Model averaging and dimension selection for the singular value decomposition

Bayesian averaging of computer models with domain discrepancies: a nuclear physics perspective

This article studies Bayesian model averaging (BMA) in the context of competing expensive computer models in a typical nuclear physics setup. While it is well known that BMA accounts for the additional uncertainty of the model itself, we show that it also decreases the posterior variance of the prediction errors via an explicit decomposition. We extend BMA to the situation where the competing models are defined on non-identical study regions. Any model's local forecasting difficulty is offset by predictions obtained from the average model, thus extending individual models to the full domain. W…

通过最优模型平均改进张量回归

Improving tensor regression by optimal model averaging

针对张量回归中CP分解秩选择的不确定性问题，提出一种对不同秩候选模型加权的模型平均方法，证明了其渐近最优性和参数一致性，实验验证了其优越性。

A Consistency Theorem for Randomized Singular Value Decomposition

The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for developing efficient large-scale SVD algorithms. Randomized SVD was proposed, and its potential was demonstrated for computing a low-rank SVD (Rokhlin et al., 2009). In this article, we provide a consistency theorem for the randomized SVD algorithm and a numerical example to show how the random projections to low dimension affect the consistency.

Perturbation expansions and error bounds for the truncated singular value decomposition

Truncated singular value decomposition is a reduced version of the singular value decomposition in which only a few largest singular values are retained. This paper presents a novel perturbation analysis for the truncated singular value decomposition for real matrices. First, we describe perturbation expansions for the singular value truncation of order $r$. We extend perturbation results for the singular subspace decomposition to derive the first-order perturbation expansion of the truncated operator about a matrix with rank greater than or equal to $r$. Observing that the first-order expansi…

Total singular value decomposition. Robust SVD, regression and location-scale

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some rank restriction. However often we are interested in the best components of the decomposition rather than in the best approximation . This conflict of objectives leads us to introduce {\em Total SVD}, where the word "Total" is taken as in "Total" least squares. SVD is a least squares method and, therefore, is very sensitive to gross errors in the data matrix.…

Singular value decomposition of large random matrices (for two-way classification of microarrays)

Asymptotic behavior of the singular value decomposition (SVD) of blown up matrices and normalized blown up contingency tables exposed to Wigner-noise is investigated.It is proved that such an m\times n matrix almost surely has a constant number of large singular values (of order \sqrt{mn}), while the rest of the singular values are of order \sqrt{m+n} as m,n\to\infty. Concentration results of Alon et al. for the eigenvalues of large symmetric random matrices are adapted to the rectangular case, and on this basis, almost sure results for the singular values as well as for the corresponding isot…