In this work we develop a distributed least squares approximation (DLSA) method, which is able to solve a large family of regression problems (e.g., linear regression, logistic regression, Cox's model) on a distributed system. By approximating the local objective function using a local quadratic form, we are able to obtain a combined estimator by taking a weighted average of local estimators. The resulting estimator is proved to be statistically as efficient as the global estimator. In the meanwhile it requires only one round of communication. We further conduct the shrinkage estimation based on the DLSA estimation by using an adaptive Lasso approach. The solution can be easily obtained by using the LARS algorithm on the master node. It is theoretically shown that the resulting estimator enjoys the oracle property and is selection consistent by using a newly designed distributed Bayesian Information Criterion (DBIC). The finite sample performance as well as the computational efficiency are further illustrated by extensive numerical study and an airline dataset. The airline dataset is 52GB in memory size. The entire methodology has been implemented by Python for a de-facto standard Spark system. By using the proposed DLSA algorithm on the Spark system, it takes 26 minutes to obtain a logistic regression estimator whereas a full likelihood algorithm takes 15 hours to reaches an inferior result.

In causal inference, a variety of causal effect estimands have been studied, including the sample, uncensored, target, conditional, optimal subpopulation, and optimal weighted average treatment effects. Ad-hoc methods have been developed for each estimand based on inverse probability weighting (IPW) and on outcome regression modeling, but these may be sensitive to model misspecification, practical violations of positivity, or both. The contribution of this paper is twofold. First, we formulate the generalized average treatment effect (GATE) to unify these causal estimands as well as their IPW estimates. Second, we develop a method based on Kernel Optimal Matching (KOM) to optimally estimate GATE and to find the GATE most easily estimable by KOM, which we term the Kernel Optimal Weighted Average Treatment Effect. KOM provides uniform control on the conditional mean squared error of a weighted estimator over a class of models while simultaneously controlling for precision. We study its theoretical properties and evaluate its comparative performance in a simulation study. We illustrate the use of KOM for GATE estimation in two case studies: comparing spine surgical interventions and studying the effect of peer support on people living with HIV.

Maintaining good cardiac function for as long as possible is a major concern for healthcare systems worldwide and there is much interest in learning more about the impact of different risk factors on cardiac health. The aim of this study is to analyze the impact of systolic blood pressure (SBP) on cardiac function while preserving the interpretability of the model using known clinical biomarkers in a large cohort of the UK Biobank population. We propose a novel framework that combines deep learning based estimation of interpretable clinical biomarkers from cardiac cine MR data with a variational autoencoder (VAE). The VAE architecture integrates a regression loss in the latent space, which enables the progression of cardiac health with SBP to be learnt. Results on 3,600 subjects from the UK Biobank show that the proposed model allows us to gain important insight into the deterioration of cardiac function with increasing SBP, identify key interpretable factors involved in this process, and lastly exploit the model to understand patterns of positive and adverse adaptation of cardiac function.

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.

Classification is a very important research topic in statist ical machine learning. There are a large amount of literature on various classification methods, ran ging from the very classical distribution-based likelihood approaches such as Fisher linear discriminant analysis (LDA) and logistic regression [3], to the margin-based approaches such as the well-known s upport vector machine (SVM) [1, 2]. Each type of classifiers has their own merits. Recently, Liu a nd his coauthors proposed in [4] the so-called large-margin unified machines (LUMs) which es tablish a unique transition between these two types of classifiers. As noted in [5], SVM may suffer fr om data piling problems in the high-dimension low-sample size (HDLSS) settings, that is, the support vectors will pile up on top of each other at the margin boundaries when projected onto th e normal vector of the separating hyperplane.

We develop a randomization-based method for inference in regression models. The basis of inference is an invariance assumption on the regression errors, such as invariance to permutations or random signs. To test significance, the randomization method repeatedly calculates a suitable test statistic over transformations of the regression residuals according to the invariant. Inversion of the test can produce confidence intervals. We prove general conditions for asymptotic validity of this residual randomization test and illustrate in many models, including clustered errors with one-way or two-way clustering structure. We also show that finite-sample validity is possible under a suitable construction, and illustrate with an exact test for a case of the Behrens-Fisher problem. The proposed method offers four main advantages over the bootstrap: (1) it addresses the inference problem in a unified way, while bootstrap typically needs to be adapted to the task; (2) it can be more powerful by exploiting a richer and more flexible set of invariances than exchangeability; (3) it does not rely on asymptotic normality; and (4) it can be valid in finite samples. In extensive empirical evaluations, including high dimensional regression and autocorrelated errors, the proposed method performs favorably against many alternatives, including bootstrap variants and asymptotic robust error methods.

Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regression relies crucially on the choice of the tuning parameter, which determines the amount of regularization and hence the sparsity level of the fitted model. The optimal choice of tuning parameter depends on both the structure of the design matrix and the unknown random error distribution (variance, tail behavior, etc). This article reviews the current literature of tuning parameter selection for high-dimensional regression from both theoretical and practical perspectives. We discuss various strategies that choose the tuning parameter to achieve prediction accuracy or support recovery. We also review several recently proposed methods for tuning-free high-dimensional regression.

--Additive Manufacturing (AM) is a manufacturing paradigm that builds three-dimensional objects from a computer-aided design model by successively adding material layer by layer . AM has become very popular in the past decade due to its utility for fast prototyping such as 3D printing as well as manufacturing functional parts with complex geometries using processes such as laser metal deposition that would be difficult to create using traditional machining. As the process for creating an intricate part for an expensive metal such as Titanium is prohibitive with respect to cost, computational models are used to simulate the behavior of AM processes before the experimental run. However, as the simulations are computationally costly and time-consuming for predicting multiscale multi-physics phenomena in AM, physics-informed data-driven machine-learning systems for predicting the behavior of AM processes are immensely beneficial. Such models accelerate not only multiscale simulation tools but also empower real-time control systems using in-situ data. In this paper, we design and develop essential components of a scientific framework for developing a data-driven model-based real-time control system. Finite element methods are employed for solving time-dependent heat equations and developing the database. The proposed framework uses extremely randomized trees - an ensemble of bagged decision trees as the regression algorithm iteratively using temperatures of prior voxels and laser information as inputs to predict temperatures of subsequent voxels. The models achieve mean absolute percentage errors below 1% for predicting temperature profiles for AM processes. Additive Manufacturing (AM) is a modern manufacturing approach in which digital 3D design data is used to build parts by sequentially depositing layers of materials [1]. AM techniques are becoming very popular compared to traditional approaches because of their success in building complicated designs, fast prototyping, and low-volume or one-of-a-kind productions across many industries. Direct Metal Deposition (DMD) [2] is an AM technology where various materials such as steel or Titanium are used to develop the finished product.

We propose a novel method for explaining the predictions of any classifier. In our approach, local explanations are expected to explain both the outcome of a prediction and how that prediction would change if 'things had been different'. Furthermore, we argue that satisfactory explanations cannot be dissociated from a notion and measure of fidelity, as advocated in the early days of neural networks' knowledge extraction. We introduce a definition of fidelity to the underlying classifier for local explanation models which is based on distances to a target decision boundary. A system called CLEAR: Counterfactual Local Explanations via Regression, is introduced and evaluated. CLEAR generates w-counterfactual explanations that state minimum changes necessary to flip a prediction's classification. CLEAR then builds local regression models, using the w-counterfactuals to measure and improve the fidelity of its regressions. By contrast, the popular LIME method, which also uses regression to generate local explanations, neither measures its own fidelity nor generates counterfactuals. CLEAR's regressions are found to have significantly higher fidelity than LIME's, averaging over 45% higher in this paper's four case studies.

Floods are among the most destructive natural disasters, which are highly complex to model. The research on the advancement of flood prediction models contributed to risk reduction, policy suggestion, minimization of the loss of human life, and reduction the property damage associated with floods. To mimic the complex mathematical expressions of physical processes of floods, during the past two decades, machine learning (ML) methods contributed highly in the advancement of prediction systems providing better performance and cost-effective solutions. Due to the vast benefits and potential of ML, its popularity dramatically increased among hydrologists. Researchers through introducing novel ML methods and hybridizing of the existing ones aim at discovering more accurate and efficient prediction models. The main contribution of this paper is to demonstrate the state of the art of ML models in flood prediction and to give insight into the most suitable models. In this paper, the literature where ML models were benchmarked through a qualitative analysis of robustness, accuracy, effectiveness, and speed are particularly investigated to provide an extensive overview on the various ML algorithms used in the field. The performance comparison of ML models presents an in-depth understanding of the different techniques within the framework of a comprehensive evaluation and discussion. As a result, this paper introduces the most promising prediction methods for both long-term and short-term floods. Furthermore, the major trends in improving the quality of the flood prediction models are investigated. Among them, hybridization, data decomposition, algorithm ensemble, and model optimization are reported as the most effective strategies for the improvement of ML methods.