Contribution of correlated noise and selective decoding to choice probability measurements in extrastriate visual cortex

Abstract

Trial by trial covariations between neural activity and perceptual decisions (quantified by choice Probability, CP) have been used to probe the contribution of sensory neurons to perceptual decisions. CPs are thought to be determined by both selective decoding of neural activity and by the structure of correlated noise among neurons, but the respective roles of these factors in creating CPs have been controversial. We used biologically-constrained simulations to explore this issue, taking advantage of a peculiar pattern of CPs exhibited by multisensory neurons in area MSTd that represent self-motion. Although models that relied on correlated noise or selective decoding could both account for the peculiar pattern of CPs, predictions of the selective decoding model were substantially more consistent with various features of the neural and behavioral data. While correlated noise is essential to observe CPs, our findings suggest that selective decoding of neuronal signals also plays important roles.

Keywords: computational; decision; macaque; neural coding; neuroscience.

Figure 1.. Comparison of models in which choice probabilities (CPs) arise through either correlated noise or selective decoding.

Each model consists of two pools of neurons (500 neurons each) with equal numbers of neurons that prefer leftward and rightward headings. In the 'pure-correlation' model (A and B), neurons in pool 2 make no contribution to the decision and activity within or across pools is correlated according to the relationship illustrated in panel B. In the 'selective decoding' model (C and D), neurons shared correlated noise within each pool but not across pools. Neurons in pool 1 were always given a decoding weight of 1, while neurons in pool 2 were given weights ranging from 0 to 1. Solid curves in D: responses of pool 2 were decoded according to each neuron's preferred stimulus; dashed curves: pool 2 responses were decoded relative to each neuron's anti-preferred stimulus. Dashed black horizontal line: CP = 0.5. DOI: http://dx.doi.org/10.7554/eLife.02670.003

Figure 2.. Responses of multisensory neurons and multisensory versions of the pure-correlation and selective-decoding models.

(A) Heading tuning curves from two example MSTd neurons measured during a fine heading discrimination task (Gu et al., 2008): one congruent cell (left) and one opposite cell (right). Red and blue data show responses measured for the visual and vestibular conditions, respectively. (B) Choice probability as a function of congruency for MSTd neurons tested in the vestibular (left) and visual (right) conditions (adapted, with permission, from Supplement Figure 8A and Figure 6C of Gu et al.(2008); respectively). Cyan and magenta symbols denote data for congruent and opposite cells, respectively (unfilled symbols: intermediate cells). (C and D) Multisensory version of the pure-correlation model (500 model neurons in each pool). Pool 1 consists of all congruent cells (same slope tuning curves for the two cues), whereas pool 2 contains all opposite neurons. Correlated noise within or across pools depends only on the similarity of tuning for cue 1. (E and F) In the selective decoding model, neurons were correlated according to the similarity of tuning for both cues (‘Materials and methods’). This rule generated correlated noise within each pool but not between pools. Neurons in pool 1 were always given a full weight of 1 in the decoding, whereas the decoding weights of neurons in pool 2 ranged from 0 to 1 (different colors in F). Dashed black horizontal line: CP = 0.5. DOI: http://dx.doi.org/10.7554/eLife.02670.004

Figure 2—figure supplement 1.. Predictions from a variant of the pure-correlation model in which correlated noise depends only on signal correlations from the visual tuning curves.

This modification reverses the patterns of CPs across stimulus conditions, as compared to Figure 2C,D. This pattern of results is not consistent with experimental data. DOI: http://dx.doi.org/10.7554/eLife.02670.005

Figure 2—figure supplement 2.. Predictions from a variant of the selective decoding model in which responses are decoded according to the visual heading tuning of each neuron, instead of the vestibular tuning.

This modification reverses the CP patterns across stimulus conditions, as compared to Figure 2E,F, and is inconsistent with experimental data. DOI: http://dx.doi.org/10.7554/eLife.02670.006

Figure 2—figure supplement 3.. Predictions from a “hybrid” model (see text for details) in which correlated noise was assigned according to vestibular signal correlations, and heading was decoded relative to the vestibular heading tuning of each neuron.

CP patterns were roughly similar to those seen in the pure-correlation model (Figure 2C,D). DOI: http://dx.doi.org/10.7554/eLife.02670.007

Figure 3.. Comparison of the structure of correlated noise between models and data.

(A) Data from pairs of neurons recorded from area MSTd (Gu et al., 2011). Noise correlation is plotted against signal correlations obtained from the vestibular (left column) or visual (right column) tuning curves. Black and gray symbols denote pairs with matched (black) or mismatched (gray) congruency. Open symbols represent undefined pairs. (B) Predicted noise correlations as a function of signal correlation based on fits of the selective decoding model. Format as in panel A. (C) Predicted noise correlations as a function of signal correlation by for the pure-correlation model fit, for which noise correlations depend only on vestibular signal correlation. DOI: http://dx.doi.org/10.7554/eLife.02670.008

Figure 3—figure supplement 1.. Comparison of vestibular and visual signal correlations for 127 pairs of neurons simultaneously recorded from area MSTd by Gu et al. (2011).

There is a fairly weak correlation between the two variables (R = 0.29, p=0.001, Spearman correlation). Histograms along the top and right side show marginal distributions of the two signal correlations. DOI: http://dx.doi.org/10.7554/eLife.02670.009

Figure 3—figure supplement 2.. Noise correlation structure of the pure correlation model computed from the signal correlations of all distinct pairings of 129 neurons that were recorded previously by Gu et al. (2011).

For the pure-correlation model, correlated noise is determined by the signal correlation in the vestibular condition, such that pairs of cells with matched (black) and mismatched (gray) congruency have opposite relationships between r_noise and r_signal in the visual condition. DOI: http://dx.doi.org/10.7554/eLife.02670.010

Figure 3—figure supplement 3.. Noise correlation structure of the selective decoding model computed from the signal correlations of all distinct pairings of 129 neurons that were recorded previously by Gu et al. (2011).

For the selective decoding model, correlated noise depends on r_signal in both stimulus conditions. As a result, the relationship between r_noise and r_signal is strong for pairs with matched congruency in both stimulus conditions (black), and this relationship is weak for pairs with mismatched congruency (gray). DOI: http://dx.doi.org/10.7554/eLife.02670.011

Figure 4.. Predictions of choice probabilities from the two models.

(A) The pattern of CPs predicted by the pure-correlation model. Format as in Figure 2B. (B) A family of weighting profiles used to consider various degrees of contribution of opposite cells to the selective decoding model. Each curve shows the decoding weight as a function of congruency between visual and vestibular heading tuning. Each curve corresponds to a specific value of the Readout Index (RI). (C) Predicted average CPs from the selective decoding model for a subset of the RI values illustrated in (B). (D) The pattern of CPs across neurons in the selective decoding model for an RI value of 0.5. Cyan symbols: congruent cells; Magenta symbols: opposite cells; Unfilled symbols: intermediate cells. Solid squares: mean CP. Dashed horizontal line: CP = 0.5. DOI: http://dx.doi.org/10.7554/eLife.02670.012

Figure 5.. Analysis of choice probabilities for the combined condition in which both visual and vestibular heading cues are present.

(A) CP values plotted as a function of congruency index for neurons from area MSTd tested in the Combined condition (adapted, with permission, from Figure 6A of Gu et al., 2008). (B and C) CP as a function of congruency for model neurons from the pure-correlation model, and model cells from the selective decoding model, respectively. (D) Distributions of CPs for opposite cells from area MSTd, the pure-correlation model and the selective decoding model. (E–G) CP values plotted as a function of neuronal discrimination thresholds for real MSTd neurons (adapted, with permission, from Figure 6B of Gu et al., 2008), units from the pure-correlation model and units from the selective decoding model, respectively. (H) Correlation coefficient of the best linear fit to the relationship between CP and neuronal threshold for MSTd data (filled black circles), pure-correlation model (open black circles) and selective decoding model (open red circles). Error bars represent 95% confidence intervals. DOI: http://dx.doi.org/10.7554/eLife.02670.013

Figure 5—figure supplement 1.. Bimodality of CP for opposite cells in the cue combined condition.

Top panels: four examples of simulations of the pure-correlation model having different values of a_vestibular ranging from 0.01 to 0.12. Both the magnitude and bimodality of the CP distribution increases with a_vestibular. To quantify bimodality, we chose cells with Congruency Index in the range [−1–0.5], and applied K-means clustering to generate two clusters. The vertical distance, d, between the centroids of the two clusters was taken as an index of the separation of the two clusters. Bottom row: (left) Summary of d values as a function of a_vestibular. Asterisks represent significant bimodality, as assessed by a modality test (‘Materials and methods’). (right) Relationship between the CP of congruent cells (congruency index from 0.5 to 1) and a_vestibular. DOI: http://dx.doi.org/10.7554/eLife.02670.014

Figure 5—figure supplement 2.. Same format as in Figure 5—figure supplement 1, but results are shown for the selective decoding model.

Top row: simulations for four different values of the Readout Index (RI). Bottom row: A bimodal distribution of CP is only seen for RI values >= 0.8, and CP of congruent cells is independent of RI. DOI: http://dx.doi.org/10.7554/eLife.02670.015

Figure 6.. Comparisons between model population threshold and psychophysical performance of the animals.

(A) Average thresholds are shown for the vestibular, visual, and combined conditions, along with the prediction from optimal cue integration theory. Data are shown for the average of two monkeys (filled symbols, dashed curve), for predictions of the pure-correlation model (black open symbols and solid curve), and for predictions of the selective decoding model with RI = 0.5 (red symbols and curve). (B) Predicted thresholds from the selective decoding model are plotted as a function of Readout Index for vestibular, visual, and combined conditions, as well as the optimal prediction from the single-cue thresholds. (C) Thresholds from the selective-decoding model (with RI = 0.5) as a function of population size. Solid curves: model predictions; dashed horizontal lines: average performance of two animals. DOI: http://dx.doi.org/10.7554/eLife.02670.016

Figure 6—figure supplement 1.. Comparison of neuronal sensitivity between the visual (ordinate) and vestibular (abscissa) stimulus conditions for 30 congruent cells.

Arrows and numbers indicate geometric mean values. Overall, visual responses were somewhat more sensitive than vestibular responses, although the animals’ behavioral performance was similar between conditions. DOI: http://dx.doi.org/10.7554/eLife.02670.017