Review of mathematical neuroscience topics for the UMN Neurosci prelim
ROC_GUI_2.py can be run offline to create an interactive GUI.
The ROC curve assumes a few things:
- You have two distributions. In health sciences, this might be sick vs. healthy. In Neuroscience, this could be a 400Hz frequency vs. a 450Hz frequency.
- You have a classifier that discriminates based on a 1-dimensional factor. This limitation is somewhat arbitrary as you can use a data-reduction method to get one dimension, such as a principal component (PCA).
The curve itself is a two dimensional summary of how well your classifier can discriminate between those two different distributions, as a function of the discrimination line. Its output is the true positive rate vs the false positive rate.
The ROC's usefulness is in this discrimination line and how you might want to alter it according to different circumstances:
- For COVID-19 screening, you might be okay with a high FPR, because you absolutely don't want to miss any sick patients. In other words, you can increase the TPR at the cost of also increasing the FPR.
- For bio-identification, you might be okay with a low TPR, such as having to scan your phone fingerprint a few times. This is because you absolutely don't want anyone else able to get on your phone. In other words, you can decrease the FPR at the cost of decreasing the TPR.
The ROC curve is the standard metric in part because in machine-learning classification tasks, you can skew the TPR/FPR to make your research look better (harder when showing ROC). In addition, it's much like looking at a scatterplot instead of a bargraph. Scientists don't like the data summarized too much.
A common practice is to report the 0.8 TPR and corresponding FPR.
Things we can learn (from Oxenham):
- results from experiments of overlapping distributions implies there is no "threshold" for detection in auditory system
- "sensitivity" is always the same. It is a function of the standard deviations and means of the distributions
Why do we need this metric in Neuroscience?
We cannot compare two spike trains directly, because we are looking at different neurons and possible different regions of the brain. But by sliding the spike trains across each other, we can determine if there is a relationship even if they are not firing at the same time.
How is the metric computed?
- Take a reference spike train and a target spike train
- slide the target across the reference, comparing only where the reference has neuron activity spikes. This creates a histogram instead of a continuous plot (also possible just not what we want.)
- Take the sum at each point and graph it. Possibly normalize.
- Y axis : coincidences / spikes / normalized counts
- X axis : sampling point of sliding
The graphs on the left shows two spike trains that are highly correlated, as evidenced by the rise in coincidence near the center (but a rise anywhere would indicate correlation.)
The graphs on the right show spike trains that are not correlated, as evidenced by a relatively flat line throughout, showing only spurious, random correlations.
Controls:
The standard way to create a negative control is to compare your cross-correlation histogram with mismatched trials, known as the "shift predictor". This creates a histogram that shows spurious, non-random correlations inherent in the system you are measuring.
Synchrony is a pretty name for cross-correlation of cell assemblies. As a coding mechanism, is still an open question with many people not convinced. Cell assemblies dynamically form and dissolve, sometimes called the dynamicist view. Ensembles and assemblies are synonymous. Important theoretical points:
- synchronized imputs have greater impact on post-synaptic neurons (temporal summation). Single neurons are noisy but many together become cohesive.
- many subthreshold neuronal spikes, when synchronized, can drive action potentials.
- synchrony can be internally generated, not subject to sensory input. This differentiates it from contextual/anatomical models.
- cell assemblies can dynamically form and dissolve.
Binocular Rivalry (such as in the chimera problem) are thought to reflect competition between neural assemblies that encode the red and green stimuli.
