Programming Language: MATLAB 3. This problem trains a simple artificial neural n

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Programming Language: MATLAB

3. This problem trains a simple artificial neural network (ANN) with a single neuron to divide the x-y plane into the classes of blue and yellow points shown below. These four points are saved in the file HW05data mat as the vectors x and y (although any four, or more!, points could be used) 0.8 0.6 0.4 0.B 0.5(x3) 0.6 0.4 0.2 0.2 0.5 0.5 Data with which to train the ANN Output of the trained ANN over the domain Output of the neural network is computed for any (r,y) point given the network parameters u, v, and b. It is desired that z be near zero in the vicinity of points 1 and 2 (blue) while producing near unity values for points 3 and 4 (yellow). Accuracy of the ANN is evaluated by the sum squared error 1+e which judges how close the ANN models the desired values for the four (x.y) pairs. Optimal values for network parameters u, v, and b are determined through gradient descent, which aims to update them depending on how

Explanation / Answer

These dendrites happen to be sensitive to a certain kind of chemicals (pardon my knowledge of biology). When there are a certain variety of chemical signals around these dendrites, they absorb them. When a certain amount of chemical is accumulated at the cell and it gets overwhelmed (let me call it crossing the threshold), it fires. It translates to generating an electrical pulse all the way down the tail – axon, into the synapse and these are picked up as a signal by the dendrites of the next cell. So essentially we have a system which looks as to how many chemicals I have around me and if it crosses my threshold I shoot. Boom! These are then picked up by the next cell.

The 2 interesting components we find:

I am not a biologist, so I seek an apology in advance if I may have trampled basic biology while attempting to be able to back my mathematical models.

2. Revisiting Logistic Regression

Logistic decision making will not seem unknown to the folks already from ML/AI field of study. Mathematician David Cox formulated the famous logit function, where the probability of occurrence or dichotomous categorical outcome was represented as a linear combination of a function.

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