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1 Learn and predict a power-function

We saw in Chapter 10 the square root function, it’s just one instance of an example of a power-function.

  • Why did we observe a decrease of the accuracy of the NN prediction of the square-root outside the interval \([0,1]\) (note we trained inside \([0,1]\))? How can you improve on the prediction of the square-root network?
  • Can you design a more generic NN network that can learn and predict a power-function for a given power parameter (\(\lambda \in \Re\))?

2 Pediatric Schizophrenia Study

Use the SOCR Normal and Schizophrenia pediatric neuroimaging study data to complete the following tasks:

  • Conduct some initial data visualization and exploration
  • Use derived neuroimaging biomarkers (e.g., Age, FS_IQ, TBV, GMV, WMV, CSF, Background, L_superior_frontal_gyrus, R_superior_frontal_gyrus, …, brainstem) to train a NN model and predict DX (Normals=1; Schizophrenia=2)
  • Try one hidden layer with different number of nodes
  • Try multiple hidden layers and compare the results to the single layer. Which model is better?
  • Compare the type I (false-positive) and type II (false-negative) errors for the alternative methods
  • Train separate models to predict DX (diagnosis) for the Male and Female cohorts, respectively. Explain your findings
  • Train an SVM (using ksvm and svm in e1071) for Age, FS_IQ, TBV, GMV, WMV, CSF, Background to predict DX. Compare the results of linear, Gaussian and polynomial SVM kernels
  • Add Sex to your models and see if this makes a difference
  • Expand the model by training on all derived neuroimaging biomarkers and re-train the SVM using Age, FS_IQ, TBV, GMV, WMV, CSF, Background, L_superior_frontal_gyrus, R_superior_frontal_gyrus, …, brainstem. Again, try linear, Gaussian and polynomial kernels. Compare the results
  • Are there differences between the alternative kernels?
  • For Age, FS_IQ, TBV, GMV, WMV, CSF, and Background, tune parameters for Gaussian and polynomial kernels
  • Draw a CV (cross-validation) plot and interpret the resulting graph
  • Use different random seed and repeat the experiment, are the results stable?
  • Inspecting the results above, explain why it makes sense to set a tune over a range such as \(exp(-5:8)\)
  • How can we design alternative tuning strategies other than greedy search?

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