A data scientist has built a model that provides the likelihood of an error occurring in a factory. The historical accuracy of the model is 90%. At a specific factory, the model is reporting a likelihood score of 0.90. Which of the following explains a confidence score of 0.90?

A model's likelihood or confidence score for a single prediction represents the estimated probability that the instance belongs to a particular class. In this scenario, a score of 0.90 means the model calculates a 90% probability that an error will occur based on the specific input data from the factory. Option D provides the correct frequentist interpretation of this probability: if the model were to encounter 100 identical situations, its prediction would be "error" in 90 of those cases. This is distinct from the model's overall historical accuracy, which measures performance over an entire dataset of past events.

A. This describes the model's recall (sensitivity) over a historical dataset, which is a performance metric, not the confidence of a single prediction.
B. This describes a concept related to confidence intervals or the reliability of model performance across different datasets, not a single prediction's score.
C. This incorrectly conflates the model's prediction with the actual outcome. It attempts to describe recall or accuracy, not the model's confidence in one prediction. ---

1. James

G.

Witten

D.

Hastie

T.

& Tibshirani

R. (2013). An Introduction to Statistical Learning: with Applications in R. Springer.

Section 4.3

Logistic Regression

pp. 130-131: The text explains that logistic regression models the probability that the response Y belongs to a particular category. The output

Pr(Y = 1|X)

is the estimated probability of the class given the predictors. A score of 0.90 is a direct estimate of this probability for a specific observation X.

2. Ng

A. (2023). CS229 Lecture Notes: Logistic Regression. Stanford University.

Part V

Generative Learning algorithms

p. 4: The notes define the hypothesis output hθ(x) for logistic regression as p(y=1|x; θ)

which is the "estimated probability that y=1 for a given x." This confirms that the model's output score is a direct probability estimate for that single instance.

3. Murphy

K. P. (2012). Machine Learning: A Probabilistic Perspective. The MIT Press.

Chapter 1

Section 1.2

p. 4: The book introduces classification

stating

"Our goal is to learn a mapping from inputs x to outputs y... We are interested in probabilistic classifiers which compute p(y=c|x

D)

where c is one of the C classes." This establishes that the output of such a classifier is a conditional probability for a given input

which is what the 0.90 score represents.