HW5

Problem 5.1 (Learning the Power Law):

Design, train, and optimize a generic neural network (NN) that can learn and predict the power-function Links to an external site. for a given power parameter ($\lambda\in R$). Assess the accuracy of the NN prediction of the power function. [Hint: Recall the example with the square-root function Links to an external site..]

Problem 5.2 (ALS Clustering):

Use the ALS dataset to study a rare but devastating progressive neurodegenerative disease, amyotrophic lateral sclerosis (ALS). Major clinically relevant questions include: What patient phenotypes can be automatically and reliably identified and used to predict the change of the ALSFRS slope over time?

• Load and prepare the data
• Report (short!) data summaries and show some preliminary visualizations
• Train a k-Means model on the data, select k
• Evaluate the model performance using bar and silhouette plots and summarize the results
• Tune and plot parameters with k-means++
• Rerun the model with the optimal parameters and interpret the clustering results
• Apply Hierarchical Clustering on three different linkages and compare the corresponding silhouette plots
• Fit a Gaussian mixture model, select the optimal model, report BIC, and display density and classification plots
• Compare the result of the above methods

Note: Some of the most clinically important ALS features to focus on include:

Age_mean; ALSFRS_slope; ALSFRS_Total_max; ALSFRS_Total_median; ALSFRS_Total_range; Blood.Urea.Nitrogen..BUN._median; Blood.Urea.Nitrogen..BUN._min; Blood.Urea.Nitrogen..BUN._range; BMI_max; bp_diastolic_median; bp_systolic_median; Calcium_median; Chloride_median; Creatinine_median; Glucose_median; Hemoglobin_median; eg_median; leg_min; leg_range; Lymphocytes_median; mouth_median; onset_delta_mean; onset_site_mean; respiratory_median; Sodium_median;  trunk_max; trunk_median;