This is a MATLAB assignment; First We have 3 files:
File1.mat, File2.mat, distortion.mat
0. We have samples (X_i, Y_i, Z_i).The X_i is unknown but Y_i, Z_i are known.We want an estimator Xhat_i based on Y_i and Z_i.
1. If you prefer to use another language, you will need to somehow extract the data from the .mat files.
2. If you run distortion.m it loads the data from File1.mat
3. The data in File1.mat contains:
Numsamples(this is 100)
Xtrain
Ytrain
Ztrain
Y
Z
All vectors are size 100.
I have generated (X_i, Y_i, Z_i) as i.i.d. vectors with a joint distribution that is unknown to you. The training data (Xtrain, Ytrain, Ztrain) includes 100 samples of “ground truth” data from which you can train your estimator (it includes the X information).The data Y, Z is independently generated the same way, but the true X is hidden from you.You need to design an estimator Xhat(i) with the goal of minimizing distortion:
distortion=(1/100) ^2
You do not yet know the X(i) values.In the distortion .m file I give a pretend value that is always 0 so you can see how distortion is calculated.
4. The file File2.mat has the same format, but the i.i.d. vectors (X_i, Y_i, Z_i) were generated using a different distribution.
5. You should write a program to generate a 100 x 1 estimate vector Xhat1 (for File1 data) and another 100 x 1 vector Xhat2 (for File2 data).Your estimate vector will be compared to the true X1 and X2 vectors (currently unknown to you) so that distortion can be calculated. You can do anything you want to estimate (linear, nonlinear, some type of machine learning)but try to design an estimator that you think is good.
6. The assignment: You will write up a brief description of the method or methods you used to estimate the X data for File1 and File2, including your computer code.You will eventually be given the true data, along with the matlab program to show how the data was generated, from which you can calculatedistortion.Then write up a retrospective note on lessons learned and/or modifications that could have been done.
I have placed the true vectors for X in scenario 1 and 2 : FileTrue1.mat and FileTrue2.mat, along with the software I used to generate them (Generate1.m, Generate2.m).
you should calculate your distortion relative to the true data in FileTrue1.mat and FileTrue2.mat, and explore some aspect of the system, for example if we change Generate1.m and Generate2.m to use NumSamples=10000 instead of NumSamples=100, how does performance change?
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