We design and analyze interacting online algorithms for multitask classification that perform better than independent learners whenever the tasks are related in a certain sense. We formalize task relatedness in different ways, and derive formal guarantees on the performance advantage provided by interaction. Our online analysis gives new stimulating insights into previously known co-regularizat...

Let f : (0; 1) ! R be a monotone matrix function of order n for some arbitrary but xed value of n. We show that f is a matrix concave function of order bn=2c and that kf(A) ? f(B)k kf(jA ? Bj)k for all n-by-n positive semideenite matrices A and B, and all unitarily invariant norms k k. Because f is not assumed to be a monotone matrix function of all orders, Loewner's integral representation of ...

A unitarily invariant projective framework is introduced to analyze the complexity of path–following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill–posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale’s γ-Theorem is proven. The main result of this paper bounds the complexity of path–following methods i...

We discuss certain aspects of random multi-matrix models: random matrices chosen at random according to a certain unitarily invariant Gibbs measure on the space of N × N matrices. Thanks to work of Voiculescu, Biane, Guionnet and others, free probability tools can be used to analyze the limiting behavior of such random matrix models. In addition to touching upon a connection between such random...

Let G be a simple non-compact linear Lie group. ? any irreducible unitary representation of with infinitesimal character ? whose continuous part is ?. The beautiful Helgason-Jonson bound in 1969 says that the norm ? upper bounded by ?(G), which stands for half sum positive roots G. current paper aims to give framework sharpen Helgason—Johnson when infinite-dimensional. We have explicit results ...

This paper characterizes the performance of massive multiuser spatial modulation MIMO systems, when a regularized form least-squares method is used for detection. For generic distortion function and right unitarily invariant channel matrices, per-antenna transmit rate asymptotic achieved by this class detectors are derived. Invoking an characterization, we address two particular applications. N...

The classical time-invariant Hankel-norm approximation problem is generalized to the time-varying context. The input-output operator of a time-varying bounded causal linear system acting in discrete time may be specified as a bounded upper-triangular operator T with block matrix entries Tij. For such an operator T, we will define the Hankel norm as a generalization of the time-invariant Hankel ...