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1 Learn and predict a power-function

We saw in Chapter 10 the ML approximation of the square root function, which is just one instance of the more general power-function.

  • Why did we observe a decrease of the accuracy of the NN square-root prediction outside the interval \([0,1]\)? (note that 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 the power-function for a given power (\(\lambda \in R\))?

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 an 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 performs 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 SVM model by training on all derived neuroimaging biomarkers - 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 graph.
  • Use different random seeds to repeat the experiment 5 times, are the results stable?
  • Inspecting the results above, explain why it makes sense to tune the parameters over a range such as \(exp(-5:8)\).
  • How can we design alternative tuning strategies other than a greedy search?

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