Related papers: Likelihood Geometry of Correlation Models
We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and…
Log-symmetric regression models are particularly useful when the response variable is continuous, strictly positive and asymmetric. In this paper, we proposed a class of log-symmetric regression models in the context of correlated errors.…
Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…
In this paper, we consider the generalized low rank approximation of the correlation matrices problem which arises in the asset portfolio. We first characterize the feasible set by using the Gramian representation together with a special…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
The uncertainties in material and other properties of structures are usually spatially correlated. We introduce an efficient technique for representing and processing spatially correlated random fields in robust topology optimisation of…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its…
Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability value at a time and observing how this affects output probabilities of interest. When one probability is varied then others are…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of…
We give a closed form for the correlation functions of ensembles of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a $2 \times 2$ matrix kernel associated to the ensemble. We also derive closed…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study the semi-algebraic geometry of these models, in particular…
In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…
Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
The generalized Bloch decomposition of a bipartite quantum state gives rise to a correlation matrix whose singular values provide rich information about non-local properties of the state, such as the dimensionality of entanglement. While…