structural:expansion, linguistic:voice_change, stylistic:tone
Other approaches

In machine learning applications where logistic regression is used for binary classification, the MLE minimises the cross-entropy loss function.

Logistic regression is an important machine learning algorithm. The goal is to model the probability of a random variable Y {\displaystyle Y} being 0 or 1 given experimental data.

Consider a generalized linear model function parameterized by θ {\displaystyle \theta },

Therefore,

and since Y ∈ { 0, 1 } {\displaystyle Y\in \{0,1\}}, we see that Pr (y ∣ X; θ) {\displaystyle \Pr(y\mid X;\theta)} is given by Pr (y ∣ X; θ) = h θ (X) y (1 − h θ (X)) (1 − y). {\displaystyle \Pr(y\mid X;\theta)=h_{\theta }(X)^{y}(1-h_{\theta }(X))^{(1-y)}.} We now calculate the likelihood function assuming that all the observations in the sample are independently Bernoulli distributed,

Typically, the log likelihood is maximized,

which is maximized using optimization techniques such as gradient descent.

Assuming the (x, y) {\displaystyle (x,y)} pairs are drawn uniformly from the underlying distribution, then in the limit of large N,

where H (Y ∣ X) {\displaystyle H(Y\mid X)} is the conditional entropy and D KL {\displaystyle D_{\text{KL}}} is the Kullback–Leibler divergence. This leads to the intuition that by maximizing the log-likelihood of a model, you are minimizing the KL divergence of your model from the maximal entropy distribution. Intuitively searching for the model that makes the fewest assumptions in its parameters.