Research Staff Member Interview Questions
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Research Staff Member interview questions shared by candidates
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.
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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
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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
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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.
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I was prepared to talk about these things and had no trouble.
Questions regarding machine learning and text mining. Conceptual questions about supervise machine learning algorithms
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How will you handle skewed datasets?
Basic questions from project and Mtech subjects
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I answered 60% of the questions correctly and was selected.
Write an algorithm to generate a solvable maze
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I came up with something depth-first search based