ar X iv : 0 90 2 . 33 47 v 1 [ st at . M L ] 1 9 Fe b 20 09 Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression ∗

Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression

The Degrees of Freedom of Kernel Partial Least Squares (KPLS) require all eigenvalues of the kernel matrix K, hence the computation is cubic in the number of observations n. •We use Kernel PLS itself to approximate the eigenvalues of the kernel matrix. −→ We can compute approximate Degrees of Freedom of KPS in O ( n2 ) ! •We can also compute approximate confidence intervals for KPLS in O ( n2 ) !

ar X iv : 0 90 2 . 33 48 v 1 [ m at h . R T ] 1 9 Fe b 20 09 On Lie algebras associated with representation directed algebras

Let B be a representation-finite C-algebra. The Z-Lie algebra L(B) associated with B has been defined by Ch. Riedtmann in [17]. If B is representation-directed there is another Z-Lie algebra associated with B defined by C. M. Ringel in [20] and denoted by K(B). We prove that the Lie algebras L(B) and K(B) are isomorphic for any representation-directed C-algebra B. 2000 Mathematics Subject Class...

ar X iv : 0 90 2 . 32 39 v 1 [ m at h . D G ] 1 8 Fe b 20 09 Gauge theory in higher dimensions , II

ar X iv : 0 90 2 . 39 12 v 1 [ m at h . G R ] 2 3 Fe b 20 09 Brent Everitt The Combinatorial Topology

ar X iv : 0 90 3 . 19 51 v 1 [ m at h . ST ] 1 1 M ar 2 00 9 Invariance principles for linear processes . Application to isotonic regression

In this paper we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights these processes can exhibit long range dependence and the limiting distribution is a fractional Brownian motion. The proofs are based on new approximations by a linear process with martingale difference...