Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.

What leads Indians to participate in clinical trials? A meta-analysis of qualitative studies.

BACKGROUND: With the globalization of clinical trials, large developing nations have substantially increased their participation in multi-site studies. This participation has raised ethical concerns, among them the fear that local customs, habits and culture are not respected while asking potential participants to take part in study. This knowledge gap is particularly noticeable among Indian subjects, since despite the large number of participants, little is known regarding what factors affect their willingness to participate in clinical trials. METHODS: We conducted a meta-analysis of all studies evaluating the factors and barriers, from the perspective of potential Indian participants, contributing to their participation in clinical trials. We searched both international as well as Indian-specific bibliographic databases, including Pubmed, Cochrane, Openjgate, MedInd, Scirus and Medknow, also performing hand searches and communicating with authors to obtain additional references. We enrolled studies dealing exclusively with the participation of Indians in clinical trials. Data extraction was conducted by three researchers, with disagreement being resolved by consensus. RESULTS: Six qualitative studies and one survey were found evaluating the main themes affecting the participation of Indian subjects. Themes included Personal health benefits, Altruism, Trust in physicians, Source of extra income, Detailed knowledge, Methods for motivating participants as factors favoring, while Mistrust on trial organizations, Concerns about efficacy and safety of trials, Psychological reasons, Trial burden, Loss of confidentiality, Dependency issues, Language as the barriers. CONCLUSION: We identified factors that facilitated and barriers that have negative implications on trial participation decisions in Indian subjects. Due consideration and weightage should be assigned to these factors while planning future trials in India.

Minor Moves: Growth, Fugitivity, and Children's Physical Movement

From tendencies to reduce the Underground Railroad to the imperative "follow the north star" to the iconic images of Ruby Bridges' 1960 "step forward" on the stairs of William Frantz Elementary School, America prefers to picture freedom as an upwardly mobile development. This preoccupation with the subtractive and linear force of development makes it hard to hear the palpable steps of so many truant children marching in the Movement and renders illegible the nonlinear movements of minors in the Underground. Yet a black fugitive hugging a tree, a white boy walking alone in a field, or even pieces of a discarded raft floating downstream like remnants of child's play are constitutive gestures of the Underground's networks of care and escape. Responding to 19th-century Americanists and cultural studies scholars' important illumination of the child as central to national narratives of development and freedom, "Minor Moves" reads major literary narratives not for the child and development but for the fugitive trace of minor and growth.

In four chapters, I trace the physical gestures of Nathaniel Hawthorne's Pearl, Harriet Beecher Stowe's Topsy, Harriet Wilson's Frado, and Mark Twain's Huck against the historical backdrop of the Fugitive Slave Act and the passing of the first compulsory education bills that made truancy illegal. I ask how, within a discourse of independence that fails to imagine any serious movements in the minor, we might understand the depictions of moving children as interrupting a U.S. preoccupation with normative development and recognize in them the emergence of an alternative imaginary. To attend to the movement of the minor is to attend to what the discursive order of a development-centered imaginary deems inconsequential and what its grammar can render only as mistakes. Engaging the insights of performance studies, I regard what these narratives depict as childish missteps (Topsy's spins, Frado's climbing the roof) as dances that trouble the narrative's discursive order. At the same time, drawing upon the observations of black studies and literary theory, I take note of the pressure these "minor moves" put on the literal grammar of the text (Stowe's run-on sentences and Hawthorne's shaky subject-verb agreements). I regard these ungrammatical moves as poetic ruptures from which emerges an alternative and prior force of the imaginary at work in these narratives--a force I call "growth."

Reading these "minor moves" holds open the possibility of thinking about a generative association between blackness and childishness, one that neither supports racist ideas of biological inferiority nor mandates in the name of political uplift the subsequent repudiation of childishness. I argue that recognizing the fugitive force of growth indicated in the interplay between the conceptual and grammatical disjunctures of these minor moves opens a deeper understanding of agency and dependency that exceeds notions of arrested development and social death. For once we interrupt the desire to picture development (which is to say the desire to picture), dependency is no longer a state (of social death or arrested development) of what does not belong, but rather it is what Édouard Glissant might have called a "departure" (from "be[ing] a single being"). Topsy's hard-to-see pick-pocketing and Pearl's running amok with brown men in the market are not moves out of dependency but indeed social turns (a dance) by way of dependency. Dependent, moving and ungrammatical, the growth evidenced in these childish ruptures enables different stories about slavery, freedom, and childishness--ones that do not necessitate a repudiation of childishness in the name of freedom, but recognize in such minor moves a fugitive way out.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.