[CSE423]
CSE423 Learning and Prediction, prac2, 2001
http:// ... /~lloyd/tilde/CSC4/CSC423/2001/prac2.html
We know that three
["obvious"]
ways of transmitting a sequence of values
sampled from a multi-state distribution
give nearly equal two-part message lengths.
The two methods that do not state an inference are shortest, and
the method that states an inferred estimate (to optimum precision)
takes a fraction of a bit more per parameter.
This exercise is make an experimental investigation
of the corresponding situation for the
[normal (Gaussian)]
distribution.
[DLD]
can give you a good normal, pseudo-random number generator.
- Write a C program
to compare two methods of transmitting a sequence of data values
sampled from a normal distribution:
- Method 1: The MML method as described at the link above.
- Method 2: An adaptive code, based on the following idea.
Transmit the first two values from the sequence using a code based
on a mean and variance from the prior.
Transmit the third and subsequent values using a code
based on a distribution N(m,s) where m and s
are calculated from the previously transmitted values,
as available to both transmitter and receiver.
- Your program must be able to do at least the following:
- carry out a (large) number of trials, tabulating the results
in some clear way,
- vary the length of the sequences,
- vary the generating parameters,
- vary the "measurement precision" of the data values.
- NB. Do not do actual coding/ decoding of the data -
just calculate what the message lengths would be.
- You should investigate some variations, e.g. the effect of using
different methods for calculating m and s for the adaptive code
such as the MML estimator v. the traditional estimator for variance.
- Systems: ISO C (not C++), Linux.
- Write a short, two to three page report
describing your investigations and results.
Append your program(s) to it.
- Due Deadline: decided in class:
Monday 23 April 2001; marks: 15%.
- Place: CSSE general office.
© L. Allison,
School of Computer Science and Software Engineering,
Monash University, Australia 3168.