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Research Staff Member interview questions shared by candidates

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Member of the Research Staff was asked...April 28, 2017

Gaussian linear models are often insufficient in practical applications, where noise can be heavy- tailed. In this problem, we consider a linear model of the form yi = a · xi + b + ei. The (ei) are independent noise from a distribution that depends on x as well as on global parameters; however, the noise distribution has conditional mean zero given x. The goal is to derive a good estimator for the parameters a and b based on a sample of observed (x, y) pairs. 1.1 Instructions: 1. Load the data, which is provided as (x, y) pairs in CSV format. Each file contains a data set generated with different values of a and b. The noise distribution, conditional on x, is the same for all data sets. 2. Formulate a model for the data-generating process. 3. Based on your model, formulate a loss function for all parameters: a, b, and any additional parameters needed for your model. 4. Solve a suitable optimization problem, corresponding to your chosen loss function, to obtain point estimates for the model parameters. 5. Formulate and carry out an assessment of the quality of your parameter estimates. 6. Try additional models if necessary, repeating steps 2 − 5.

I think we need to use Generalized Method of Moments to get the estimates. Since E[e|x] = 0, we have E[h(x)e] = 0 by the law of iterated expectation for any give function h(x). Now we need to find a best function h*(x) such that it will give you efficient GMM estimator. Less

Actually, you will get least squares estimate as the best estimator in the following sense: y = ax+b+e E(e|x)=0 For any h(x), E(h(x)*e) = E(E(h(x)*e)|x) (where the outer expectation is over X E(h(x)*e|x) = h(x)*E(e|x) = 0 Therefore E(h(x)*e)=0 Take h(x) = y-a-b*x The moment condition is: E(e*(y-a-b*x))=0 This would lead to Least Squares. Less

I believe the true model was y = ax + b + sigma*(x^2). You can use least squares to define the likelihood or use an L1 penalty. Less

Went over my resume and experience, why I wanted to work there, why I thought I was a good fit etc.

I was prepared to talk about these things and had no trouble.

Questions regarding bayesian statistics which I was unfamiliar with.

I couldn't answer really but it ended up being more of a discussion and the researchers teaching me which was nice. Less

One unexpected question was: how to measure the length of Huang He River.

it's a kind of problem solving question. Thinks of every possible methods to test the length of the river. Less

Questions regarding machine learning and text mining. Conceptual questions about supervise machine learning algorithms

How will you handle skewed datasets?

Why did you take more than 5 years to earn your doctoral degree?

I worked as a consultant following my coursework to further expertise in the subject of interest. I also conducted "field research" for my dissertation data. Less

Research specific

Research specific

Where do you see yourself in 5 years.

I will like to grow as a researcher as well as have practical impact in the company's product offerings. Less

Basic questions from project and Mtech subjects

I answered 60% of the questions correctly and was selected.