Everything else is ready: study the parts, the key terms and the quiz below.
- Part 11A probability is unknown until we fit it
- Part 22Construct a likelihood from the fixed outcomes
- Part 33Find the maximum, rather than choosing two guesses
- Part 44Turn the same calculation into log loss
- Part 55Let one recorded feature change the fitted probability
- Part 66Reproduce and challenge the fit
Maximum Likelihood Estimation
Choose the probability that best explains observed yes/no outcomes, then connect it to logistic-regression log loss.
In this lesson6 parts
- 01A probability is unknown until we fit it
- 02Construct a likelihood from the fixed outcomes
- 03Find the maximum, rather than choosing two guesses
- 04Turn the same calculation into log loss
- 05Let one recorded feature change the fitted probability
- 06Reproduce and challenge the fit
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- Bernoulli outcome
- One recorded zero or one under this model.
- parameter
- Numerical value chosen within a model, such as the churn probability p.
- likelihood
- Model probability of the observed labels, treated as a function of the candidate parameter.
- log likelihood
- Sum of log probabilities assigned to observed outcomes.
- maximum likelihood estimate
- Parameter value where the observed-data likelihood is largest.
- p-hat
- Estimate of p from these observed rows: 495 / 3,150.
- negative log likelihood
- Log likelihood multiplied by minus one.
- log loss
- Mean negative log likelihood per observed row.
- nat
- Unit produced when information is measured with natural logarithms.
- feature
- Recorded input used to vary a model's prediction.
- linear score (narration)
- An intercept plus a coefficient times the feature, before the sigmoid.
- sigmoid
- Function mapping any real score into a value between zero and one.
- logistic regression
- Model that maps a feature-dependent linear score to a probability.
- intercept
- Score when x is zero.
- coefficient
- Score change when x rises by one.
Quiz 5 questions
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.
Practice
Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.
The self-checking notebook for this lesson is Maximum likelihood estimation.
Common mistakes
What you will see when it goes wrong, why it happens, and the fix.
Where it’s used
Where this lesson’s ideas turn up in real work.
Builds on
This lesson stands on its own. These go deeper into what it uses.
- Maths 1.2
- 4.1–4.2