Selecting an appropriate set for confounding control is essential for causal inference. The strong ignorability is a strong assumption. With observational data, researchers are unsure the strong ignorability assumption holds. To reduce the possibility of the bias caused by unmeasured confounders, one solution is to include the widest range of pre-treatment covariates, which has been demonstrated to be problematic. Subjective knowledge-based covariate screening is a common approach that has been applied widely. However, under high dimensional settings, it becomes difficult for domain experts to screen thousands of covariates. Machine learning based automatic causal estimation makes it possible for high dimensional causal estimation. While the theoretical properties of these techniques are desirable, they are only necessarily applicable asymptotically (i.e., requiring large sample sizes to be guaranteed to hold), and their performance in smaller samples is sometimes less clear. Data-based pre-processing approaches may fill this gap. Nevertheless, there is no clear guidance on when and how covariate selection should be involved in high dimensional causal estimation. In this dissertation, I address the above issues by (a) providing a classification scheme for major causal covariate selections methods (b) extending causal covariate selection framework (c) conducting a comprehensive empirical Monte Carlo simulation study to illustrate theoretical properties of causal covariate selection and estimation methods, and (d) following-up with a case study to compare different covariate selection approaches in a real data testing ground. Under small sample and/or high dimensional settings, study results indicate choosing an appropriate covariate selection method as pre-processing tool is necessary for causal estimation. Under relatively large sample and low dimensional settings, covariate selection is not necessary for machine learning based automatic causal estimation. Careful pre-processing guided by subjective knowledge is essential.

We propose the idea of deep probabilistic programming, a synthesis of advances for systems at the intersection of probabilistic modeling and deep learning. Such systems enable the development of new probabilistic models and inference algorithms that would otherwise be impossible: enabling unprecedented scales to billions of parameters, distributed and mixed precision environments, and AI accelerators; integration with neural architectures for modeling massive and high-dimensional datasets; and the use of computation graphs for automatic differentiation and arbitrary manipulation of probabilistic programs for flexible inference and model criticism. After describing deep probabilistic programming, we discuss applications in novel variational inference algorithms and deep probabilistic models. First, we introduce the variational Gaussian process (VGP), a Bayesian nonparametric variational family, which adapts its shape to match complex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity of the true posterior. Second, we introduce hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling, thereby defining models via simulators of data with rich hidden structure.

Reinforcement learning (RL) has attracted rapidly increasing interest in the machine learning and artificial intelligence communities in the past decade. With tremendous success already demonstrated for Game AI, RL offers great potential for applications in more complex, real world domains, for example in robotics, autonomous driving and even drug discovery. Although researchers have devoted a lot of engineering effort to deploy RL methods at scale, many state-of-the art RL techniques still seem mysterious - with limited theoretical guarantees on their behaviour in practice. In this thesis, we focus on understanding convergence guarantees for two key ideas in reinforcement learning, namely Temporal difference learning and policy gradient methods, from an optimization perspective. In Chapter 2, we provide a simple and explicit finite time analysis of Temporal difference (TD) learning with linear function approximation. Except for a few key insights, our analysis mirrors standard techniques for analyzing stochastic gradient descent algorithms, and therefore inherits the simplicity and elegance of that literature. Our convergence results extend seamlessly to the study of TD learning with eligibility traces, known as TD(λ), and to Q-learning for a class of high-dimensional optimal stopping problems. In Chapter 3, we turn our attention to policy gradient methods and present a simple and general understanding of their global convergence properties. The main challenge here is that even for simple control problems, policy gradient algorithms face non-convex optimization problems and are widely understood to converge only to a stationary point of the objective. We identify structural properties -- shared by finite MDPs and several classic control problems -- which guarantee that despite non-convexity, any stationary point of the policy gradient objective is globally optimal. In the final chapter, we extend our analysis for finite MDPs to show linear convergence guarantees for many popular variants of policy gradient methods like projected policy gradient, Frank-Wolfe, mirror descent and natural policy gradients.

Modern machine learning consists of both task forces from classical statistics and modern computation. On the one hand, this field becomes rich and quick-growing; on the other hand, different convention from different schools becomes harder and harder to communicate over time. A lot of the times, the problem is not about who is absolutely right or wrong, but about from which angle that one should approach the problem. This is the moment when we feel there should be a unifying machine learning framework that can withhold different schools under the same umbrella. So we propose one of such a framework and call it ``representation learning''. Representations are for the data, which is almost identical to a statistical model. However, philosophically, we would like to distinguish from classical statistical modeling such that (1) representations are interpretable to the scientist, (2) representations convey the pre-existing subject view that the scientist has towards his/her data before seeing it (in other words, representations may not align with the true data generating process), and (3) representations are task-oriented. To build such a representation, we propose to use partition-based models. Partition-based models are easy to interpret and useful for figuring out the interactions between variables. However, the major challenge lies in the computation, since the partition numbers can grow exponentially with respect to the number of variables. To solve the problem, we need a model/representation selection method over different partition models. We proposed to use I-Score with backward dropping algorithm to achieve the goal. In this work, we explore the connection between the I-Score variable selection methodology to other existing methods and extend the idea into developing other objective functions that can be used in other applications. We apply our ideas to analyze three datasets, one is the genome-wide association study (GWAS), one is the New York City Vision Zero, and, lastly, the MNIST handwritten digit database. On these applications, we showed the potential of the interpretability of the representations can be useful in practice and provide practitioners with much more intuitions in explaining their results. Also, we showed a novel way to look at causal inference problems from the view of partition-based models. We hope this work serve as an initiative for people to start thinking about approaching problems from a different angle and to involve interpretability into the consideration when building a model so that it can be easier to be used to communicate with people from other fields.

Includes bibliography. / Ocean waves represent an important design factor in many coastal engineering applications. Although extreme wave height is usually considered the single most important of these factors there are other important aspects that require consideration. These include the probability distribution of wave heights, the seasonal variation and the persistence, or duration, of calm and storm periods. If one is primarily interested in extreme wave height then it is possible to restrict one's attention to events which are sufficiently separated in time to be effectively independently (and possibly even identically) distributed. However the independence assumption is not tenable for the description of many other aspects of wave height behaviour, such as the persistence of calm periods. For this one has to take account of the serial correlation structure of observed wave heights, the seasonal behaviour of the important statistics, such as mean and standard deviation, and in fact the entire seasonal probability distribution of wave heights. In other words the observations have to be regarded as a time series.

This study evaluates the results of three widely used methods for preparing postcensa estimates of counties. The methods are Census Bureau’s Component Method II, the Ratio Correlation Method and the Bogue-Duncan Composite Method. Hypotheses based upon empirical generalizations from previous comparative studies are tested. Statistical tools used are Average Percent Deviation (without regard to sign) and Standard Deviation of Percent Errors. Directional bias and frequency of extreme error are also examined. Evaluations are conducted of the accuracy of the estimates for groups of counties stratified in terms of density and growth rate dimensions. With few exceptions, Ratio Correlation produces consistently better results. The ecological fallacy is illustrated in the application of national migration assumptions, to groups of constituent counties. Averaging the results of different methods does not produce appreciably greater accuracy. Other techniques may be useful in Oregon as benchmarks upon which to evaluate the reasonableness of Ratio Correlation estimates. Efforts in Oregon should be directed toward developing additional and/or more refined data series to be used in Ratio Correlation.

Stormwater treatment is commonly performed with a combination of approaches including the utilization of natural systems and engineered devices. Before using a proprietary treatment instrument it is required to verify its performance and efficiency in reducing different pollution components including the TSS. Different states have developed strategies and regulations for accepting new instruments. In this thesis the stormwater management plan of the City of Portland, Oregon(2008), is analyzed in order to improve the current regulations. These rules apply to new technologies which are proposed by vendors to be used in Portland's stormwater treatment plans. Each requirement which should be met by the applying vendors is thoroughly analyzed followed by a comparison with the Stormwater management plan(2008)regulations of the state of Washington the so called Technology Assessment Plan-Ecology TAPE (Howie, 2011). Because of the similarities in the climate and land use between these two testing frameworks in order to evaluate the potential applicability of data submitted by vendors who had devices approved by Washington, to be utilized by Portland. The treatment of total suspended solids (TSS) is the focus of this thesis since it is central to the testing process and since most of the other pollutions are attached to TSS and will get treated if TSS is treated. The overall analysis shows that Portland adopts more restrictive requirements on the characterization of stormwater event samples to be treated by a technological instrument while Washington's restriction are more stringent on the efficiency of total suspended solid removal, in which it demands higher standards on the treatment of TSS compared to Portland's efficiency requirements. In order to study practical context in which regulations are administrated by Portland, rainfall data from 66 gauges covering the period of 1980-2011 was studied and the impacts of seasonality, land use, land form, periods of no rain before and after an event and Portland's Modified Performance line on the number of accepted rain events were analyzed. The results which were accepted by state of Washington were also compared with the results accepted by the city of Portland on Portland's Standard Performance line. Our seasonality study suggests that Portland's requirements are unnecessarily restrictive which results in the disqualification of many otherwise useful stormwater events, sometimes allowing no natural events to be available for testing in dry years. The analysis of land use showed that land use has no statistically significant impact on the concentration levels of TSS, thereby indicating that land use restrictions in the testing rules could be usefully relaxed. Decreasing the interevent no-rain period significantly increases the total number of events providing sufficient data to assess the performance of treatment facilities. We also showed that many more events become suitable for performance testing if events separated by one hours or less are considered a single, longer event. Finally we identified a statistical relationship between number of forecasted accepted stormwater events and the total average daily precipitation in a given year.

Indiana University-Purdue University Indianapolis (IUPUI) / With the availability of electronic medical records, medication dispensing data offers an unprecedented opportunity for researchers to explore complex relationships among longterm medication use, disease progression and potential side-effects in large patient populations. However, these data also pose challenges to existing statistical models because both medication exposure status and its intensity vary over time. This dissertation focused on flexible models to investigate the association between time-varying exposures and different types of outcomes. First, a penalized functional regression model was developed to estimate the effect of time-varying exposures on multivariate longitudinal outcomes. Second, for survival outcomes, a regression spline based model was proposed in the Cox proportional hazards (PH) framework to compare disease risk among different types of time-varying exposures. Finally, a penalized spline based Cox PH model with functional interaction terms was developed to estimate interaction effect between multiple medication classes. Data from a primary care patient cohort are used to illustrate the proposed approaches in determining the association between antidepressant use and various outcomes. / NIH grants, R01 AG019181 and P30 AG10133.

Indiana University-Purdue University Indianapolis (IUPUI) / A semi-parametric approach incorporates parametric and nonparametric functions in the model and is very useful in situations when a fully parametric model is inadequate. The objective of this dissertation is to extend statistical methodology employing the semi-parametric modeling approach to analyze data in health science research areas. This dissertation has three parts. The first part discusses the modeling of the dose-response relationship with correlated data by introducing overall drug effects in addition to the deviation of each subject-specific curve from the population average. Here, a penalized spline regression method that allows modeling of the smooth dose-response relationship is applied to data in studies monitoring malaria drug resistance through the ex-vivo assays.The second part of the dissertation extends the SiZer map, which is an exploratory and a powerful visualization tool, to detect underlying significant features (increase, decrease, or no change) of the curve at various smoothing levels. Here, Penalized Spline Significant Zero Crossings of Derivatives (PS-SiZer), using a penalized spline regression, is introduced to investigate significant features in correlated data arising from longitudinal settings. The third part of the dissertation applies the proposed PS-SiZer methodology to analyze HIV data. The durability of significant weight change over a period is explored from the PS-SiZer visualization. PS-SiZer is a graphical tool for exploring structures in curves by mapping areas where rate of change is significantly increasing, decreasing, or does not change. PS-SiZer maps provide information about the significant rate of weigh change that occurs in two ART regimens at various level of smoothing. A penalized spline regression model at an optimum smoothing level is applied to obtain an estimated first-time point where weight no longer increases for different treatment regimens.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science, Faculty of Science University of the Witwatersrand, Johannesburg 2018 / Canteen Kopje has yielded rare in-situ assemblages of the Fauresmith, a poorly defined industry often associated with the later Acheulean. The Fauresmith contains precocious developments in technology as early as ~0.5 Ma–features which only become widespread in the ensuing Middle Stone Age. The Fauresmith as a regional industry provides insight into technological practices during the period of significant behavioural diversification associated with archaic Homo sapiens. Previous excavations were conducted with relatively low spatial resolution. A new excavation, Pit 4 West, was conducted to investigate the spatial, stratigraphic and contextual association of the Fauresmith horizon in more detail. A multi-disciplinary fineresolution geoarchaeological approach was applied. A nuanced assessment of the Fauresmith’s context was developed, with macroscopic and microscopic analyses allowing for the identification of site formation processes influencing assemblages. The artefact sample size for the site was increased and the presence of diagnostic tools has aided in formally defining the Fauresmith at Canteen Kopje. / XL2019