Maximum Likelihood and Data Science Interviews

Maximum Likelihood and Data Science Interviews

Maximum Likelihood (MLE) is a favorite interview topic at many companies and their interviewers, and in this short post, we are going to discuss two simple problems involving MLEs.

In [previous post_](https://medium.com/swlh/linear-regression-and-maximum-likelihood-1dcb9435c71e), _we saw how we can derive Maximum Likelihood Estimator of a linear regression problem, and showed that it is same as the least-squared-error(LSE) estimator. Maximum Likelihood (MLE) is a favorite interview topic at many companies and their interviewers, and in this short post, we are going to discuss two simple problems involving MLEs.

How to approach MLE problems?

  1. Start with the data points and distribution given in the problem statement. Always remember that the data points are fixed (constants), and the parameters of the random distribution are the variables to be estimated in these problems. So, for example, for a normal distribution, the data points {(x₁, y₁), (x₂, y₂), …, } form the constants, and the mean/standard deviation of the distribution form the parameters to be estimated.
  2. Write the expression for probability distribution _(More formally, the _probability density function (pdf)) for a single data point.
  3. Assuming data points to be independent, write the expression for the _joint probability distribution _by multiplying the individual probability density functions. (NOTE: We are yet to encounter an interview problem where different data points are not independent). This joint distribution is also called the _likelihood _of the data.
  4. Maximize the likelihood. Use _log likelihood _if it simplifies the calculation.

With this general outline, let’s now solve a few interview problems on MLE.

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