We consider the problem of rank loss minimization in the setting of multilabel classification, which is usually tackled by means of convex surrogate losses defined on pairs of labels. Very recently, this approach was put into question by a negative result showing that commonly used pairwise surrogate losses, such as exponential and logistic losses, are inconsistent. In this paper, we show a pos...

We present a cgal-based univariate algebraic kernel, which provides certi ed real-root isolation of univariate polynomials with integer coe cients and standard functionalities such as basic arithmetic operations, greatest common divisor (gcd) and square-free factorization, as well as comparison and sign evaluations of real algebraic numbers. We compare our kernel with other comparable kernels, ...

The so-called S-lemma has played an important role in optimization, both in theory and in applications. The significance of S-lemma is especially pronounced in control theory, robust optimization, and non-convex quadratic optimization. Hitherto, S-lemma is however established only in the domain of quadratic functions. In this paper we shall extend the notion of S-lemma to the class of univariat...

Logistic regression is a popular statistical method in studying the effects of covariates on binary outcomes. It has been widely used in both clinical trials and observational studies. However, the results from the univariate regression and from the multiple logistic regression tend to be conflicting. A covariate may show very strong effect on the outcome in the multiple regression but not in t...

This paper contains a survey of univariate models of conditional heteroskedasticity. The classical ARCH model is mentioned, and various extensions of the standard Generalized ARCH model are highlighted. This includes the Exponential GARCH model. Stochastic volatility models remain outside this review.

We pose and solve the equivalence problem for subspaces of Pn, the (n+ 1) dimensional vector space of univariate polynomials of degree ≤ n. The group of interest is SL2 acting by projective transformations on the Grassmannian variety GkPn of k-dimensional subspaces. We establish the equivariance of the Wronski map and use this map to reduce the subspace equivalence problem to the equivalence pr...

We compare the two main competing methods for fast univariate polynomial GCD computation over an algebraic number field, namely, the modular method of Langymyr et al (1987), and the heuristic method of Smedley et al (1988). Because of recent improvements to the modular method by Encarnacion (1994), we expected that the modular method, if implemented “properly”, would now be the method of choice...

We present two moment-ratio diagrams along with guidance for their interpretation. The first momentratio diagram is a graph of skewness versus kurtosis for common univariate probability distributions. The second moment-ratio diagram is a graph of coefficient of variation versus skewness for common univariate probability distributions. Both of these diagrams, to our knowledge, are the most compr...

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It is very well-known that this system has a non-trivial solution if and only if AD −BC equals to zero. One can generalize the previous situation in two different directions. The most classical one is the notion of determinant, which is the condition under which a system of n homogeneous equations in n unknowns    A11x1 + A12x2 + . . . + A1nxn = 0 A21x1 + A22x2 + . . . + A2nxn = 0 .. .. ...