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Initialize the weights, evaluate the feature matrix and repeat gradient descent updates until the loss or gradient stabilizes. If ${\tilde{\mathbf{z}}}_i=(1,{\mathbf{z}}_i)$ includes the intercept, thenA positive step size $\eta$ chosen by a convergence rule or line search gives a practical optimization algorithm. Mini-batch updates or a Newton-type method are alternatives. Fit feature scaling, choose regularization and choose any nonstandard threshold using training or validation data, then freeze the procedure before using the held-out test set.

For $M$ held-out examples, set ${\hat{Y}}_i=1\{h({\mathbf{Z}}_i;\hat{\mathbf{w}})\ge t\}$, with $t=0.5$ unless selected otherwise. The requested classification accuracy isAlways predicting the majority class already gives about 90% accuracy. Report a confusion matrix, classification recall and classification precision as well, especially for the minority class. A precision-recall curve shows the threshold tradeoff without confusing high majority-class accuracy with successful minority-class detection. No numerical test accuracy can be calculated without the held-out predictions and labels.

For a binary classifier, classification precision is $TP/(TP+FP)$, the fraction of predicted positives that are correct, while classification recall is $TP/(TP+FN)$, the fraction of actual positives recovered. If a search returns ten items, six relevant, from a collection containing fifteen relevant items, precision is $6/10$ and recall is $6/15$. Raising a decision threshold often trades recall for precision, traced by a precision-recall curve, but precision need not improve at every threshold. Zero denominators require an explicit reporting convention. Both measures depend on which class is called positive; precision also depends strongly on prevalence.