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Reduce overfitting and explain the mean squared error loss

UiPathMachine Learning Engineer · HR Screen
MediumMachine Learning EngineerHR ScreenMachine Learning

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A machine learning phone screen on how to diagnose and reduce overfitting, and on the mean squared error loss: its definition, what minimizing it estimates, its probabilistic interpretation, and when another loss works better. Tests fundamentals, mechanisms and trade-off reasoning.

A machine learning phone screen asks several short conceptual questions in quick succession. Two of them are reconstructed below: how to reduce overfitting, and the mean squared error loss. Answer each as you would aloud, concisely, but give the reasoning behind every claim rather than a list of terms. Unless told otherwise, assume supervised learning with a held-out validation set.

Clarifying Questions

  • What kind of model is in play (a linear model, gradient-boosted trees, a deep network)? The most effective overfitting remedies differ between them.
  • How much labeled data is there relative to the number of features or parameters, and can more be collected?
  • For the loss question, is the target continuous, and are there outliers or heavy-tailed errors?

Part 1 — Reducing overfitting

A model scores much better on its training data than on held-out data. How do you confirm that the gap is overfitting, and what would you do to reduce it? For each remedy, explain why it works and what it costs.

What This Part Should Cover

  • Diagnosis from training and validation curves, and ruling out leakage or distribution shift
  • Remedies grouped by mechanism, with the reason each one reduces variance
  • The cost of each remedy, and how its strength is tuned on held-out data

Part 2 — The mean squared error loss

Define the mean squared error (MSE) loss for a regression model. What does minimizing it make the model predict, why might you choose it, and when is it a poor choice? Compare it with at least one alternative loss.

What This Part Should Cover

  • The formula and its gradient with respect to a prediction
  • What MSE minimization estimates, and the noise assumption under which it is maximum likelihood
  • Sensitivity to outliers, and the losses used instead when that matters

Hints

Hint 1

Diagnose before fixing: Decide what evidence shows that the gap comes from the model fitting noise, rather than from leakage or from a difference between the training and evaluation data.

Hint 2

The best constant: Ask which single number minimizes the average squared error over a set of targets, and what happens to that number when one target is extreme.

Follow-up questions

  • Add an L2 penalty to linear regression trained with MSE. What is the closed-form solution, and what does the penalty do to it?
  • Decompose the expected squared error on a new point into bias, variance and noise. Which term does each Part 1 remedy target?
  • Why is MSE on a sigmoid output usually avoided for binary classification?
  • Your validation set has only a few hundred examples. How does that change the way you detect and tune against overfitting?