A general model is proposed for studying ranking problems. We investigate learning methods based on empirical minimization of the natural estimates of the ranking risk. The empirical estimates are of the form of a U -statistic. Inequalities from the theory of U -statistics and U processes are used to obtain performance bounds for the empirical risk minimizers. Convex risk minimization methods a...

The recently proposed Optimized Cutting Plane Algorithm (OCA) is an efficient method for solving large-scale quadratically regularized risk minimization problems. Existing open-source library LIBOCAS implements the OCA algorithm for two important instances of such problems, namely, the Support Vector Machines algorithms for training linear two-class classifier (SVM) and for training linear mult...

In this paper, we propose a general technique for solving support vector classifiers (SVCs) for an arbitrary loss function, relying on the application of an iterative reweighted least squares (IRWLS) procedure. We further show that three properties of the SVC solution can be written as conditions over the loss function. This technique allows the implementation of the empirical risk minimization...

In this paper we study the pricing and hedging of a very general class of life insurance liabilities by means of the risk-minimization approach. We find the price and risk-minimizing strategy in two cases, first in the case when the financial market consists only of one risky asset, e.g. a stock, and a bank account, and second in an extended financial market, allowing for investments in two add...

In Learning Using Privileged Information (LUPI) paradigm, along with the standard training data in the decision space, a teacher supplies a learner with the privileged information in the correcting space. The goal of the learner is to find a classifier with a low generalization error in the decision space. We consider an empirical risk minimization algorithm, called Privileged ERM, that takes i...

ROC curves are one of the most widely used displays to evaluate performance of scoring functions. In the paper, we propose a statistical method for directly optimizing the ROC curve. The target is known to be the regression function up to an increasing transformation and this boils down to recovering the level sets of the latter. We propose to use classifiers obtained by empirical risk minimiza...

Question classification is a crucial preprocessing for question answering system; it can help to make sure the user’s intention. Most of previous researches focus on the feature driven methods that represent a question with a bag of features, which ignore the important information contained in the words order and distance. To take such information into account, this paper proposes to describe t...

The melting point of gallium (29.7646 °C) is a defining thermometric fixed point of the International Temperature Scale of 1990 (ITS-90). Realization of this melting point is performed using a fixedpoint cell containing high-purity (≥99.999 99 wt. % pure) gallium. A 30 kg single lot of gallium (99.999 9956 wt. % pure) constituting Standard Reference Material (SRM) 1751 was evaluated, and certif...

In many structured prediction problems, the highest-scoring labeling is hard to compute exactly, leading to the use of approximate inference methods. However, when inference is used in a learning algorithm, a good approximation of the score may not be sufficient. We show in particular that learning can fail even with an approximate inference method with rigorous approximation guarantees. There ...

We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk minimization for model selection. We demonstrate our methods by predicting interest rate movements.