We can define a logistic regression function with Incanter's minimize function as follows:

(defn logistic-regression [ys xs]
  (let [cost-fn (fn [coefs]
                  (let [classify (sigmoid-function coefs)
                        y-hats   (map (comp classify i/trans) xs)]
                    (logistic-cost ys y-hats)))
        init-coefs (repeat (i/ncol xs) 0.0)]
    (o/minimize cost-fn init-coefs)))

The cost-fn accepts a matrix of coefficients. We create a classifier from the coefficients using the sigmoid-function previously defined, and a sequence of predictions, y-hats, based on the input data. Finally, we can calculate and return the logistic-cost value based on the provided coefficients.

To perform logistic regression, we minimize the logistic cost-fn by selecting the optimal parameters to the sigmoid-function. Since we have to start somewhere, our initial coefficients are simply 0.0 for each parameter.

The minimize function expects to...