Logistic regression is a technique to map the input feature to the posterior probability for a binary class. The optimal parameter of regression function is obtained by maximizing log likelihood of training data. In this report, we implement two optimization techniques 1) stochastic gradient decent (SGD); 2) limited-memory BroydenFletcherGoldfarbShanno (L-BFGS) to optimize the log likelihood fu...

This paper presents a tutorial introduction to the logistic function as a statistical object. Beyond the discussion of the whys and wherefores of the logistic function, I also hope to illuminate the general distinction between the \generative/causal/class-conditional" and the \discriminative/diagnostic/ predictive" directions for the modeling of data. Crudely put, the belief network community h...

In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...