# 243

Staff Research Associate interview questions shared by candidates

## Top Interview Questions

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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.

### If you find a coworker who is going against procedure, what would you do?

I said I would ask them about it to see if the procedure has changed or been updated, and if not explain why the current procedure is in place and why we should follow it. Less

I talked about my research experience.

### Suppose the driver of a push-button ignition vehicle finds his/her vehicle is suddenly accelerating out of control. What would their first reaction be? What improvements need to be made to today's systems to address this?

If the driver is outside the vehicle, his/her initial reaction would run after it. If the driver is in the driver's seat, his/her initial reaction would be "slam on foot padle[s]" (hopefully the brakes) and grab the steering wheel. Excluding involuntary/limbic/fight or flight'reactions. Hmm, today's systems I shall first assume refers to the vehicle. In that case, A steering sensor which cuts power to the engine if the wheel has close to zero resistance relative to its torque baseline as the vehicle accelerates. That same system can be applied to engage the brakes. If we are talking about systems in general, the dealership can simply inform/emphasize to the buyer that the vehicle doesn't use keys... Less

### 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?

### Stupid questions from a nope

better than what he didn't know about it