  Sparse logistic regression, as an effective tool of classification, has been
developed tremendously in recent two decades, from its origination the
$\ell_1$-regularized version to the sparsity constrained models. This paper is
carried out on the sparsity constrained logistic regression by the Newton
method. We begin with establishing its first-order optimality condition
associated with a $\tau$-stationary point. This point can be equivalently
interpreted as a system of equations which is then efficiently solved by the
Newton method. The method has a considerably low computational complexity and
enjoys global and quadratic convergence properties. Numerical experiments on
random and real data demonstrate its superior performance when against seven
state-of-the-art solvers.
