Related papers: Bayes linear adjustment for variance matrices

We propose a geometric framework to assess sensitivity of Bayesian procedures to modeling assumptions based on the nonparametric Fisher-Rao metric. While the framework is general in spirit, the focus of this article is restricted to…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

We consider a financial market in which traders potentially face restrictions in trading some of the available securities. Traders are heterogeneous with respect to their beliefs and risk profiles, and the market is assumed thin: traders…

Building models that comply with the invariances inherent to different domains, such as invariance under translation or rotation, is a key aspect of applying machine learning to real world problems like molecular property prediction,…

In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by…

Understanding how neural representations respond to geometric transformations is essential for evaluating whether learned features preserve meaningful spatial structure. Existing approaches primarily assess robustness primarily by comparing…

In recent years there has been interest in the theory of local computation over probabilistic Bayesian graphical models. In this paper, local computation over Bayes linear belief networks is shown to be amenable to a similar approach.…

Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence…

According to recent findings [1,2], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can…

We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and…

This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window…

We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…

The human visual system is able to recognize objects despite transformations that can drastically alter their appearance. To this end, much effort has been devoted to the invariance properties of recognition systems. Invariance can be…

The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…

We propose a novel variational Bayes approach to estimate high-dimensional vector autoregression (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural VAR representation of the parameter…

Variational Bayes methods are popular due to their computational efficiency and adaptability to diverse applications. In specifying the variational family, mean-field classes are commonly used, which enables efficient algorithms such as…

The vacuum sector of the Brans-Dicke theory is studied from the viewpoint of a non-conformally invariant gravitational model. We show that, this theory can be conformally symmetrized using an appropriate conformal transformation. The…

There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…