Several Inverse Problems In Computational Medicine

The computational medicine is one of the most important applications for statistical machine learning.The overall goal of the computational medicine is to understand,control and predict complex human diseases based on high-throughput experimental data.Further more achieving precise personalized medical,ultimately.Generally speaking,this problem is a typical inverse problem,which needs multi-crossed disciplines of statistical machine learning,stochastic process,biophysics and other fields.A theme for this thesis is to seek the low complexity solution for the ill posed problem.In this paper,we mainly focus on several problems,such as the reconstruction of biomolecular network and the representation of cancer phenotypes.The main contribution of our work are summarized as following:1.A graphical model of smoking-induced global instability in lung cancer.Smoking is the major cause of lung cancer and the leading cause of cancer-related death in the world.The most current view about lung cancer is no longer limited to individual genes being mutated by any carcinogenic insults from smoking.Instead,tumorigenesis is a phenotype conferred by many systematic and global alterations,leading to extensive heterogeneity and variation for both the genotypes and phenotypes of individual cancer cells.Thus,strategically it is foremost important to develop a methodology to capture any consistent and global alterations presumably shared by most of the cancerous cells for a given population.This is particularly true that almost all of the data collected from solid cancers?including lung cancers?are usually distant apart over a large span of temporal or even spatial contexts.Here we report a multiple non-Gaussian graphical model to reconstruct the gene interaction network using two previously published gene expression datasets.Our graphical model aims to selectively detect gross structural changes at the level of gene interaction networks.Our methodology is extensively validated,demonstrating good robustness,as well as the selectivity and specificity expected based on our biological insights.In summary,gene reg- ulatory networks are still relatively stable during presumably the early stage of neoplastic transformation.But drastic structural differences can be found between lung cancer and its normal control,including the gain of functional modules for cellular proliferations such as EGFR and PDGFRA,as well as the lost of the important IL6 module,supporting their roles as potential drug targets.Interestingly,our method can also detect early modular changes, with the ALDH3A1 and its associated interactions being strongly implicated as a potential early marker,whose activations appear to alter LCN2 module as well as its interactions with the important TP53-MDM2 circuitry.Our strategy using the graphical model to reconstruct gene interaction work with biologically-inspired constraints exemplifies the importance and beauty of biology in developing any bio-computational approach.2.Learning latent variable Gaussian graphical model for biomolecular network with low sample complexity.Learning a Gaussian graphical model with latent variables is ill posed when there is insufficient sample complexity,thus having to be appropriately regularized.A common choice is convex?₁plus nuclear norm to regularize the searching process.How- ever,the best estimator performance is not always achieved with this additive convex reg- ularizations,especially when the sample complexity is low.In this paper,we consider a concave additive regularization which does not require the strong irrepresentable condition. We use concave regularization to correct the intrinsic estimation biases from Lasso and nu- clear penalty as well.We establish the proximity operators for our concave regularizations respectively,which induces sparsity and low rankness.In addition,we extend our method to also allowing the decomposition of fused structure-sparsity plus low-rankness,providing a powerful tool for models with temporal information.Specifically,we develop a non-trivial modified alternating direction method of multipliers with at least local convergence.Finally, we use both synthetic and real data to validate the excellence of our method.In the ap- plication of reconstructing two stage cancer networks,”the Warbug effect”can be revealed directly.3.Learning a structural and functional representation for gene expressions:To robustly dissect complex cancer phenotypes Cancer is a heterogeneous disease,thus one of the cen- tral problems is how to dissect the resulting complex phenotypes in terms of their biological building blocks.Computationally,this is to represent and interpret high dimensional obser- vations through a structural and conceptual abstraction into the most influential determinants underlying the problem.The working hypothesis of this report is to consider gene interaction to be largely responsible for the manifestation of complex cancer phenotypes,thus where the representation is to be conceptualized.Here we report a representation learning strategy combined with regularizations,in which gene expressions are described in terms of a regu- larized product of meta-genes and their expression levels.The meta-genes are constrained by gene interactions thus representing their original topological contexts.The expression levels are supervised by their conditional dependencies among the observations thus providing a cluster-specific constraint.We obtain both of these structural constraints using a node-based graphical model.Our representation allows the selection of more influential modules,thus implicating their possible roles in neoplastic transformations.We validate our representa-tion strategy by its robust recognitions of various cancer phenotypes comparing with various classical methods.The modules discovered are either shared or specify for different types or stages of human cancers,all of which are consistent with literature and biology.