A precision medicine (PM) pipeline was developed to determine the optimal treatment regime for participants in an exercise (E), dietary weight loss (D), and D+E randomized clinical trial for knee osteoarthritis to maximize their expected outcomes. Using data from 343 participants of the Intensive Diet and Exercise for Arthritis (IDEA) trial, we applied 24 machine-learning models to develop individualized treatment rules on seven outcomes: SF-36 physical component score, weight loss, WOMAC pain/function/stiffness scores, compressive force, and IL-6. The optimal precision medicine model (PMM) was selected based on jackknife value function estimates that indicate improvement in the outcome(s) had future participants followed the estimated decision rule, which is then compared against the optimal single, fixed treatment model called zero-order model (ZOM) with a Z-test. Multiple outcome random forest was the optimal model for the WOMAC outcomes. The PMMs supported the overall findings from IDEA that the D+E intervention was optimal for most participants, but there was evidence that a subgroup of participants would likely benefit more from diet alone for two outcomes. This article provides detailed technical background for the clinical data analysis.

The goal of regression analysis is to predict the value of a numeric outcome variable y given a vector of joint values of other (predictor) variables x. Usually a particular x-vector does not specify a repeatable value for y, but rather a probability distribution of possible y--values, p(y|x). This distribution has a location, scale and shape, all of which can depend on x, and are needed to infer likely values for y given x. Regression methods usually assume that training data y-values are perfect numeric realizations from some well behaived p(y|x). Often actual training data y-values are discrete, truncated and/or arbitrary censored. Regression procedures based on an optimal transformation strategy are presented for estimating location, scale and shape of p(y|x) as general functions of x, in the possible presence of such imperfect training data. In addition, validation diagnostics are presented to ascertain the quality of the solutions.

In surface mount technology (SMT), mounted components on soldered pads are subject to move during reflow process. This capability is known as self-alignment and is the result of fluid dynamic behaviour of molten solder paste. This capability is critical in SMT because inaccurate self-alignment causes defects such as overhanging, tombstoning, etc. while on the other side, it can enable components to be perfectly self-assembled on or near the desire position. The aim of this study is to develop a machine learning model that predicts the components movement during reflow in x and y-directions as well as rotation. Our study is composed of two steps: (1) experimental data are studied to reveal the relationships between self-alignment and various factors including component geometry, pad geometry, etc. (2) advanced machine learning prediction models are applied to predict the distance and the direction of components shift using support vector regression (SVR), neural network (NN), and random forest regression (RFR). As a result, RFR can predict components shift with the average fitness of 99%, 99%, and 96% and with average prediction error of 13.47 (um), 12.02 (um), and 1.52 (deg.) for component shift in x, y, and rotational directions, respectively. This enhancement provides the future capability of the parameters' optimization in the pick and placement machine to control the best placement location and minimize the intrinsic defects caused by the self-alignment.

Surface mount technology (SMT) is an enhanced method in electronic packaging in which electronic components are placed directly on soldered printing circuit board (PCB) and are permanently attached on PCB with the aim of reflow soldering process. During reflow process, once deposited solder pastes start melting, electronic components move in a direction that achieve their highest symmetry. This motion is known as self-alignment since can correct potential mounting misalignment. In this study, two noticeable machine learning algorithms, including support vector regression (SVR) and random forest regression (RFR) are proposed as a prediction technique to (1) diagnose the relation among component self-alignment, deposited solder paste status and placement machining parameters, (2) predict the final component position on PCB in x, y, and rotational directions before entering in the reflow process. Based on the prediction result, a non-linear optimization model (NLP) is developed to optimize placement parameters at initial stage. Resultantly, RFR outperforms in terms of prediction model fitness and error. The optimization model is run for 6 samples in which the minimum Euclidean distance from component position after reflow process from ideal position (i.e., the center of pads) is outlined as 25.57 ({\mu}m) regarding defined boundaries in model.

This is where one needs to be careful. Our instinct might be to simply exponentiate the log-scale predictions back to raw-scale y. But our instinct would be wrong. Let's see why that is. If you like, you can skip the little bit of math that follows and scroll down to the section called Duan's smearing estimator.

We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as if the covariates were fully observed. Recent literature on this subject proposes instead to design a specific, often complicated or non-convex, algorithm tailored to the case of missing covariates. We investigate a simpler approach where we fill-in the missing entries with their conditional mean given the observed covariates. We show that this imputation scheme coupled with standard off-the-shelf procedures such as the LASSO and square-root LASSO retains the minimax estimation rate in the random-design setting where the covariates are i.i.d.\ sub-Gaussian. We further show that the square-root LASSO remains \emph{pivotal} in this setting. It is often the case that the conditional expectation cannot be computed exactly and must be approximated from data. We study two cases where the covariates either follow an autoregressive (AR) process, or are jointly Gaussian with sparse precision matrix. We propose tractable estimators for the conditional expectation and then perform linear regression via LASSO, and show similar estimation rates in both cases. We complement our theoretical results with simulations on synthetic and semi-synthetic examples, illustrating not only the sharpness of our bounds, but also the broader utility of this strategy beyond our theoretical assumptions.

This 20-hour Machine Learning with Python course covers all the basic machine learning methods and Python modules (especially Scikit-Learn) for implementing them. The five sessions cover: simple and multiple Linear regressions; classification methods including logistic regression, discriminant analysis and naive bayes, support vector machines (SVMs) and tree based methods; cross-validation and feature selection; regularization; principal component analysis (PCA) and clustering algorithms. After successfully completing of this course, you will be able to explain the principles of machine learning algorithms and implement these methods to analyze complex datasets and make predictions in Python.

Recently, the term explainable AI became known as an approach to produce models from artificial intelligence which allow interpretation. Since a long time, there are models of symbolic regression in use that are perfectly explainable and mathematically tractable: in this contribution we demonstrate how to use symbolic regression methods to infer the optimal control of a dynamical system given one or several optimization criteria, or cost functions. In previous publications, network control was achieved by automatized machine learning control using genetic programming. Here, we focus on the subsequent analysis of the analytical expressions which result from the machine learning. In particular, we use AUTO to analyze the stability properties of the controlled oscillator system which served as our model. As a result, we show that there is a considerable advantage of explainable models over less accessible neural networks.

Throughout the course of the paper, we assume that y and X have been centered at 0 so there is no intercept in the model, where y is the n 1 vector of centered responses, X is the n p matrix of standardized regressors, β is the p 1 vector of coefficients to be estimated, and null is the n 1 vector of independent and identically distributed normal errors with mean 0 and variance σ 2 . Compared to traditional penalization functions that are usually symmetric about 0, continuous and nondecreasing in (0,), the rLASSO penalty functions are decreasing in (0,), discontinuous at 0, and converge to infinity when the coefficients approach zero. From a theoretical standpoint, rLASSO shares the same oracle property and same rate of estimation error with other LASSOtype penalty functions. An early reference to this class of models can be found in Song and Liang (2015), with more recent papers focusing on large sample asymptotics, along with computational strategies for frequentist estimation (Shin et al., 2018; Song, 2018). Our approach differs from this line of work in adopting a Bayesian perspective on rLASSO estimation. Ideally, a Bayesian solution can be obtained by placing appropriate priors on the regression coefficients that will mimic the effects of the rLASSO penalty. As apparent from (1), this arises in assuming a prior for β that decomposes as a product of independent inverse Laplace (double exponential) densities: π (β) p null j 1 λ 2β 2 j exp{ λ β j }I { β j null 0 }.

In this paper, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well-known that the group lasso estimator is not simultaneously estimation consistent and model selection consistent in structural break settings. Hence, we use a first step group lasso estimation of a diverging number of breakpoint candidates to produce weights for a second adaptive group lasso estimation. We prove that parameter changes are estimated consistently by group lasso if it is tuned correctly and show that the number of estimated breaks is greater than the true number but still sufficiently close to it. Then, we use these results and prove that the adaptive group lasso has oracle properties if weights are obtained from our first step estimation and the tuning parameter satisfies some further restrictions. Simulation results show that the proposed estimator delivers the expected results. An economic application to the long-run US money demand function demonstrates the practical importance of this methodology.