Data Science via Machine Learning and Statistical Modeling

Mathematical Model on Marriage Success

• Prompt | Report
• Creates a Mathematical Model to numerically estimate what makes a success marriage. It incorporates feature selection, data training methods, and possible output errors.

Predicting Apartment Prices in Queens

• Prompt | Report | R Code
• Uses Supervised Machine Learning to beat Zillow.com’s “zestimates”
• Developed in R and incorporates data modeling and manipulation techniques such as data removal, munging, and imputation, and linear and forest regressions

Results:

✓ Random Forest Model predicts within $27,000. (The Average Home Price is $315,000)

✗ Model Requires more observations to accurately predict extrapolated data, however performs well within the included zipcodes.

Course Overview:

• Syllabus
• Philosophy of modeling and learning using data
• Prediction via the ordinary linear model including orthogonal projections, sum of squares identity, R2 and RMSE
• Polynomial and interaction regressions
• Prediction with machine learning including neural nets (the perceptron), support vector machines and the tree methods CART, bagged trees and Random Forests
• Probability estimation using logistic regression, asymmetric cost classifiers and the ROC / DET performance curves
• Underfitting vs. overfitting and the bias-variance decomposition / tradeoff
• Model validation including out of sample techniques such as cross validation and bootstrap validation
• Correlation vs. causation, causal models, lurking variables and interpretations of linear model coefficients
• Extrapolation
• The R language will be taught formally from the ground and up as well as visualization using the ggplot library and manipulation using the dplyr and data.table libraries.

Incorporated Topics

• Basic Probability Theory: axioms, conditional probability, in/dependence
• Modeling with discrete random variables: Bernoulli, Hypergeometric, Binomial, Poisson, Geometric, Negative Binomial, Uniform Discrete and others
• Expectation and variance
• Modeling with continuous random variables: Exponential, Uniform and Normal
• Frequentist confidence intervals and hypothesis testing for one-sample proportions
• Basic visualization of data: plots, histograms, bar charts
• Linear algebra: Vectors, matrices, rank, transpose
• Programming: basic data types, vectors, arrays, control flow (for, while, if, else), functions