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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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While variables are sometimes correlated because one does cause the other, it could also be that some other factor, a confounding variable, is actually causing the systematic movement in our variables of interest. For instance, as sales in ice cream increase, so does the overall rate of crime. Is it possible that indulging in your favorite flavor of ice cream could send you on a crime spree? Or, after committing crime do you think you might decide to treat yourself to a cone?
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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
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In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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Information-limiting correlations.

Rubén Moreno-Bote1, Jeffrey Beck2, Ingmar Kanitscheider3

  • 11] Research Unit, Parc Sanitari Sant Joan de Déu and Universitat de Barcelona, Esplugues de Llobregat, Barcelona, Spain. [2] Centro de Investigación Biomédica en Red de Salud Mental (CIBERSAM), Esplugues de Llobregat, Barcelona, Spain.

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Summary
This summary is machine-generated.

Brain computations rely on population activity, influenced by noise correlations. Contrary to popular belief, reducing these correlations does not necessarily boost information storage; only differential correlations limit information. Detecting these subtle correlations is key.

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Information Theory

Background:

  • Brain computations depend on population activity and noise correlations.
  • Positive noise correlations, common in vivo, are often linked to tuning similarity and thought to limit information.
  • Previous research suggested decorrelation as a strategy to increase information storage.

Purpose of the Study:

  • To investigate the relationship between noise correlations and information storage in neural population activity.
  • To determine if decorrelation universally increases information.
  • To identify the specific types of correlations that limit information.

Main Methods:

  • Analytical calculations.
  • Numerical simulations.
  • Analysis using simple decoders to detect specific correlation patterns.

Main Results:

  • Decorrelation does not inherently lead to an increase in information.
  • Identified 'differential correlations' (proportional to the product of tuning curve derivatives) as the sole information-limiting correlations.
  • Demonstrated that the impact of differential correlations can be detected even when they are small and masked by other correlations.

Conclusions:

  • The impact of noise correlations on information storage is more nuanced than previously assumed.
  • Differential correlations, though difficult to detect, are the critical factor limiting information in neural populations.
  • Simple decoding methods can reveal the presence and effect of these crucial differential correlations.