This note is just a collection of past useful notes to know to apply machine learning methods for the analysis of topics interesting in the neural sciences.
Estimators
You need to know all Parametric Modeling. We want to estimate unknown random variables with some observations.
Maximum Likelihood
See Bayesian Linear Regression.
Bias-Variance Decomposition
Fisher Information
See Parametric Modeling#Fisher information.
Applications
Echo-locating bats
Egyptian fruit flies bats use echo location to locate the target, emitting clicks and capturing echo to navigate the environment. Bats use to click slightly left and right compared to their direction of motion. It is interesting to observe and study how these bats are clicking around to move.
Bats Locking behaviour
Before looking the bat uses right and left click and also middle, probably to look for the target (you can have the emission intensity). After looking the distribution was very narrow, but not much about the target part (double distribution). If we look using fisher information, we see they are using a distribution with high information, it gets the most information for the environment (this is the second row in the image, which is very cool thing).
Tuning Curve Neural Decoding
The point is that the neuron is most informative when the signal is slightly off its most preferred position.
The fisher information reaches a minimum at the peak of the curve, that is where the neuron likes to fire. The neuron is more informative in regions where the tuning curve is steep. This is an argument against the tuning hypothesis, where the idea of neurons acting as feature detectors that fire when you expose them to preferred stimulus, or most stimulus-specific information about sound frequency when they fire at that frequency.