In this paper we consider weighted nonnegative matrix factorizations and we show that the popular algorithms of Lee and Seung can incorporate such a weighting. We then prove that for appropriately chosen weighting matrices, the weighted Euclidean distance function and the weighted generalized Kullback-Leibler divergence function are essentially identical. We finally show that the weighting can ...

The context-tree weighting method (Willems, Shtarkov, and Tjalkens [1995]) is a sequential universal source coding method that achieves the Rissanen lower bound [1984] for tree sources. The same authors also proposed context-tree maximizing, a two-pass version of the context-tree weighting method [1993]. Later Willems and Tjalkens [1998] described a method based on ratios (betas) of sequence pr...

A fundamental task in the analysis of datasets with many variables is screening for associations. This can be cast as a multiple testing task, where objective achieving high detection power while controlling type I error. We consider $m$ hypothesis tests represented by pairs $((P_i, X_i))_{1\leq i \leq m}$ p-values $P_i$ and covariates $X_i$, such that $P_i \perp X_i$ if $H_i$ null. Here, we sh...

PURPOSE The goal of this paper is to extend our recently developed FBP (filtered backprojection) algorithm, which has the same characteristics of an iterative Landweber algorithm, to an FBP algorithm with the same characteristics of an iterative MAP (maximum a posteriori) algorithm. The newly developed FBP algorithm also works when the angular sampling interval is not uniform. The projection no...