We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$ of the minimizer $\boldsymbol{x}^*$ is based on a version of the projected gradient descent with the gradient estimated by a regularized local polynomial algorithm. Next, we propose a two-stage procedure for estimation of the minimum value $f^*$ of regression function $f$. At the first stage, we construct an accurate enough estimator of $\boldsymbol{x}^*$, which can be, for example, $\boldsymbol{z}_n$. At the second stage, we estimate the function value at the point obtained in the first stage using a rate optimal nonparametric procedure. We derive non-asymptotic upper bounds for the quadratic risk and optimization error of $\boldsymbol{z}_n$, and for the risk of estimating $f^*$. We establish minimax lower bounds showing that, under certain choice of parameters, the proposed algorithms achieve the minimax optimal rates of convergence on the class of smooth and strongly convex functions.

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model parameters. In this paper, we proposed a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are required through the use of plug-in empirical Bayes estimates of hyperparameters. Efficient maximum a posteriori (MAP) estimation is completed through a Parameter-Expanded Expectation-Conditional-Maximization (PX-ECM) algorithm. The PX-ECM results in a robust computationally efficient coordinate-wise optimization which -- when updating the coefficient for a particular predictor -- adjusts for the impact of other predictor variables. The completion of the E-step uses an approach motivated by the popular two-group approach to multiple testing. The result is a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm applied to sparse high-dimensional linear regression, which can be completed using one-at-a-time or all-at-once type optimization. We compare the empirical properties of PROBE to comparable approaches with numerous simulation studies and analyses of cancer cell drug responses. The proposed approach is implemented in the R package probe.

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of finding a global optimum of an expensive-to-evaluate black-box function efficiently. In general, a probabilistic regression model, e.g., Gaussian processes and Bayesian neural networks, is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based Bayesian optimization, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, a supervised classifier can be employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for a global solution candidate. To solve this problem, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning. Finally, we demonstrate the experimental results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool. Bayesian optimization (Brochu et al., 2010; Garnett, 2023) has attracted immense attention from various research areas such as hyperparameter optimization (Bergstra et al., 2011), battery lifetime optimization (Attia et al., 2020), and chemical reaction optimization (Shields et al., 2021), since it is capable of finding a global optimum of an expensive-to-evaluate black-box function in a sampleefficient manner. As studied in previous literature on Bayesian optimization (Snoek et al., 2012; Martinez-Cantin et al., 2018; Springenberg et al., 2016; Hutter et al., 2011), a probabilistic regression model, which can estimate a distribution of function evaluations over inputs, is widely used as a surrogate function; Gaussian process (GP) regression (Rasmussen & Williams, 2006) is a predominant choice for the surrogate function.

We study the problem of online prediction, in which at each time step $t$, an individual $x_t$ arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Machine learning and deep learning have been celebrating many successes in the application to biological problems, especially in the domain of protein folding. Another equally complex and important question has received relatively little attention by the machine learning community, namely the one of prediction of complex traits from genetics. Tackling this problem requires in-depth knowledge of the related genetics literature and awareness of various subtleties associated with genetic data. In this guide, we provide an overview for the machine learning community on current state of the art models and associated subtleties which need to be taken into consideration when developing new models for phenotype prediction. We use height as an example of a continuous-valued phenotype and provide an introduction to benchmark datasets, confounders, feature selection, and common metrics.

Boosting methods have been introduced in the late 1980's. They were born following the theoritical aspect of PAC learning. The main idea of boosting methods is to combine weak learners to obtain a strong learner. The weak learners are obtained iteratively by an heuristic which tries to correct the mistakes of the previous weak learner. In 1995, Freund and Schapire [18] introduced AdaBoost, a boosting algorithm that is still widely used today. Since then, many views of the algorithm have been proposed to properly tame its dynamics. In this paper, we will try to cover all the views that one can have on AdaBoost. We will start with the original view of Freund and Schapire before covering the different views and unify them with the same formalism. We hope this paper will help the non-expert reader to better understand the dynamics of AdaBoost and how the different views are equivalent and related to each other.

This paper addresses challenges in robust transfer learning stemming from ambiguity in Bayes classifiers and weak transferable signals between the target and source distribution. We introduce a novel quantity called the ''ambiguity level'' that measures the discrepancy between the target and source regression functions, propose a simple transfer learning procedure, and establish a general theorem that shows how this new quantity is related to the transferability of learning in terms of risk improvements. Our proposed ''Transfer Around Boundary'' (TAB) model, with a threshold balancing the performance of target and source data, is shown to be both efficient and robust, improving classification while avoiding negative transfer. Moreover, we demonstrate the effectiveness of the TAB model on non-parametric classification and logistic regression tasks, achieving upper bounds which are optimal up to logarithmic factors. Simulation studies lend further support to the effectiveness of TAB. We also provide simple approaches to bound the excess misclassification error without the need for specialized knowledge in transfer learning.

While the test-negative design (TND), which is routinely used for monitoring seasonal flu vaccine effectiveness (VE), has recently become integral to COVID-19 vaccine surveillance, it is susceptible to selection bias due to outcome-dependent sampling. Some studies have addressed the identifiability and estimation of causal parameters under the TND, but efficiency bounds for nonparametric estimators of the target parameter under the unconfoundedness assumption have not yet been investigated. We propose a one-step doubly robust and locally efficient estimator called TNDDR (TND doubly robust), which utilizes sample splitting and can incorporate machine learning techniques to estimate the nuisance functions. We derive the efficient influence function (EIF) for the marginal expectation of the outcome under a vaccination intervention, explore the von Mises expansion, and establish the conditions for $\sqrt{n}-$consistency, asymptotic normality and double robustness of TNDDR. The proposed TNDDR is supported by both theoretical and empirical justifications, and we apply it to estimate COVID-19 VE in an administrative dataset of community-dwelling older people (aged $\geq 60$y) in the province of Qu\'ebec, Canada.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show using Wiener's Tauberian theorem that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

Water resources are essential for sustaining human livelihoods and environmental well being. Accurate water quality prediction plays a pivotal role in effective resource management and pollution mitigation. In this study, we assess the effectiveness of five distinct predictive models linear regression, Random Forest, XGBoost, LightGBM, and MLP neural network, in forecasting pH values within the geographical context of Georgia, USA. Notably, LightGBM emerges as the top performing model, achieving the highest average precision. Our analysis underscores the supremacy of tree-based models in addressing regression challenges, while revealing the sensitivity of MLP neural networks to feature scaling. Intriguingly, our findings shed light on a counterintuitive discovery: machine learning models, which do not explicitly account for time dependencies and spatial considerations, outperform spatial temporal models. This unexpected superiority of machine learning models challenges conventional assumptions and highlights their potential for practical applications in water quality prediction. Our research aims to establish a robust predictive pipeline accessible to both data science experts and those without domain specific knowledge. In essence, we present a novel perspective on achieving high prediction accuracy and interpretability in data science methodologies. Through this study, we redefine the boundaries of water quality forecasting, emphasizing the significance of data driven approaches over traditional spatial temporal models. Our findings offer valuable insights into the evolving landscape of water resource management and environmental protection.