LinkedIn·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

LinkedIn ML engineer screen, one meaty theory question about logistic regression that sounds straightforward until you're actually in it.

Questions Asked (1)

How does the log-likelihood loss function used in logistic regression connect to the principle of maximum likelihood estimation?

Technical Trade-offsAlgorithms & Data Structures

Author's notes

I knew the mechanics but fumbled the explanation.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by defining maximum likelihood estimation (MLE) as the principle of choosing parameters that maximize the probability of the observed data. Then show that for binary classification, maximizing the likelihood is equivalent to minimizing the negative log-likelihood, which is exactly the log-loss function used in logistic regression. Conclude by highlighting that this connection ensures logistic regression is a probabilistic model with well-calibrated outputs.

Pro tip: Emphasize that the log-loss is not just a convenient choice but a direct consequence of MLE under the Bernoulli assumption, and mention that this leads to desirable properties like consistency and asymptotic normality of the parameter estimates.

1. Define Maximum Likelihood Estimation

Explain MLE as a method to estimate parameters by maximizing the likelihood function, which measures how well the model explains the observed data.

2. Model the Probability with Logistic Function

Describe how logistic regression models the probability of the positive class as a sigmoid function of the linear combination of inputs.

3. Write the Likelihood for Binary Outcomes

For each data point, the likelihood is p if y=1 and 1-p if y=0, which can be written compactly as p^y * (1-p)^(1-y).

4. Take the Negative Log-Likelihood

Taking the log and negating gives the negative log-likelihood, which is the sum of -[y log(p) + (1-y) log(1-p)] over all points.

5. Connect to Log-Loss and Optimization

This negative log-likelihood is exactly the log-loss (or cross-entropy) function, so minimizing log-loss is equivalent to maximizing likelihood.

Key Points to Mention

Maximum likelihood estimation (MLE) principle: choose parameters that maximize the probability of the observed data.
Logistic regression assumes a Bernoulli distribution for the target variable.
Likelihood function for binary classification: product of p for positive examples and (1-p) for negative examples.
Log-loss is the negative log-likelihood, so minimizing it is equivalent to maximizing likelihood.
The log transform simplifies the product into a sum and prevents numerical underflow.
This connection justifies the use of log-loss and provides statistical guarantees for logistic regression.

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