Non-parametric and semi-parametric methods for parsimonious statistical learning with complex data

In clinical research, non-parametric and semi-parametric methods are increasingly gathering importance as statistical tools to infer on accumulated data. They require fewer assumptions and their applicability is much wider than the corresponding parametric methods. Being robust, these methods are seen by some statisticians as leaving less room for improper use and misunderstanding. In this dissertation we study some of these nonparametric and semiparametric methods in statistical learning and their applications to various areas of biomedical research. In the first part of our dissertation, we study the application of temporal process regression in the study of medical adherence. Adherence refers to the act of conforming to the recommendations made by the provider with respect to timing, dosage, and frequency of medication taking. Here we assess the effect of drug adherence in the study of viral resistance to antiviral therapy for chronic Hepatitis C. We use Temporal Process Regression (Fine, Yan, and Kosorok 2004) to model adherence as a longitudinal predictor of SVR. We show that adherence has a significant effect on SVR and this analysis can serve as an archetype for more statistically efficient analyses of medical adherence in studies where the common theme till now has been to report summary statistics. In the second part of the dissertation, we develop an approach for feature elimination in support vector machines, based on recursive elimination of features. We present theoretical properties of this method and show that this is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present case studies to show that the assumptions are met in most practical situations and give simulation studies to demonstrate performance of the proposed approach. In the third part of the dissertation we focus our attention to feature selection in Q-learning. Here we discuss three different methods for feature selection, based on the same vital idea of feature screening through ranking in a sequential backward selection scheme. We discussed the applicability of the methods, reasoned on heuristics stemming from our previous work on feature selection in support vector machines and gave results showing their performance in various simulated settings.Doctor of Philosoph

Probing composite Higgs boson substructure at the HL-LHC

The Higgs boson may well be a composite scalar with a finite extension in space. Owing to the momentum dependence of its couplings, the imprints of such a composite pseudo Goldstone Higgs may show up in the tails of various kinematic distributions at the LHC, distinguishing it from an elementary state. From the bottom up, we construct the momentum-dependent form factors to capture the interactions of the composite Higgs with the weak gauge bosons. We demonstrate their impact in the differential distributions of various kinematic parameters for the pp -> Z*H -> l+l-bb over bar channel. We show that this channel can provide an important handle to probe the Higgs\u27 substructure at the HL-LHC

Kinematics of deformable media

We investigate the kinematics of deformations in two and three dimensional media by explicitly solving (analytically) the evolution equations (Raychaudhuri equations) for the expansion, shear and rotation associated with the deformations. The analytical solutions allow us to study the dependence of the kinematical quantities on initial conditions. In particular, we are able to identify regions of the space of initial conditions that lead to a singularity in finite time. Some generic features of the deformations are also discussed in detail. We conclude by indicating the feasibility and utility of a similar exercise for fluid and geodesic flows in flat and curved spacetimes.Comment: 28 pages, 12 figure

A docking interaction study of the effect of critical mutations in ribonuclease a on protein-ligand binding

Enzymes with ribonucleolytic activity play a pivotal role in gene expression and cellular homeostasis by altering the levels of cellular RNA. Ribonuclease A has been the most well studied of such enzymes whose histidine residues (His12 and His119) play a crucial role in the catalytic mechanism of the protein. The ligands chosen for this study, 2′CMP and 3′CMP, act as competitive substrate analog inhibitors of this enzyme. Using molecular graphics software freely available for academic use, AutoDock and PyMol, we demonstrate that substitution of either histidine residue by alanine causes marked changes in the distances between these critical residues of the enzyme. The ligands in the docked conformation (particularly on mutation of His119 to Ala) compensate for the altered free energy and hydrogen bonding abilities in these new protein‐ligand complexes