New Advancements of Scalable Statistical Methods for Learning Latent Structures in Big Data

Constant technology advances have caused data explosion in recent years. Accord- ingly modern statistical and machine learning methods must be adapted to deal with complex and heterogeneous data types. This phenomenon is particularly true for an- alyzing biological data. For example DNA sequence data can be viewed as categorical variables with each nucleotide taking four different categories. The gene expression data, depending on the quantitative technology, could be continuous numbers or counts. With the advancement of high-throughput technology, the abundance of such data becomes unprecedentedly rich. Therefore efficient statistical approaches are crucial in this big data era.

Previous statistical methods for big data often aim to find low dimensional struc- tures in the observed data. For example in a factor analysis model a latent Gaussian distributed multivariate vector is assumed. With this assumption a factor model produces a low rank estimation of the covariance of the observed variables. Another example is the latent Dirichlet allocation model for documents. The mixture pro- portions of topics, represented by a Dirichlet distributed variable, is assumed. This dissertation proposes several novel extensions to the previous statistical methods that are developed to address challenges in big data. Those novel methods are applied in multiple real world applications including construction of condition specific gene co-expression networks, estimating shared topics among newsgroups, analysis of pro- moter sequences, analysis of political-economics risk data and estimating population structure from genotype data.

A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.