Newsbreak·Machine Learning Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Phone screen for an ML infra role at Newsbreak that turned into a statistics/regression problem. Wasn't expecting that kind of question for what was supposed to be a systems-leaning position.

Questions Asked (1)

Given a piecewise constant model where the prediction is b1 if x is at or below some threshold t, and b2 otherwise, how do you find the values of b1, b2, and t that minimize mean squared error?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Wasn't expecting this on a phone screen for an infra-leaning ML role.

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AI HintsAI Generated

Suggested Approach

Frame the problem as a two-stage optimization: first, for a fixed threshold t, derive the closed-form optimal b1 and b2 as the means of the target values in each region. Then, substitute these into the MSE and minimize over t by evaluating candidate thresholds (e.g., midpoints between sorted unique x values) or using a sweep algorithm.

Pro tip: Mention that this is a 1D decision stump and that the optimal threshold can be found in O(n log n) by sorting and using prefix sums, which is efficient and exact. Also note that if the data is noisy, regularization or cross-validation may be needed to avoid overfitting the threshold.

1. Formulate the objective

Write the MSE as a function of b1, b2, and t, summing squared errors over all data points. Emphasize that for a fixed t, the problem decouples into two independent mean estimation problems.

2. Solve for b1 and b2 given t

For a fixed t, the optimal b1 is the mean of y for x <= t, and optimal b2 is the mean of y for x > t. Derive these by setting derivatives to zero.

3. Reduce to a 1D search over t

Substitute the optimal b1 and b2 back into the MSE to get a function of t alone. The optimal t lies between two consecutive sorted x values, so only consider midpoints (or the sorted x values themselves).

4. Efficiently compute the optimal t

Sort the data by x, compute prefix sums of y and y^2, and evaluate the MSE for each candidate threshold in O(1) per candidate, yielding an O(n log n) algorithm overall.

5. Discuss practical considerations

Mention handling of ties, edge cases (e.g., all points on one side), and potential need for regularization or validation to avoid overfitting, especially with small datasets.

Key Points to Mention

For fixed t, optimal b1 and b2 are the means of the two groups (closed-form solution).
The problem reduces to a 1D search over t, which can be solved exactly by evaluating candidate thresholds between sorted unique x values.
Efficient implementation uses sorting and prefix sums to compute MSE for each candidate in O(1), total O(n log n).
This is equivalent to fitting a decision stump (a depth-1 decision tree) for regression.
Edge cases: empty groups (t outside data range), ties in x, and the need for a minimum number of points per group.
Potential overfitting if t is chosen too finely; consider regularization or cross-validation.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.