Related papers: Polynomial-time kernel reductions
We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all…
The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…
We consider a problem of learning kernels for use in SVM classification in the multi-task and lifelong scenarios and provide generalization bounds on the error of a large margin classifier. Our results show that, under mild conditions on…
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…
In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…
We introduce a new framework for the analysis of preprocessing routines for parameterized counting problems. Existing frameworks that encapsulate parameterized counting problems permit the usage of exponential (rather than polynomial) time…
We study the existence of polynomial kernels for the problem of deciding feasibility of integer linear programs (ILPs), and for finding good solutions for covering and packing ILPs. Our main results are as follows: First, we show that the…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
The verification of reductions, representative subsets of interleavings, simplifies correctness proofs of parameterized concurrent programs. We introduce an expressive class of syntactic reductions, which we call natural reductions. Natural…
Nowhere dense classes of graphs are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness,…
Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…
The propositional planning problem is a notoriously difficult computational problem. Downey et al. (1999) initiated the parameterized analysis of planning (with plan length as the parameter) and B\"ackstr\"om et al. (2012) picked up this…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…