computational neuroscience

Machine Learning Advent Calendar 2012 The seventh day is the field of computational neuroscience, among the neuroscience, which is commonly referred to as brain science. In academic introductory books, I first learn the neural cell mechanism of the brain and a mathematical model of many neurons, but leave them to a good book of reference literature, what is computational theory neuroscience I would like to write about it.

What is computational neuroscience
There is a thing to understand the mechanism of the brain as a goal of neuroscience, but how to say that you truly understood the brain is a difficult problem. In this computational neuroscience, let us infer the mechanism of the brain by reasoning theoretically and top-down using a mathematical model and contrasting it with the bottom-up knowledge such as actual brain structure and experimental results It is a field to be.

Relationship between computational neuroscience and machine learning
The origins of machine learning and computational neuroscience are very similar, while machine learning is based on perceptron devised by Frank Rosenblat in 1957 as the origin of machine learning, whereas in the late 1960s to early 1970s Contemporary computational neuroscience has been established by the achievements such as hypotheses that considered the cerebellum proposed by David Ma et al as perceptron.

However, recent years ‘neuroscience’ seems to have a large deviation from machine learning. For example, a paper [Kawmitani +, 2005] that classifies easily what was considered from the results output by fMRI (brain activity measuring instrument) using SVM was announced in 2005, and it is big in the field of neuroscience He seems to have responded well. From a machine learning which should be a close field, I feel a little late.

I do not know how much researchers in computational neuroscience recognize machine learning, but I am a book written by Mr. Katsuyuki Sakai who is a cognitive neuroscientist [Brain science of the mind (Chuo Shinsha)] [ When reading the article [brain and mind (Newton separate volume)] of Mr. Yukiyasu Kamiya belonging to the same ATR brain information laboratory as Mr. Mitsuo Kawatami who is the author of this paper, the truth of brain science (Kawakide Books) It shows how to use learning was a breakthrough in neuroscience at the time of 2005.

Today, such research has progressed until foggy indications of what fMRI is seeing. However, even if I look at this paper etc, I do not think much about both studies being recognized between machine learning and neuroscience. [Shinji +, 2011] [Yoichi +, 2008]

However, researchers in machine learning can not be said to have a good understanding of neuroscience. Except for some researchers, we can hardly see examples applied to machine learning by a model considered by a computational theologist. So, taking the approach of the same mathematical model as machine learning, learning computerized neuroscience which is an independent field with many similarities thought that many researchers of machine learning can obtain many discoveries I will.

What is a neuron?
I will explain roughly about neurons.
The brain is made up of neurons called neurons. To model the brain, you must first know neurons neurobiologically. This nerve cell is one cell consisting of cell body, dendrite, axon, synapse, etc.
Diagram of neurons

Image cited from “Neuron’s Mathematical Model and Electronic Circuit Implementation”
The electrical signal input to the neuron accumulates, and when it exceeds the threshold value, electric nerve spike is output (ignited state). Then it sends its spike through the ion channel to the next neuron. The details of the electric signal of the nerve including the neuron are only explained roughly in the introductory book of the neuroscience, so it is recommended to read the specialized book for more detailed mechanism. [Bioelectrical signals are something (Blue Bucks)]

In experiments etc., we investigate the mechanism of biological spike by piercing the neuron with an electrode, giving artificial stimulation current, artificially generating a spike, etc.

McCulloch-Pitts model
Here we introduce the McCulloch-Pitts model as a major one of computational neuroscience models. This model is famous as a typical example of perceptron, and it is easy to understand how electric signals are modeled for people accustomed to machine learning models.

As described in the previous section, when the neuron is stabbed with an electrode and the stimulation current is raised, its potential rises, and spike occurs when it exceeds a certain threshold value. Since the potential difference of this spike is nearly constant, it is modeled as a logic element taking an output of 0 or 1. It is the McCulloch-Pitts model that theorized this, with input as a threshold
Other sigmoid functions are also used.

If the time of occurrence of individual spikes is important for information processing in the brain, we need a model that treats nerve activity continuously at the spike time series level. The model based on this way of thinking is handled in continuous time. However, this perceptron is discrete time, and interpretation similar to a neuron treats firing as a macro amount like the average firing frequency (the number of spike firings per second).

As I said at the beginning, initially such pre-existing famous models are also listed in the primer, but since most models are continuous time, it is this model that I can recognize in the form of expressions in computational theory of neuroscience I think that it is.

the end
Introduction of computational neuroscience and relation to machine learning, one famous model actually introduced. Computational brain science Although it seemed interesting, it would be too wide and ended with a survey, but it seems to be like it, but if you are interested just a little bit, you can have a good quality introductory book I will write it.