Machine Learning Problems
k-means minimizes L=∑j∑x∈Sj∥x−μj∥2. Cluster k currently has mean μk=5.0. Using the stochastic-gradient-descent update μk←μk+ε(xi−μk) with learning rate ε=0.1, a newly assigned point xi=8 arrives. What is the updated μk?
Enter a number (at most 1 decimal place).
Using “higher dimension”, explain:
Describe the kernel trick in SVMs and give a simple example. How do you decide what kernel to choose?
Minimum 1 words. Your answer must include: “higher dimension”.
Meet the writing requirements, then you can open the model answer.
You have N=5 i.i.d. draws from a Gaussian distribution: 4,6,5,7,3. What is the maximum-likelihood estimate μ^?
Enter a number (at most 0 decimal places — integer).
Using “posterior”, explain:
Say you're using a Gaussian mixture model (GMM) for anomaly detection of fraudulent transactions, classifying incoming transactions into K classes. Describe the model setup and how you'd determine if a new transaction is fraudulent.
Your answer must include: “posterior”.
Meet the writing requirements, then you can open the model answer.
Using “churn”, explain:
Walk through how you'd build a model to predict whether a particular Robinhood user will churn.
Your answer must include: “churn”.
Meet the writing requirements, then you can open the model answer.
Using “likelihood”, explain:
Say you run a linear regression and model the error terms as normally distributed. Show that maximizing the likelihood of the data is equivalent to minimizing the sum of squared residuals.
Minimum 1 words. Your answer must include: “likelihood”.
Meet the writing requirements, then you can open the model answer.
Using “eigenvector”, explain:
Describe the idea behind Principal Components Analysis (PCA) and its formulation in matrix form. Walk through the constrained-maximization derivation.
Your answer must include: “eigenvector”.
Meet the writing requirements, then you can open the model answer.
Using “log-likelihood”, explain:
Describe the model formulation behind logistic regression. How do you maximize the log-likelihood in the two-class case?
Your answer must include: “log-likelihood”.
Meet the writing requirements, then you can open the model answer.
Using “cold start”, explain:
How would you approach creating a music recommendation algorithm for Discover Weekly — a 30-song weekly playlist personalized to an individual user?
Your answer must include: “cold start”.
Meet the writing requirements, then you can open the model answer.
Using “unbiased”, explain:
Derive the variance-covariance matrix of the least-squares parameter estimates in matrix form.
Minimum 1 words. Your answer must include: “unbiased”.
Meet the writing requirements, then you can open the model answer.
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