004 Datenverarbeitung; Informatik
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Background: For heterogeneous tissues, such as blood, measurements of gene expression are confounded by relative proportions of cell types involved. Conclusions have to rely on estimation of gene expression signals for homogeneous cell populations, e.g. by applying micro-dissection, fluorescence activated cell sorting, or in-silico deconfounding. We studied feasibility and validity of a non-negative matrix decomposition algorithm using experimental gene expression data for blood and sorted cells from the same donor samples. Our objective was to optimize the algorithm regarding detection of differentially expressed genes and to enable its use for classification in the difficult scenario of reversely regulated genes. This would be of importance for the identification of candidate biomarkers in heterogeneous tissues.
Results: Experimental data and simulation studies involving noise parameters estimated from these data revealed that for valid detection of differential gene expression, quantile normalization and use of non-log data are optimal. We demonstrate the feasibility of predicting proportions of constituting cell types from gene expression data of single samples, as a prerequisite for a deconfounding-based classification approach. Classification cross-validation errors with and without using deconfounding results are reported as well as sample-size dependencies. Implementation of the algorithm, simulation and analysis scripts are available.
Conclusions: The deconfounding algorithm without decorrelation using quantile normalization on non-log data is proposed for biomarkers that are difficult to detect, and for cases where confounding by varying proportions of cell types is the suspected reason. In this case, a deconfounding ranking approach can be used as a powerful alternative to, or complement of, other statistical learning approaches to define candidate biomarkers for molecular diagnosis and prediction in biomedicine, in realistically noisy conditions and with moderate sample sizes.
This document presents a formula selection system for classical first order theorem proving based on the relevance of formulae for the proof of a conjecture. It is based on unifiability of predicates and is also able to use a linguistic approach for the selection. The scope of the technique is the reduction of the set of formulae and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the formula set, it can be used as a preprocessor for automated theorem proving. The document contains the conception, implementation and evaluation of both selection concepts. While the one concept generates a search graph over the negation normal forms or Skolem normal forms of the given formulae, the linguistic concept analyses the formulae and determines frequencies of lexemes and uses a tf-idf weighting algorithm to determine the relevance of the formulae. Though the concept is built for first order logic, it is not limited to it. The concept can be used for higher order and modal logik, too, with minimal adoptions. The system was also evaluated at the world championship of automated theorem provers (CADE ATP Systems Competition, CASC-24) in combination with the leanCoP theorem prover and the evaluation of the results of the CASC and the benchmarks with the problems of the CASC of the year 2012 (CASC-J6) show that the concept of the system has positive impact to the performance of automated theorem provers. Also, the benchmarks with two different theorem provers which use different calculi have shown that the selection is independent from the calculus. Moreover, the concept of TEMPLAR has shown to be competitive to some extent with the concept of SinE and even helped one of the theorem provers to solve problems that were not (or slower) solved with SinE selection in the CASC. Finally, the evaluation implies that the combination of the unification based and linguistic selection yields more improved results though no optimisation was done for the problems.