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. Author manuscript; available in PMC: 2021 Mar 5.
Published in final edited form as: Curr Opin Neurobiol. 2020 Nov 1;65:59–69. doi: 10.1016/j.conb.2020.09.009

Figure 3.

Figure 3

Interpretational challenges and considerations of multivariate methods. (a) Recorded areas A and B (shaded gray) are just two areas of a larger network made up of areas A–F. Thus the identified statistical associations between these areas reflect both direct and indirect interactions. Interactions may be asymmetric, and occur over connections with different latencies (τ1, τ2). (b) A change in the variance (var) of input from area F to area B can change the strength of the correlation (corr) between areas A and B. In this case, one can be led to believe that the interaction between areas A and B changed, even though the only change was in the input from area F to area B. (c) The regression weight for each source neuron can depend on which other source neurons are included in the regression. Leaving out neurons in the regression can dramatically change the regression weights of remaining neurons. (d) (Left) One may identify a dimension in population activity space that encodes a variable of interest (z1), for example, the stimulus or a behavioral variable (grayscale shading of dots). Then, in an effort to find a variable unrelated to the activity projected onto z1, one could identify projections of activity onto an orthogonal dimension (z2) or projections onto an uncorrelated dimension (z3). This uncorrelated dimension is not, in general, orthogonal to z1, and depends on the covariance of the population activity. (Upper right) Changing to the orthogonal basis, where the axes represent z1 and z2, reveals that these dimensions are correlated. Bottom inset shows one-dimensional projections onto z1, which was identified so that the dot coloring would be ordered. Right inset shows one-dimensional projections of population activity onto z2, which show some ordering based on dot color. (Lower right) Changing to the uncorrelated basis, where the axes represent z1 and z3, illustrates that these variables are uncorrelated. Right inset shows one-dimensional projections of population activity onto z3, which show little to no ordering based on dot color.