h05-4 - T . 1. (50 points) You are now set to learn this...

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CIS6930/4930 Intro to Computational Neuroscience Spring 2005 Home Work Assignment 4: Due Tuesday 04/19/05 before class This project is about constructing a Linear Time-Invariant system and another with a static non-lineartity and seeing how well you can learn these systems thru a simple gradient descent rule, given just the input and the output signal. Begin by constructing an input signal x ( t ) that is a gaussian white noise signal. You may want to check on the web as to how to construct such a signal. Now consider the kernel h ( t ) = A * e - t/γ . Choose values for A and γ . Produce the output y ( t ) = R T 0 x ( t - τ ) h ( τ ) for a large enough value of
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Unformatted text preview: T . 1. (50 points) You are now set to learn this kernel. Hand the input and the output signal to a new program that attempts to learn the kernel h ( t ) via a simple gradient descent rule. Quantify how well your program learns the kernel by plotting the square-error on the output signal as time progresses. 2. (50 points) Now assume that the output signal passes thru the static nonlinearity y ( t ) = ( y ( t )) 3 . Ask your program to learn a kernel for this pair of input and output, i.e., x ( t ) and y ( t ) . Quantify how well your system performs on this case. 1...
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