ECS 171: Homework Set 3
Instructor: llias Tagkopoulos

Due on November 30,2019
General Instructions: The homework package should be submitted electronically through Canvas, Each submission should be a zip file that includes the following: (a) a report in pdf format (“report_HW3.pdf ) that includes your answers to all questions, plots, figures and any instructions to run your code, (b) the source code files. Please note: (a) do not include any other files, for instance files that we have provided such as datasets, (b) each function should be written with the appropriate remarks in the code so it is generally understand-able (what it does, how it does it), (c) you are allowed to use sklearn, numpy, matplotlib and pandas, or implement yourself. Late submissions have 20% penalty per day.

1 CREATING A VIRTUAL CELL: PREDICTING PHENOTYPIC AND ENVIRONMENTAL CHARACTERISTICS [90PT1
In this exercise, you will use a set of 223 transcriptional profiling samples from the gram-negative bacterium Esthetkhia co/i. E. eoli is the most well-studied organism with great importance to human health and biotechnology. This meta-dataset has been created by curating several published datasets and annotaUng the entries with meta-data. It contains 4501 features, the first 6 corresponding to gene It), strain, medium, environmental and genetic perturbation, and Information about the growth rate. The last 4496 entries correspond to the expression of all genes in the bacterium. The dataset can be downloaded from Canvas (under the HW3-data folder). The main file is ‘ccs 171.dataset. txt~ la xls version is also available), the ‘ccsl 71.readme, txt” and ’ecsl7l.genes.txt’ files has the definition of the features and gene names, respectively. Perform and report (code and results) the following:

1. Create a predictor of the bacterial growth attribute by using only the expression of the genes as attributes. Not all genes are informative for this task, so use a regularized regression technique (e.g. lasso, ridge or elastic net) and explain what it does (we discussed these techniques in class, but you might have to read some more on how each method works). Which one is the optimal constrained parameter value (usually denoted by A)? Report the number of features that have non-zero coefficients and the 5-fold cross-validation generalization error of the technique. |20pt|
2. Extend your predictor to report the confidence interval of the prediction by using the bootstrapping method. Clearly state the methodology and your assumptions. (You need not report the confidence interval here, you only need add that functionality to your code) 110pt|
3. Use your bootstrap model from 2 to find the confidence interval of predicted growth for a bacterium whose genes are expressed exactly at the mean expression value. (Note: for each gene, there is a corresponding mean expression value) |5pt|
4. Create four separate SVM classifiers to categorize the strain type, medium type, environmental and gene perturbation, given all the gene transcriptional profiles. The classifier should select as features a small subset of the genes, either by performing feature selection (wrapper method) or by using only the non-zero weighted features from the regularized regression technique of the first aim. For each classifier (4 total) report the number of features and the classification performance through 5-fold cross-validation by plotting the ROC and PR curves and reporting the AUC/AUPRC values. |20pt)
5. Create one composite SVM classifier to simultaneously predict medium and environmental perturbations and report the 10-fold cross-validation AUC/AUPRC value. Does this classifier perform better or worse than the two individual classifiers together for these predictions? That is, are we better off building one composite or two separate classifiers to simultaneously predict these two features? What is the baseline prediction performance (null hypothesis)? |15pt|
6. Reduce the dimensionality of gene expression profiles (i.e. last 4496 columns) to two dimensions only using both Principal Component Analysis (PCA) and t-SNE. Visualize the dataset