A New Smooth Approximation to the Zero One Loss with a Probabilistic Interpretation We examine a new form of smooth approximation to the zero one loss in which learning is performed using a reformulation of the widely used logistic function. Our approach is based on using the posterior mean of a novel generalized BetaBernoulli formulation. This leads to a generalized logistic function that approximates the zero one loss, but retains a probabilistic formulation conferring a number of useful properties. The approach is easily generalized to kernel logistic regression and easily integrated into methods for structured prediction. We present experiments in which we learn such models using an optimization method consisting of a combination of gradient descent and coordinate descent using localized grid search so as to escape from local minima. Our experiments indicate that optimization quality is improved when learning metaparameters are themselves optimized using a validation set. Our experiments show improved performance relative to widely used logistic and hinge loss methods on a wide variety of problems ranging from standard UC Irvine and libSVM evaluation datasets to product review predictions and a visual information extraction task. We observe that the approach: 1) is more robust to outliers compared to the logistic and hinge losses; 2) outperforms comparable logistic and max margin models on larger scale benchmark problems; 3) when combined with GaussianLaplacian mixture prior on parameters the kernelized version of our formulation yields sparser solutions than Support Vector Machine classifiers; and 4) when integrated into a probabilistic structured prediction technique our approach provides more accurate probabilities yielding improved inference and increasing information extraction performance.

KernelBased Ensemble Learning in Python We propose a new supervised learning algorithm for classification and regression problems where two or more preliminary predictors are available. We introduce KernelCobra, a nonlinear learning strategy for combining an arbitrary number of initial predictors. KernelCobra builds on the COBRA algorithm introduced by , which combined estimators based on a notion of proximity of predictions on the training data. While the COBRA algorithm used a binary threshold to declare which training data were close and to be used, we generalise this idea by using a kernel to better encapsulate the proximity information. Such a smoothing kernel provides more representative weights to each of the training points which are used to build the aggregate and final predictor, and KernelCobra systematically outperforms the COBRA algorithm. While COBRA is intended for regression, KernelCobra deals with classification and regression. KernelCobra is included as part of the open source Python package Pycobra (0.2.4 and onward), introduced by . Numerical experiments were undertaken to assess the performance (in terms of pure prediction and computational complexity) of KernelCobra on reallife and synthetic datasets.