Databricks·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Databricks ML Engineer screen, one meaty coding question about implementing linear regression from scratch with gradient descent. No ML libraries allowed, which sounds easy until you're actually deriving the gradients on the spot and someone's watching.

Questions Asked (1)

Implement simple linear regression from scratch using gradient descent. No sklearn or torch, numpy is fine. You need to define the model, use MSE loss, derive and implement the gradients for both weights and bias, build the training loop with configurable learning rate and iteration count, and then discuss how you'd choose the learning rate, when to stop training, and how to detect if the model is diverging.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The coding part I was fine with.

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AI HintsAI Generated

Suggested Approach

Start by clearly defining the linear model and MSE loss, then derive the gradients for weights and bias. Implement the training loop with configurable hyperparameters, and finally discuss practical strategies for learning rate selection, stopping criteria, and divergence detection.

Pro tip: Mention that you would standardize features and monitor the loss curve for divergence, and that you can use a simple learning rate schedule like reducing the rate if loss increases.

1. Define Model and Loss

State the linear model: y_pred = X @ w + b. Define MSE loss: (1/n) * sum((y_pred - y)^2).

2. Derive Gradients

Compute gradients: dw = (2/n) * X.T @ (y_pred - y), db = (2/n) * sum(y_pred - y). Explain the derivation briefly.

3. Implement Training Loop

Initialize weights and bias to zeros. For each iteration: compute predictions, loss, gradients, and update parameters: w -= lr * dw, b -= lr * db. Track loss.

4. Hyperparameter Tuning and Stopping

Choose learning rate via grid search or adaptive methods; stop when loss change is below a threshold or after fixed iterations. Detect divergence if loss increases or becomes NaN.

Key Points to Mention

Feature scaling (standardization) to improve gradient descent convergence
Learning rate selection: try values like 0.1, 0.01, 0.001; use learning rate schedules
Stopping criteria: fixed iterations, early stopping based on validation loss, or convergence threshold
Divergence detection: monitor loss for increase or NaN, reduce learning rate or use gradient clipping
Vectorized implementation using numpy for efficiency
Discussion of trade-offs: batch vs stochastic gradient descent, computational cost

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