Factorization in molecular modeling and belief propagation algorithms.

Factorization reduces computational complexity, and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for (junction) trees, and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is the common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development of factorization algorithms for physical modeling of complex molecular systems.

Corrigendum to "Classification of Non-Small Cell Lung Cancer Using Significance Analysis of Microarray-Gene Set Reduction Algorithm".

[This corrects the article DOI: 10.1155/2016/2491671.].

Classification of Non-Small Cell Lung Cancer Using Significance Analysis of Microarray-Gene Set Reduction Algorithm.

Among non-small cell lung cancer (NSCLC), adenocarcinoma (AC), and squamous cell carcinoma (SCC) are two major histology subtypes, accounting for roughly 40% and 30% of all lung cancer cases, respectively. Since AC and SCC differ in their cell of origin, location within the lung, and growth pattern, they are considered as distinct diseases. Gene expression signatures have been demonstrated to be an effective tool for distinguishing AC and SCC. Gene set analysis is regarded as irrelevant to the identification of gene expression signatures. Nevertheless, we found that one specific gene set analysis method, significance analysis of microarray-gene set reduction (SAMGSR), can be adopted directly to select relevant features and to construct gene expression signatures. In this study, we applied SAMGSR to a NSCLC gene expression dataset. When compared with several novel feature selection algorithms, for example, LASSO, SAMGSR has equivalent or better performance in terms of predictive ability and model parsimony. Therefore, SAMGSR is a feature selection algorithm, indeed. Additionally, we applied SAMGSR to AC and SCC subtypes separately to discriminate their respective stages, that is, stage II versus stage I. Few overlaps between these two resulting gene signatures illustrate that AC and SCC are technically distinct diseases. Therefore, stratified analyses on subtypes are recommended when diagnostic or prognostic signatures of these two NSCLC subtypes are constructed.