Intro to Statistics and Machine Learning

Day 1

• See [Intro to Statistics](slides/estimators-and-sampling.pptx] slides
• Write code to simulate flipping a biased coin and estimating the bias on the coin:
  • Create a function flip_coin(N,p) that simulates flipping a coin with probability p of landing heads N times and returns an estimate of the bias using the sample mean p_hat
  • Run this simulation 1000 times, for all combinations of N = {10,100,100} and p = {0.1, 0.5, 0.9}
  • Plot the distribution of p_hat values for each N, p setting
  • Plot the standard deviation of the p_hat distribution as a function of the sample size N
  • Create one plot of the p_hat distributions, faceted by different N values for p = 0.5 using ggplot
• Inspect the Citibike trip duration data for outliers, comparing the mean and median trip length time
• Review the first chapter of An Introduction to Statistical Learning
• Also check out Chapters 7, 8, and 9 of Introduction to Statistical Thinking (With R, Without Calculus)
• See a recent op-ed on recent challenges in polling

Day 2

• See Intro to Regression slides
• Review these tutorials on simple linear regression and multiple linear regression
• Coin-flipping simulations review. Check out the examples and code here. Get the code running in R.
• Modeling city bike trips
  • Complete the portion of the assignment in trips_vs_weather.Rmd for modeling trips per day as a function of the minimum recorded temperature
  • Quantify how well we can predict trips per day for various degree polynomial function, and generate the described plots
  • What order polynomial best fits the data in terms of adjusted R-squared (use summary(your_model) to see the regression results)?
• Reading assignment: Section 2.1 of ISL.

Day 3

• Fernando gave a guest lecture on how to read research papers
• Read Exposure to ideologically diverse news and opinion on Facebook. Also check out the supplemental material and open sourced data and code
• Revisit modeling the citibike trips
  • Add additional features that you think will be useful to predict number of trips per day, for instance, rain and snow.
  • How much does fit improve? Try out polynomials for each feature and compare the fit
  • What if you create a new variable did_rain which is 1 if rain>0 and 0 if rain=0. Run a model with this variable. Does this model out-perform including rain as a continuous measure? Do the same thing for snow.
  • Add a column to your data frame that gives day of the week (i.e. Sat, Sun...) as a factor. A quick web search will tell you how to do this if you don't know already. Add this new day_of_week variable to your model and report the results summary (e.g. summary(your_model)). What happened? How did the model treat the day of week variable? How much did fit improve?
  • What is your overall best combined model? What is the adjusted R-squared of this model?
  • What model has the best overall performance in terms of R-squared and RMSE on the test set?
  • Inspect the fitted model to determine which features are significant
• Read assignment: Chapter 3 of ISL.
• See here for detailed information abouut specifying formulas in R

Day 4

• Review the lecture slides from today
• Also see these slides on nonparametric inference in R, specifically locfit
• Here's a (hopefully) intuitive explanation of overfitting
• Install and load the locfit package
• Revisit modeling the citibike trips again, this time with locfit
  • Specifically, explore how the fit changes with different parameter values for smoothing and polynomial degree
  • Sweep over different values for the nn smoothing parameter and deg degree parameter and evaluate the train and test performance
  • What values of nn and deg give the best performance in terms of R-squared and RMSE on the test set?
  • How does this compare to fits you obtained earlier in the week?
  • Tips for using locfit:

# to fit number of trips to tmin with smoothing at 0.5 and 2nd degree interpolation
model <- locfit(num_trips ~ lp(tmin, nn=0.5, deg=2), data=trips_by_day)

# then the usual fitted(), predict(), etc

# to plot the same data with the fitted model overlayed
ggplot(data=trips_by_day, aes(x=tmin, y=num_trips)) +
  geom_point() +
  geom_smooth(method=locfit, formula=y ~ lp(x, nn=0.5, deg=2))

Day 5

• See the Intro to Classification slides
• Read Chapter 4 of ISL
• Read Hadley Wickham's Tidy Data paper and Garrett Grolemund's Data tidying
• Install swirl, an interactive tutorial for R, that runs in R
  • You may need to install libcurl first: sudo apt-get install libcurl4-openssl-dev in the terminal
• Go through the "Getting and Cleaning Data" tutorial and the ggplot2 portions of the "Exploratory Data Analysis" tutorial

# install and load the library
install.packages('swirl')
library(swirl)

# install courses
# be patient, these downloads takes a while
install_from_swirl("Getting and Cleaning Data")
install_from_swirl("Exploratory Data Analysis")

# run the tutorial
swirl()