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Improved estimation and interpretation of correlations in neural circuits.

Yatsenko D, Josić K, Ecker AS, Froudarakis E, Cotton RJ, Tolias AS - PLoS Comput. Biol. (2015)

Bottom Line: Estimation can be improved by regularization, i.e. by imposing a structure on the estimate.These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive 'excitatory' interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative 'inhibitory' interactions were less selective.Because of its superior performance, this 'sparse+latent' estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.

View Article: PubMed Central - PubMed

Affiliation: Department of Neuroscience, Baylor College of Medicine, Houston, Texas, United States of America.

ABSTRACT
Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150-350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive 'excitatory' interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative 'inhibitory' interactions were less selective. Because of its superior performance, this 'sparse+latent' estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.

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Properties of Csparse+latent estimates from all imaged sites.Each point represents an imaged site with its color indicating the population size as shown in panels A and B. The example site from Figs. 3 and 5 is circled in blue.A. The number of inferred latent units vs. population size. B. The connectivity of the sparse component of partial correlations as a function of population size. C. The average sample correlations vs. the average partial correlations (Eq. 4) of the Csparse+latent estimate. D. The percentage of negative interactions vs. connectivity in the Csparse+latent estimates.
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pcbi.1004083.g006: Properties of Csparse+latent estimates from all imaged sites.Each point represents an imaged site with its color indicating the population size as shown in panels A and B. The example site from Figs. 3 and 5 is circled in blue.A. The number of inferred latent units vs. population size. B. The connectivity of the sparse component of partial correlations as a function of population size. C. The average sample correlations vs. the average partial correlations (Eq. 4) of the Csparse+latent estimate. D. The percentage of negative interactions vs. connectivity in the Csparse+latent estimates.

Mentions: We examined the composition of the Csparse+latent estimates for each imaged site (Fig. 5 and Fig. 6). Although the regularized estimates were similar to the sample correlation matrix (Fig. 5 A and B), the corresponding partial correlation matrices differed substantially (Fig. 5 C and D). The estimates separated two sources of correlations: a network of linear interactions expressed by the sparse component of the inverse and latent units expressed by the low-rank components of the inverse (Fig. 5 E). The sparse partial correlations revealed a network that differed substantially from the network composed of the greatest coefficients in the sample correlation matrix (Fig. 5 F, G, H, and I).


Improved estimation and interpretation of correlations in neural circuits.

Yatsenko D, Josić K, Ecker AS, Froudarakis E, Cotton RJ, Tolias AS - PLoS Comput. Biol. (2015)

Properties of Csparse+latent estimates from all imaged sites.Each point represents an imaged site with its color indicating the population size as shown in panels A and B. The example site from Figs. 3 and 5 is circled in blue.A. The number of inferred latent units vs. population size. B. The connectivity of the sparse component of partial correlations as a function of population size. C. The average sample correlations vs. the average partial correlations (Eq. 4) of the Csparse+latent estimate. D. The percentage of negative interactions vs. connectivity in the Csparse+latent estimates.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4380429&req=5

pcbi.1004083.g006: Properties of Csparse+latent estimates from all imaged sites.Each point represents an imaged site with its color indicating the population size as shown in panels A and B. The example site from Figs. 3 and 5 is circled in blue.A. The number of inferred latent units vs. population size. B. The connectivity of the sparse component of partial correlations as a function of population size. C. The average sample correlations vs. the average partial correlations (Eq. 4) of the Csparse+latent estimate. D. The percentage of negative interactions vs. connectivity in the Csparse+latent estimates.
Mentions: We examined the composition of the Csparse+latent estimates for each imaged site (Fig. 5 and Fig. 6). Although the regularized estimates were similar to the sample correlation matrix (Fig. 5 A and B), the corresponding partial correlation matrices differed substantially (Fig. 5 C and D). The estimates separated two sources of correlations: a network of linear interactions expressed by the sparse component of the inverse and latent units expressed by the low-rank components of the inverse (Fig. 5 E). The sparse partial correlations revealed a network that differed substantially from the network composed of the greatest coefficients in the sample correlation matrix (Fig. 5 F, G, H, and I).

Bottom Line: Estimation can be improved by regularization, i.e. by imposing a structure on the estimate.These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive 'excitatory' interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative 'inhibitory' interactions were less selective.Because of its superior performance, this 'sparse+latent' estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.

View Article: PubMed Central - PubMed

Affiliation: Department of Neuroscience, Baylor College of Medicine, Houston, Texas, United States of America.

ABSTRACT
Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150-350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive 'excitatory' interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative 'inhibitory' interactions were less selective. Because of its superior performance, this 'sparse+latent' estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.

Show MeSH
Related in: MedlinePlus