We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by the maximum marginal likelihood estimator can be regarded as a variational approximation to a hierarchical Bayes posterior distribution. This connection between empirical Bayes and variational Bayes allows us to leverage the recent results in the variational Bayes literature, and directly obtains the convergence rates of empirical Bayes posterior distributions from a variational perspective. For a more general hyperparameter set that is not necessarily discrete, we introduce a new technique called "prior decomposition" to deal with prior distributions that can be written as convex combinations of probability measures whose supports are low-dimensional subspaces. This leads to generalized versions of the classical "prior mass and testing" conditions for the convergence rates of empirical Bayes. Our theory is applied to a number of statistical estimation problems including nonparametric density estimation and sparse linear regression.

Machine learning (ML) offers a collection of powerful approaches for detecting and modeling associations, often applied to data having a large number of features and/or complex associations. Currently, there are many tools to facilitate implementing custom ML analyses (e.g. scikit-learn). Interest is also increasing in automated ML packages, which can make it easier for non-experts to apply ML and have the potential to improve model performance. ML permeates most subfields of biomedical research with varying levels of rigor and correct usage. Tremendous opportunities offered by ML are frequently offset by the challenge of assembling comprehensive analysis pipelines, and the ease of ML misuse. In this work we have laid out and assembled a complete, rigorous ML analysis pipeline focused on binary classification (i.e. case/control prediction), and applied this pipeline to both simulated and real world data. At a high level, this 'automated' but customizable pipeline includes a) exploratory analysis, b) data cleaning and transformation, c) feature selection, d) model training with 9 established ML algorithms, each with hyperparameter optimization, and e) thorough evaluation, including appropriate metrics, statistical analyses, and novel visualizations. This pipeline organizes the many subtle complexities of ML pipeline assembly to illustrate best practices to avoid bias and ensure reproducibility. Additionally, this pipeline is the first to compare established ML algorithms to 'ExSTraCS', a rule-based ML algorithm with the unique capability of interpretably modeling heterogeneous patterns of association. While designed to be widely applicable we apply this pipeline to an epidemiological investigation of established and newly identified risk factors for pancreatic cancer to evaluate how different sources of bias might be handled by ML algorithms.

The objective of this study is to create and test a hybrid deep learning model, FastGRNN-FCN (Fast, Accurate, Stable and Tiny Gated Recurrent Neural Network-Fully Convolutional Network), for urban flood prediction and situation awareness using channel network sensors data. The study used Harris County, Texas as the testbed, and obtained channel sensor data from three historical flood events (e.g., 2016 Tax Day Flood, 2016 Memorial Day flood, and 2017 Hurricane Harvey Flood) for training and validating the hybrid deep learning model. The flood data are divided into a multivariate time series and used as the model input. Each input comprises nine variables, including information of the studied channel sensor and its predecessor and successor sensors in the channel network. Precision-recall curve and F-measure are used to identify the optimal set of model parameters. The optimal model with a weight of 1 and a critical threshold of 0.59 are obtained through one hundred iterations based on examining different weights and thresholds. The test accuracy and F-measure eventually reach 97.8% and 0.792, respectively. The model is then tested in predicting the 2019 Imelda flood in Houston and the results show an excellent match with the empirical flood. The results show that the model enables accurate prediction of the spatial-temporal flood propagation and recession and provides emergency response officials with a predictive flood warning tool for prioritizing the flood response and resource allocation strategies.

Reconstructing parameters of physical models is an important task in science. Usually, such problems are severely under determined and sophisticated reconstruction techniques are necessary. Whereas classical regularisation methods focus on finding just the most desirable or most likely solution of an inverse problem, more recent methods focus on analyzing the complete distribution of possible parameters. In particular, this provides us with a way to quantify how trustworthy the obtained solution is. Among the most popular methods for uncertainty quantification are Bayesian methods [16], which build up on evaluating the posterior using Bayes theorem, and Markov Chain Monte Carlo (MCMC) [38].

We formulate meta learning using information theoretic concepts such as mutual information and the information bottleneck. The idea is to learn a stochastic representation or encoding of the task description, given by a training or support set, that is highly informative about predicting the validation set. By making use of variational approximations to the mutual information, we derive a general and tractable framework for meta learning. We particularly develop new memorybased meta learning algorithms based on Gaussian processes and derive extensions that combine memory and gradient-based meta learning. We demonstrate our method on few-shot regression and classification by using standard benchmarks such as Omniglot, mini-Imagenet and Augmented Omniglot. Such systems require training deep neural networks from a set of tasks drawn from a common distribution, where each task is described by a small amount of experience, typically divided into a training or support set and a validation set. By sharing information across tasks the neural network can learn to rapidly adapt to new tasks and generalize from few examples at test time. Several few-shot learning algorithms use memory-based (Vinyals et al., 2016; Ravi & Larochelle, 2017) or gradient-based procedures (Finn et al., 2017; Nichol et al., 2018), with the gradient-based model agnostic meta learning algorithm (MAML) by Finn et al. (2017) being very influential in the literature. Despite the success of specific schemes, one fundamental issue in meta learning is concerned with deriving unified principles that can allow to relate different approaches and invent new schemes.

Question classification (QC) is a prime constituent of automated question answering system. The work presented here demonstrates that the combination of multiple models achieve better classification performance than those obtained with existing individual models for the question classification task in Bengali. We have exploited state-of-the-art multiple model combination techniques, i.e., ensemble, stacking and voting, to increase QC accuracy. Lexical, syntactic and semantic features of Bengali questions are used for four well-known classifiers, namely Naïve Bayes, kernel Naïve Bayes, Rule Induction, and Decision Tree, which serve as our base learners. Single-layer question-class taxonomy with 8 coarse-grained classes is extended to two-layer taxonomy by adding 69 fine-grained classes. We carried out the experiments both on single-layer and two-layer taxonomies. Experimental results confirmed that classifier combination approaches outperform single classifier classification approaches by 4.02% for coarse-grained question classes. Overall, the stacking approach produces the best results for fine-grained classification and achieves 87.79% of accuracy. The approach presented here could be used in other Indo-Aryan or Indic languages to develop a question answering system. Both theoretical [22, 23] and empirical [24-26] studies confirm that the classifier combination approach is generally more accurate than any of the individual classifiers making up the ensemble. Furthermore, a number of studies [27, 30] were successfully carried out on classifier combination methods for the QC task which outperformed the individual classifiers.

Introduced by Kiefer and Wolfowitz \cite{KW56}, the nonparametric maximum likelihood estimator (NPMLE) is a widely used methodology for learning mixture odels and empirical Bayes estimation. Sidestepping the non-convexity in mixture likelihood, the NPMLE estimates the mixing distribution by maximizing the total likelihood over the space of probability measures, which can be viewed as an extreme form of overparameterization. In this paper we discover a surprising property of the NPMLE solution. Consider, for example, a Gaussian mixture model on the real line with a subgaussian mixing distribution. Leveraging complex-analytic techniques, we show that with high probability the NPMLE based on a sample of size $n$ has $O(\log n)$ atoms (mass points), significantly improving the deterministic upper bound of $n$ due to Lindsay \cite{lindsay1983geometry1}. Notably, any such Gaussian mixture is statistically indistinguishable from a finite one with $O(\log n)$ components (and this is tight for certain mixtures). Thus, absent any explicit form of model selection, NPMLE automatically chooses the right model complexity, a property we term \emph{self-regularization}. Extensions to other exponential families are given. As a statistical application, we show that this structural property can be harnessed to bootstrap existing Hellinger risk bound of the (parametric) MLE for finite Gaussian mixtures to the NPMLE for general Gaussian mixtures, recovering a result of Zhang \cite{zhang2009generalized}.

Machine learning models suffer from overfitting, which is caused by a lack of labeled data. To tackle this problem, we proposed a framework of regularization methods, called density-fixing, that can be used commonly for supervised and semi-supervised learning. Our proposed regularization method improves the generalization performance by forcing the model to approximate the class's prior distribution or the frequency of occurrence. This regularization term is naturally derived from the formula of maximum likelihood estimation and is theoretically justified. We further provide the several theoretical analyses of the proposed method including asymptotic behavior. Our experimental results on multiple benchmark datasets are sufficient to support our argument, and we suggest that this simple and effective regularization method is useful in real-world machine learning problems.

This thesis develops a conceptual framework considering social data as representing the surface layer of a hierarchy of human social behaviours, needs and cognition which is employed to transform social data into representations that preserve social behaviours and their causalities. Based on this framework two platforms were built to capture insights from fast-paced and slow-paced social data. For fast-paced, a self-structuring and incremental learning technique was developed to automatically capture salient topics and corresponding dynamics over time. An event detection technique was developed to automatically monitor those identified topic pathways for significant fluctuations in social behaviours using multiple indicators such as volume and sentiment. This platform is demonstrated using two large datasets with over 1 million tweets. The separated topic pathways were representative of the key topics of each entity and coherent against topic coherence measures. Identified events were validated against contemporary events reported in news. Secondly for the slow-paced social data, a suite of new machine learning and natural language processing techniques were developed to automatically capture self-disclosed information of the individuals such as demographics, emotions and timeline of personal events. This platform was trialled on a large text corpus of over 4 million posts collected from online support groups. This was further extended to transform prostate cancer related online support group discussions into a multidimensional representation and investigated the self-disclosed quality of life of patients (and partners) against time, demographics and clinical factors. The capabilities of this extended platform have been demonstrated using a text corpus collected from 10 prostate cancer online support groups comprising of 609,960 prostate cancer discussions and 22,233 patients.

The increased computerization in recent years has resulted in the production of a variety of different software, however measures need to be taken to ensure that the produced software isn't defective. Many researchers have worked in this area and have developed different Machine Learning-based approaches that predict whether the software is defective or not. This issue can't be resolved simply by using different conventional classifiers because the dataset is highly imbalanced i.e the number of defective samples detected is extremely less as compared to the number of non-defective samples. Therefore, to address this issue, certain sophisticated methods are required. The different methods developed by the researchers can be broadly classified into Resampling based methods, Cost-sensitive learning-based methods, and Ensemble Learning. Among these methods. This report analyses the performance of the Online Sequential Extreme Learning Machine (OS-ELM) proposed by Liang et.al. against several classifiers such as Logistic Regression, Support Vector Machine, Random Forest, and Na\"ive Bayes after oversampling the data. OS-ELM trains faster than conventional deep neural networks and it always converges to the globally optimal solution. A comparison is performed on the original dataset as well as the over-sampled data set. The oversampling technique used is Cluster-based Over-Sampling with Noise Filtering. This technique is better than several state-of-the-art techniques for oversampling. The analysis is carried out on 3 projects KC1, PC4 and PC3 carried out by the NASA group. The metrics used for measurement are recall and balanced accuracy. The results are higher for OS-ELM as compared to other classifiers in both scenarios.