There are several important details in the implementation of this algorithm. When p ≫ N, one cannot run λ all the way to zero, because the saturated logistic regression fit is undefined (parameters wander off to ±∞ in order to achieve probabilities of 0 or 1). Hence the default λ sequence runs down to λmin = ελmax > 0.Care is taken to avoid coefficients diverging in order to achieve fitted probabilities of 0 or 1. When a probability is within ε = 10−5 of 1, we set it to 1, and set the weights to ε. 0 is treated similarly.Our code has an option to approximate the Hessian terms by an exact upper-bound. This is obtained by setting the wi in (17) all equal to 0.25 [Krishnapuram and Hartemink, 2005].We allow the response data to be supplied in the form of a two-column matrix of counts, sometimes referred to as grouped data. We discuss this in more detail in Section 4.2.The Newton algorithm is not guaranteed to converge without step-size optimization [in Lee et al., 2006]. Our code does not
