Related papers: A Linear Relationship between Correlation and Cohe…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
In this paper we analyse some questions concerning trees on $\kappa$, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in…
Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields.…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
Canonical Correlation Analysis (CCA) is a classical tool for finding correlations among the components of two random vectors. In recent years, CCA has been widely applied to the analysis of genomic data, where it is common for researchers…
We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…
Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do…
For a cardinal kappa and a model M of cardinality kappa let No(M) denote the number of non-isomorphic models of cardinality kappa which are L_{infty,kappa}--equivalent to M. In [Sh:133] Shelah established that when kappa is a weakly compact…
Let $G$ be a graph, $C$ a longest cycle in $G$ and $\overline{p}$, $\overline{c}$ the lengths of a longest path and a longest cycle in $G\backslash C$, respectively. Almost all lower bounds for the circumference base on a standard…
Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between…
In the first part of this paper we develop some theorems in linear algebra applicable to information theory when all random variables involved are linear functions of the individual bits of a source of independent bits. We say that a…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…
The concept of generalized $k$-connectivity $\kappa_{k}(G)$ of a graph $G$ was introduced by Chartrand et al. in recent years. In our early paper, extremal theory for this graph parameter was started. We determined the minimal number of…
In the negative perceptron problem we are given $n$ data points $({\boldsymbol x}_i,y_i)$, where ${\boldsymbol x}_i$ is a $d$-dimensional vector and $y_i\in\{+1,-1\}$ is a binary label. The data are not linearly separable and hence we…
We study local computation algorithms (LCA) for maximum matching. An LCA does not return its output entirely, but reveals parts of it upon query. For matchings, each query is a vertex $v$; the LCA should return whether $v$ is matched -- and…
Measurement of the interrater agreement (IRA) is critical in various disciplines. To correct for potential confounding chance agreement in IRA, Cohen's kappa and many other methods have been proposed. However, owing to the varied strategies…
Network alignment, or the task of finding corresponding nodes in different networks, is an important problem formulation in many application domains. We propose CAPER, a multilevel alignment framework that Coarsens the input graphs, Aligns…
It is well known the concept of the condition number $\kappa(A) = \|A\|\|A^{-1}\|$, where $A$ is a $n \times n$ real or complex matrix and the norm used is the spectral norm. Although it is very common to think in $\kappa(A)$ as "the"…
In this paper we use infinitary Turing machines with tapes of length $\kappa$ and which run for time $\kappa$ as presented, e.g., by Koepke \& Seyfferth, to generalise the notion of type two computability to $2^{\kappa}$, where $\kappa$ is…