Beyond correlation analysis: Transfer entropy

Posted on March 19, 2014 by P.T.R. Rupprecht

When reading through the first informative web pages on transfer entropy, it turns out how closely its concept is related to mutual information, and even closer to incremental mutual information; and, although it’s based on a totally different approach, it tries to create a measure of time-shifted influences similar to Granger-causality. The main difference: the latter is based on simple linear fit prediction, whereas the former is based on information theory.

I haven’t found something in the net which explains transfer entropy in simple pictures for the layman – quite a shame, considering the attention transfer entropy has recently gained in neuroscience. So I will refer to a highly cited article by Thomas Schreiber, which is freely available in the arXiv (link). On the first two pages, almost everything which is needed is explained. I suppose, however, that Schreiber’s background is theoretical physics.

It’s instructive to compare mutual information with transfer entropy. Continue reading →

Posted in Data analysis, Network analysis | 1 Comment

Beyond correlation analysis: Granger causality

Posted on March 15, 2014 by P.T.R. Rupprecht

Granger causality has been named after the econometrician Clive Granger and has been adapted in the last 10-15 years as time-series analysis tool for neuroscience. The best account for this topic that I have found, is on scholarpedia again (link). The idea is quite simple: you have a timeseries (e.g. activity trace) X, and a timeseries Y. You want to know if the past of timeseries Y can, in addition to the past of timeseries X itself, help to predict the future of timeseries X. Prediction here is nothing but linear regression, somehow a mixture of auto- and cross-regression (copied from scholarpedia):

X_1(t) = \sum_{j=1}^p{A_{11,j}X_1(t-j)} + \sum_{j=1}^p{A_{12,j}X_2(t-j)+E_1(t)} X_2(t) = \sum_{j=1}^p{A_{21,j}X_1(t-j)} + \sum_{j=1}^p{A_{22,j}X_2(t-j)+E_2(t)}

Continue reading →

Posted in Uncategorized | 1 Comment

Some interesting 2-photon microscopy papers

Posted on March 13, 2014 by P.T.R. Rupprecht

In the last few months, I built a special kind of 2P-microsope. In the meantime, I encountered some papers on microscope techniques which I found interesting and worth a side-note.

  • Using AODs instead of galvoscanners for point-scanning: High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision. In contrast to resonant galvoscanners, you can still define arbitrary scanning paths. In a more recent paper which I don’t find right now, it is shown that by defining a scanning path for the AODs not by the path but only the endpoints of the path, you can go effectively as fast as you want. (This is not shown for population calcium imaging, but imaging of dendrites/spines.) The perspective of not being limited by scanning in principle is quite promising.
  • Using several beams for scanning several z-layers: Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing. The idea is quite simple, it’s based on the fact that the typical fluorophor lifetime (1-3 ns) is shorter than the time window between two laser pulses (typically 12.5 ns), so that pulses with different z-focus are delayed by some nanoseconds; the fluorescence can be gated.
  • Instead of using a moving objective, they used a moving mirror to do the z-scan: Aberration-free three-dimensional multiphoton imaging of neuronal activity at kHz rates. I liked very much the idea of putting the mirror on two two galvanometers instead of a fast piezo as I would have done it in the first place. Piezos at the objective holder as the standard method to change the z-focus are quite fast right now (settling time 2-4 ms at maximum), but they induce vibrations in the setup and are only that fast if they carry a light load and have a limited traveling range (ca. 100 µm).
  • Temporal Focusing is a method to provide z-sectioning in a widefield setup. This was the reason why I came to Vienna in 2013: Brain-wide 3D imaging of neuronal activity in Caenorhabditis elegans with sculpted light. I spent five months on improving this setup.
Posted in Uncategorized | Tagged , , , | Leave a comment

Beyond correlation analysis: incremental mutual information

Posted on March 12, 2014 by P.T.R. Rupprecht

Incremental Mutual Information: A New Method for Characterizing the Strength and Dynamics of Connections in Neuronal Circuits is a 2010 paper by A. Singh and N. Lesica in PLoS Computational Biology that describes a method which can be used as an alternative to correlation analysis for some cases.*

What is the promise of Incremental Mutual Information (IMI), compared to correlation analysis and correlation functions? First, similar to mutual information, which I have discussed before, it also considers non-linear dependencies of neuronal activities. Second, “it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e.g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales” (taken from the abstract). This sounds interesting, but we have to consider ‘appropriate timescales’ in more detail later.

Continue reading →

Posted in Uncategorized | Tagged , | Leave a comment

Beyond correlation analysis: mutual information

Posted on February 15, 2014 by P.T.R. Rupprecht

Last time, I mentioned a website which gives an overview of methods to analyze neuronal (and other) networks. Let’s have a closer look. Here’s a list of the methods:

  • Cross-correlation (the standard method)
  • Mutual Information
  • Incremental Mutual Information
  • Granger Causality
  • Transfer Entropy
  • Incremental Transfer Entropy
  • Generalized Transfer Entropy
  • Bayesian Inference
  • Anatomical Reconstruction

To be honest, I never heard of most of them. So let’s simply go into it and start with ‘Mutual Information’.

Continue reading →

Posted in Data analysis, Network analysis | 6 Comments

Beyond correlation analysis

Posted on February 8, 2014 by P.T.R. Rupprecht

There are many papers out that use calcium imaging of a lot (tens to thousands) of neurons in animal brains. When I first encountered these kind of publications (roughly a year ago), it took me some hours to become familiar with the mode of presentation, which was very often a correlation matrix.

Yesterday, I was testing my 2-photon widefield microscope on C. elegans with nuclear GCamp5-labeled neurons. So I had the opportunity to do this kind of analysis on my own. Note that 1) I don’t know very much about these neurons 2) I don’t care really much; I’m more interested in the ways of analyzing this kind of data. Continue reading →

Posted in Calcium Imaging, Data analysis, Neuronal activity | 2 Comments