Kernel methods provide an attractive framework for aggregating and learning from ranking data, and so understanding the fundamental properties of kernels over permutations is a question of broad interest. We provide a detailed analysis of the Fourier spectra of the standard Kendall and Mallows kernels, and a new class of polynomial-type kernels. We prove that the Kendall kernel has exactly two ...

In the last years, kernelization with structural parameters has been an active area of research within the field of parameterized complexity. As a relevant example, Gajarskỳ et al. [ESA 2013] proved that every graph problem satisfying a property called finite integer index admits a linear kernel on graphs of bounded expansion and an almost linear kernel on nowhere dense graphs, parameterized by...

In the Possible Winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the Possible Winner problem, with number of candida...

Small Area estimation is a technique used to estimate parameters of subpopulations with small sample sizes.  Small area estimation is needed  in obtaining information on a small area, such as sub-district or village.  Generally, in some cases, small area estimation uses parametric modeling.  But in fact, a lot of models have no linear relationship between the small area average and the covariat...

—The problem of determination of a minimal polynomial basis of a rational vector space is the starting point of many control analysis, synthesis and design techniques. In this paper, we propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s). The proposed method exploits the structure of the left null space of generalized W...

We price moneyness-based portfolio returns on the LIBOR futures options in an Intertemporal CAPM framework as an extension of the pricing kernel approach. In contrast to existing studies for pricing index options, our results show that only the real interest rate is significant in the pricing kernel for LIBOR options. The polynomial pricing kernel with linear interpretation outperforms the iso-...

We construct near-optimal coresets for kernel density estimate for points in Rd when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size O( √ d log(1/ε)/ε), and we show a near-matching lower bound of size Ω( √ d/ε). The upper bound is a polynomial in 1/ε improvement when d ∈ [3, 1/ε2) (for all kernels except the Gaussian kernel which had a ...

The literature on meshless methods observed that kernel-based numerical differentiation formulae are robust and provide high accuracy at low cost. This paper analyzes the error of such formulas, using the new technique of growth functions. It allows to bypass certain technical assumptions that were needed to prove the standard error bounds on interpolants and their derivatives. Since differenti...

It is known that the problem of deleting at most k vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we answers this question in affirmative by obtaining a polynomial kernel for Proper Interval Vertex Deletion. This resolves an open question of van Bevern, Komu...

We show that for any fixed i, j ≥ 1, the k-Dominating Set problem restricted to graphs that do not have Ki,j as a subgraph is fixed parameter tractable (FPT) and has a polynomial kernel. This result implies that this problem restricted to bounded-degenerate graphs has a polynomial kernel, solving an open problem posed by Alon and Gutner in [3]. Our result extends the class of graphs for which t...