Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =

Bayesian nonparametric inference for unimodal and multimodal random probability measures on a finite dimensional Euclidean space is examined. After a short discussion on several concepts of multivatiate unimodality, we introduce and study a new class of nonparametric prior distributions on the subspace of random multivariate multimodal distributions. This class in a way generalizes the very res...

We give a general overview of the state-of-the-art in subspace system identification methods. We have restricted ourselves to the most important ideas and developments since the methods appeared in the late eighties. First, the basis of linear subspace identification are summarized. Different algorithms one finds in literature (Such as N4SID, MOESP, CVA) are discussed and put into a unifyin...

The term “the Curse of Dimensionality” refers to the difficulty of organizing and applying machine learning to data in a very high dimensional space. The reason for this difficulty is that as the dimensionality increases, the volume between different training examples increases rapidly and the data becomes sparse and difficult to classify. So, the predictive power of a machine learning algorith...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

We develop a projection-based dimension reduction approach for partial differential equations with high-dimensional stochastic coefficients. This technique uses samples of the gradient of the quantity of interest (QoI) to partition the uncertainty domain into “active” and “passive” subspaces. The passive subspace is characterized by near-constant behavior of the quantity of interest, while the ...

Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =

Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =