories in the MEKMI paradigm compared to the KMI paradigm solely.

Complementary representations of time in the prefrontal cortex and hippocampus.

Episodic memory binds the spatial and temporal relationships between the elements of experience. The hippocampus encodes space through place cells that fire at specific spatial locations. Similarly, time cells fire sequentially at specific time points within a temporally organized experience. Recent studies in rodents, monkeys, and humans have identified time cells with discrete firing fields and cells with monotonically changing activity in supporting the temporal organization of events across multiple timescales. Using in vivo electrophysiological tetrode recordings, we simultaneously recorded neurons from the prefrontal cortex and dorsal CA1 of the hippocampus while rats performed a delayed match to sample task. During the treadmill mnemonic delay, hippocampal time cells exhibited sparser firing fields with decreasing resolution over time, consistent with previous results. In comparison, temporally modulated cells in the prefrontal cortex showed more monotonically changing firing rates, ramping up or decaying with the passage of time, and exhibited greater temporal precision for Bayesian decoding of time at long time lags. These time cells show exquisite temporal resolution both in their firing fields and inthe fine timing of spikes relative to the phase of theta oscillations. Here, we report evidence of theta phase precession in both the prefrontal cortex and hippocampus during the temporal delay, however, hippocampal cells exhibited steeper phase precession slopes and more punctate time fields. To disentangle whether time cell activity reflects elapsed time or distance traveled, we varied the treadmill running speed on each trial. While many neurons contained multiplexed representations of time and distance, both regions were more strongly influenced by time than distance. Overall, these results demonstrate the flexible integration of spatiotemporal dimensions and reveal complementary representations of time in the prefrontal cortex and hippocampus in supporting memory-guided behavior.

Phase coding of spatial representations in the human entorhinal cortex.

The grid-like activity pattern of cells in the mammalian entorhinal cortex provides an internal reference frame for allocentric self-localization. The same neurons maintain robust phase couplings with local field oscillations. We found that neurons of the human entorhinal cortex display consistent spatial and temporal phase locking between spikes and slow gamma band local field potentials (LFPs) during virtual navigation. The phase locking maintained an environment-specific map over time. The phase tuning of spikes to the slow gamma band LFP revealed spatially periodic phase grids with environment-dependent scaling and consistent alignment with the environment. Using a Bayesian decoding model, we could predict the avatar’s position with near perfect accuracy and, to a lesser extent, that of heading direction as well. These results imply that the phase of spikes relative to spatially modulated gamma oscillations encode allocentric spatial positions. We posit that a joint spatiotemporal phase code can implement the combined neural representation of space and time in the human entorhinal cortex.

Cross-fixation interactions of orientations suggest high-to-low-level decoding in visual working memory

Sensory encoding (how stimuli evoke sensory responses) is known to progress from low- to high-level features. Decoding (how responses lead to perception) is less understood but is often assumed to follow the same hierarchy. Accordingly, orientation decoding must occur in low-level areas such as V1, without cross-fixation interactions. However, a study, Ding, Cueva, Tsodyks, and Qian (2017), provided evidence against the assumption and proposed that visual decoding may often follow a high-to-low-level hierarchy in working memory, where higher-to-lower-level constraints introduce interactions among lower-level features. If two orientations on opposite sides of the fixation are both task relevant and enter working memory, then they should interact with each other. We indeed found the predicted cross-fixation interactions (repulsion and correlation) between orientations. Control experiments and analyses ruled out alternative explanations such as reporting bias and adaptation across trials on the same side of the fixation. Moreover, we explained the data using a retrospective high-to-low-level Bayesian decoding framework.

Bayesian Algorithmic Decoding of Acceleration and Speed Software (BADASS)

<h2>Abstract</h2> An important question in neuroscience is how the brain encodes the environment and the self, and how accurate these codes are. Bayesian decoding techniques have been used to determine the position of an animal based on neuron spike rate in the brain's hippocampus. In this software package, Bayesian Algorithmic Decoding of Acceleration and Speed Software (BADASS), we expand on existing decoding algorithms to decode speed and acceleration using cell spiking. BADASS can be used to determine the extent of speed and acceleration coding in different brain regions during movement, as well as during periods of memory consolidation and planning.

Modelling the neural code in large populations of correlated neurons.

Neurons respond selectively to stimuli, and thereby define a code that associates stimuli with population response patterns. Certain correlations within population responses (noise correlations) significantly impact the information content of the code, especially in large populations. Understanding the neural code thus necessitates response models that quantify the coding properties of modelled populations, while fitting large-scale neural recordings and capturing noise correlations. In this paper, we propose a class of response model based on mixture models and exponential families. We show how to fit our models with expectation-maximization, and that they capture diverse variability and covariability in recordings of macaque primary visual cortex. We also show how they facilitate accurate Bayesian decoding, provide a closed-form expression for the Fisher information, and are compatible with theories of probabilistic population coding. Our framework could allow researchers to quantitatively validate the predictions of neural coding theories against both large-scale neural recordings and cognitive performance.

Time coding in rat dorsolateral striatum

To assess the role of dorsolateral striatum (DLS) in time coding, we recorded neuronal activity in rats tasked with comparing the durations of two sequential vibrations. Bayesian decoding of population activity revealed a representation of the unfolding of the trial across time. However, further analyses demonstrated a distinction between the encoding of trial time and perceived time. First, DLS did not show a privileged representation of the stimulus durations compared with other time spans. Second, higher intensity vibrations were perceived as longer; however, time decoded from DLS was unaffected by vibration intensity. Third, DLS did not encode stimulus duration differently on correct versus incorrect trials. Finally, in rats trained to compare the intensities of two sequential vibrations, stimulus duration was encoded even though it was a perceptually irrelevant feature. These findings lead us to posit that temporal information is inherent to DLS activity irrespective of the rat's ongoing percept.

Pheniqs 2.0: accurate, high-performance Bayesian decoding and confidence estimation for combinatorial barcode indexing

BackgroundSystems biology increasingly relies on deep sequencing with combinatorial index tags to associate biological sequences with their sample, cell, or molecule of origin. Accurate data interpretation depends on the ability to classify sequences based on correct decoding of these combinatorial barcodes. The probability of correct decoding is influenced by both sequence quality and the number and arrangement of barcodes. The rising complexity of experimental designs calls for a probability model that accounts for both sequencing errors and random noise, generalizes to multiple combinatorial tags, and can handle any barcoding scheme. The needs for reproducibility and community benchmark standards demand a peer-reviewed tool that preserves decoding quality scores and provides tunable control over classification confidence that balances precision and recall. Moreover, continuous improvements in sequencing throughput require a fast, parallelized and scalable implementation.Results and discussionWe developed a flexible, robustly engineered software that performs probabilistic decoding and supports arbitrarily complex barcoding designs. Pheniqs computes the full posterior decoding error probability of observed barcodes by consulting basecalling quality scores and prior distributions, and reports sequences and confidence scores in Sequence Alignment/Map (SAM) fields. The product of posteriors for multiple independent barcodes provides an overall confidence score for each read. Pheniqs achieves greater accuracy than minimum edit distance or simple maximum likelihood estimation, and it scales linearly with core count to enable the classification of > 11 billion reads in 1 h 15 m using < 50 megabytes of memory. Pheniqs has been in production use for seven years in our genomics core facility.ConclusionWe introduce a computationally efficient software that implements both probabilistic and minimum distance decoders and show that decoding barcodes using posterior probabilities is more accurate than available methods. Pheniqs allows fine-tuning of decoding sensitivity using intuitive confidence thresholds and is extensible with alternative decoders and new error models. Any arbitrary arrangement of barcodes is easily configured, enabling computation of combinatorial confidence scores for any barcoding strategy. An optimized multithreaded implementation assures that Pheniqs is faster and scales better with complex barcode sets than existing tools. Support for POSIX streams and multiple sequencing formats enables easy integration with automated analysis pipelines.

Investigating the representation of uncertainty in neuronal circuits.

Skilled behavior often displays signatures of Bayesian inference. In order for the brain to implement the required computations, neuronal activity must carry accurate information about the uncertainty of sensory inputs. Two major approaches have been proposed to study neuronal representations of uncertainty. The first one, the Bayesian decoding approach, aims primarily at decoding the posterior probability distribution of the stimulus from population activity using Bayes’ rule, and indirectly yields uncertainty estimates as a by-product. The second one, which we call the correlational approach, searches for specific features of neuronal activity (such as tuning-curve width and maximum firing-rate) which correlate with uncertainty. To compare these two approaches, we derived a new normative model of sound source localization by Interaural Time Difference (ITD), that reproduces a wealth of behavioral and neural observations. We found that several features of neuronal activity correlated with uncertainty on average, but none provided an accurate estimate of uncertainty on a trial-by-trial basis, indicating that the correlational approach may not reliably identify which aspects of neuronal responses represent uncertainty. In contrast, the Bayesian decoding approach reveals that the activity pattern of the entire population was required to reconstruct the trial-to-trial posterior distribution with Bayes’ rule. These results suggest that uncertainty is unlikely to be represented in a single feature of neuronal activity, and highlight the importance of using a Bayesian decoding approach when exploring the neural basis of uncertainty.

Perceptual Behavior Depends Differently on Pupil-Linked Arousal and Heartbeat Dynamics-Linked Arousal in Rats Performing Tactile Discrimination Tasks

Several physiology signals, including heart rate and pupil size, have been widely used as peripheral indices of arousal to evaluate the effects of arousal on brain functions. However, whether behavior depends differently on arousal indexed by these physiological signals remains unclear. We simultaneously recorded electrocardiogram (ECG) and pupil size in head-fixed rats performing tactile discrimination tasks. We found both heartbeat dynamics and pupil size co-varied with behavioral outcomes, indicating behavior was dependent upon arousal indexed by the two physiological signals. To estimate the potential difference between the effects of pupil-linked arousal and heart rate-linked arousal on behavior, we constructed a Bayesian decoder to predict animals' behavior from pupil size and heart rate prior to stimulus presentation. The performance of the decoder was significantly better when using both heart rate and pupil size as inputs than when using either of them alone, suggesting the effects of the two arousal systems on behavior are not completely redundant. Supporting this notion, we found that, on a substantial portion of trials correctly predicted by the heart rate-based decoder, the pupil size-based decoder failed to correctly predict animals' behavior. Taken together, these results suggest that pupil-linked and heart rate-linked arousal systems exert different influences on animals' behavior.

Statistical Analysis of Decoding Performances of Diverse Populations of Neurons.

A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. Here we consider this question with data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli; we use a generalized linear model (GLM) to assess the accuracy of (Bayesian) decoding of stimulus given a population spiking response. The long recordings enable us to consider many uncoupled networks and a relatively wide range of heterogeneity, as well as many instances of the stimuli, thus enabling us to address this question with statistical power. The GLM decoding is performed on a single long time series of data to mimic realistic conditions rather than using trial-averaged data for better model fits. For a variety of fixed network sizes, we generally find that the optimal levels of heterogeneity are at intermediate values, and this holds in all core components of GLM. These results are robust to several measures of decoding performance, including the absolute value of the error, error weighted by the uncertainty of the estimated stimulus, and the correlation between the actual and estimated stimulus. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low values. Taken together, intermediate levels of neural heterogeneity are indeed a prominent attribute for efficient coding even within a single time series, but the performance is highly variable.

A Bayesian and efficient observer model explains concurrent attractive and repulsive history biases in visual perception.

Human perceptual decisions can be repelled away from (repulsive adaptation) or attracted towards recent visual experience (attractive serial dependence). It is currently unclear whether and how these repulsive and attractive biases interact during visual processing and what computational principles underlie these history dependencies. Here we disentangle repulsive and attractive biases by exploring their respective timescales. We find that perceptual decisions are concurrently attracted towards the short-term perceptual history and repelled from stimuli experienced up to minutes into the past. The temporal pattern of short-term attraction and long-term repulsion cannot be captured by an ideal Bayesian observer model alone. Instead, it is well captured by an ideal observer model with efficient encoding and Bayesian decoding of visual information in a slowly changing environment. Concurrent attractive and repulsive history biases in perceptual decisions may thus be the consequence of the need for visual processing to simultaneously satisfy constraints of efficiency and stability.

A Probabilistic Framework for Decoding Behavior From in vivo Calcium Imaging Data.

Understanding the role of neuronal activity in cognition and behavior is a key question in neuroscience. Previously, in vivo studies have typically inferred behavior from electrophysiological data using probabilistic approaches including Bayesian decoding. While providing useful information on the role of neuronal subcircuits, electrophysiological approaches are often limited in the maximum number of recorded neurons as well as their ability to reliably identify neurons over time. This can be particularly problematic when trying to decode behaviors that rely on large neuronal assemblies or rely on temporal mechanisms, such as a learning task over the course of several days. Calcium imaging of genetically encoded calcium indicators has overcome these two issues. Unfortunately, because calcium transients only indirectly reflect spiking activity and calcium imaging is often performed at lower sampling frequencies, this approach suffers from uncertainty in exact spike timing and thus activity frequency, making rate-based decoding approaches used in electrophysiological recordings difficult to apply to calcium imaging data. Here we describe a probabilistic framework that can be used to robustly infer behavior from calcium imaging recordings and relies on a simplified implementation of a naive Baysian classifier. Our method discriminates between periods of activity and periods of inactivity to compute probability density functions (likelihood and posterior), significance and confidence interval, as well as mutual information. We next devise a simple method to decode behavior using these probability density functions and propose metrics to quantify decoding accuracy. Finally, we show that neuronal activity can be predicted from behavior, and that the accuracy of such reconstructions can guide the understanding of relationships that may exist between behavioral states and neuronal activity.