Fast and robust imputation for miRNA expression data using constrained least squares

High dimensional transcriptome profiling, whether through next generation sequencing techniques or high-throughput arrays, may result in scattered variables with missing data. Data imputation is a common strategy to maximize the inclusion of samples by using statistical techniques to fill in missing values. However, many data imputation methods are cumbersome and risk introduction of systematic bias. Here we present a new data imputation method using constrained least squares and algorithms from the inverse problems literature and present applications for this technique in miRNA expression analysis. The proposed technique is shown to offer an imputation orders of magnitude faster, with greater than or equal accuracy when compared to similar methods from the literature.

Sparse Constrained Least-Squares Reverse Time Migration Based on Kirchhoff Approximation

Least-squares reverse time migration (LSRTM) is powerful for imaging complex geological structures. Most researches are based on Born modeling operator with the assumption of small perturbation. However, studies have shown that LSRTM based on Kirchhoff approximation performs better; in particular, it generates a more explicit reflected subsurface and fits large offset data well. Moreover, minimizing the difference between predicted and observed data in a least-squares sense leads to an average solution with relatively low quality. This study applies L1-norm regularization to LSRTM (L1-LSRTM) based on Kirchhoff approximation to compensate for the shortcomings of conventional LSRTM, which obtains a better reflectivity image and gets the residual and resolution in balance. Several numerical examples demonstrate that our method can effectively mitigate the deficiencies of conventional LSRTM and provide a higher resolution image profile.

Construction of stochastic simulation metamodels with segmented polynomials

Metamodels are an important tool in simulation analysis as they can provide insight about the behavior of the simulation response. Modeling the response with low-degree polynomial segments allows the identification of different behavior zones and the parameters still have relation with the physical world. The purpose of this paper is to extend the use of segmented polynomial functions for simulation metamodeling, where the segments have at most identical value and slope at the breaks. Our approach is to build segmented polynomials metamodels where the hypothesis of degree and continuity of splines are less exigent, allowing more flexibility of the approximation. When breaks are known, constrained least squares are used for metamodel estimation, taking into account the linear formulation of the problem. If breaks have to be estimated, the unconstrained nonlinear regression theory is used, when it can be applied. Otherwise, the estimation is performed using an iterative algorithm which is applied repeatedly in a cyclic manner for estimating the breaks, and jackknifing yields the confidence intervals.