In the classic regression problem, the value of a real-valued random variable $Y$ is to be predicted based on the observation of a random vector $X$, taking its values in $\mathbb{R}^d$ with $d\geq 1$ say. The statistical learning problem consists in building a predictive function $\hat{f}:\mathbb{R}^d\to \mathbb{R}$ based on independent copies of the pair $(X,Y)$ so that $Y$ is approximated by $\hat{f}(X)$ with minimum error in the mean-squared sense. Motivated by various applications, ranging from environmental sciences to finance or insurance, special attention is paid here to the case of extreme (i.e. very large) observations $X$. Because of their rarity, they contribute in a negligible manner to the (empirical) error and the predictive performance of empirical quadratic risk minimizers can be consequently very poor in extreme regions. In this paper, we develop a general framework for regression in the extremes. It is assumed that $X$'s conditional distribution given $Y$ belongs to a non parametric class of heavy-tailed probability distributions. It is then shown that an asymptotic notion of risk can be tailored to summarize appropriately predictive performance in extreme regions of the input space. It is also proved that minimization of an empirical and non asymptotic version of this 'extreme risk', based on a fraction of the largest observations solely, yields regression functions with good generalization capacity. In addition, numerical results providing strong empirical evidence of the relevance of the approach proposed are displayed.

In recent years, there has been a flurry of research focusing on the fairness of machine learning models, and in particular on quantifying and eliminating bias against protected subgroups. One line of work generalizes the notion of protected subgroups beyond simple discrete classes by introducing the notion of a "rich subgroup", and seeks to train models that are calibrated or equalize error rates with respect to these richer subgroup classes. Largely orthogonally, local model explanation methods have been developed that given a classifier h and test point x, attribute influence for the prediction h(x) to the individual features of x. This raises a natural question: Do local model explanation methods attribute different feature importance values on average across different protected subgroups, and can we detect these disparities efficiently? If the model places high weight on a given feature in a specific protected subgroup, but not on the dataset overall (or vice versa), this could be a potential indicator of bias in the predictive model or the underlying data generating process, and is at the very least a useful diagnostic that signals the need for a domain expert to delve deeper. In this paper, we formally introduce the notion of feature importance disparity (FID) in the context of rich subgroups, design oracle-efficent algorithms to identify large FID subgroups, and conduct a thorough empirical analysis that establishes auditing for FID as an important method to investigate dataset bias. Our experiments show that across 4 datasets and 4 common feature importance methods our algorithms find (feature, subgroup) pairs that simultaneously: (i) have subgroup feature importance that is often an order of magnitude different than the importance on the dataset as a whole (ii) generalize out of sample, and (iii) yield interesting discussions about potential bias inherent in these datasets.

Randomized Controlled Trials (RCTs) represent a gold standard when developing policy guidelines. However, RCTs are often narrow, and lack data on broader populations of interest. Causal effects in these populations are often estimated using observational datasets, which may suffer from unobserved confounding and selection bias. Given a set of observational estimates (e.g. from multiple studies), we propose a meta-algorithm that attempts to reject observational estimates that are biased. We do so using validation effects, causal effects that can be inferred from both RCT and observational data. After rejecting estimators that do not pass this test, we generate conservative confidence intervals on the extrapolated causal effects for subgroups not observed in the RCT. Under the assumption that at least one observational estimator is asymptotically normal and consistent for both the validation and extrapolated effects, we provide guarantees on the coverage probability of the intervals output by our algorithm. To facilitate hypothesis testing in settings where causal effect transportation across datasets is necessary, we give conditions under which a doubly-robust estimator of group average treatment effects is asymptotically normal, even when flexible machine learning methods are used for estimation of nuisance parameters. We illustrate the properties of our approach on semi-synthetic and real world datasets, and show that it compares favorably to standard meta-analysis techniques.

In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including the iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage-thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness.

We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an inverse problem for $\theta$ with the undesirable feature that its forward operator is generally non-compact (even if $\theta$ is assumed to be compact or of $p$-Schatten class). However, we prove that, in terms of spectral properties and regularisation theory, this inverse problem is equivalent to the known compact inverse problem associated with scalar response regression. Our framework allows for the elegant derivation of dimension-free rates for generic learning algorithms under H\"older-type source conditions. The proofs rely on the combination of techniques from kernel regression with recent results on concentration of measure for sub-exponential Hilbertian random variables. The obtained rates hold for a variety of practically-relevant scenarios in functional regression as well as nonlinear regression with operator-valued kernels and match those of classical kernel regression with scalar response.

Most of the standard image and video codecs are block-based and depending upon the compression ratio the compressed images/videos suffer from different distortions. At low ratios, blurriness is observed and as compression increases blocking artifacts occur. Generally, in order to reduce blockiness, images are low-pass filtered which leads to more blurriness. Also, in bokeh mode images they are commonly seen: blurriness as a result of intentional blurred background while blocking artifact and global blurriness arising due to compression. Therefore, such visual media suffer from both blockiness and blurriness distortions. Along with this, noise is also commonly encountered distortion. Most of the existing works on quality assessment quantify these distortions individually. This paper proposes a methodology to blindly measure overall quality of an image suffering from these distortions, individually as well as jointly. This is achieved by considering the sum of absolute values of low and high-frequency Discrete Frequency Transform (DFT) coefficients defined as sum magnitudes. The number of blocks lying in specific ranges of sum magnitudes including zero-valued AC coefficients and mean of 100 maximum and 100 minimum values of these sum magnitudes are used as feature vectors. These features are then fed to the Machine Learning (ML) based Gaussian Process Regression (GPR) model, which quantifies the image quality. The simulation results show that the proposed method can estimate the quality of images distorted with the blockiness, blurriness, noise and their combinations. It is relatively fast compared to many state-of-art methods, and therefore is suitable for real-time quality monitoring applications.

Catastrophic events create uncertain situations for humanitarian organizations locating and providing aid to affected people. Many people turn to social media during disasters for requesting help and/or providing relief to others. However, the majority of social media posts seeking help could not properly be detected and remained concealed because often they are noisy and ill-formed. Existing systems lack in planning an effective strategy for tweet preprocessing and grasping the contexts of tweets. This research, first of all, formally defines request tweets in the context of social networking sites, hereafter rweets, along with their different primary types and sub-types. Our main contributions are the identification and categorization of rweets. For rweet identification, we employ two approaches, namely a rule-based and logistic regression, and show their high precision and F1 scores. The rweets classification into sub-types such as medical, food, and shelter, using logistic regression shows promising results and outperforms existing works. Finally, we introduce an architecture to store intermediate data to accelerate the development process of the machine learning classifiers.

Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the parameter vector of a generalized linear regression model contaminated by a non-parametric nuisance component. We construct suitably weighted estimating equations that account for adaptivity in data collection, and provide conditions under which the associated estimates are asymptotically normal. Our results characterize the degree of "explorability" required for asymptotic normality to hold. For the simpler problem of estimating a linear functional, we provide similar guarantees under much weaker assumptions. We illustrate our general theory with concrete consequences for various problems, including standard linear bandits and sparse generalized bandits, and compare with other methods via simulation studies.

This research aims to examine the usefulness of integrating various feature selection methods with regression algorithms for sleep quality prediction. A publicly accessible sleep quality dataset is used to analyze the effect of different feature selection techniques on the performance of four regression algorithms - Linear regression, Ridge regression, Lasso Regression and Random Forest Regressor. The results are compared to determine the optimal combination of feature selection techniques and regression algorithms. The conclusion of the study enriches the current literature on using machine learning for sleep quality prediction and has practical significance for personalizing sleep recommendations for individuals.

Merging satellite products and ground-based measurements is often required for obtaining precipitation datasets that simultaneously cover large regions with high density and are more accurate than pure satellite precipitation products. Machine and statistical learning regression algorithms are regularly utilized in this endeavour. At the same time, tree-based ensemble algorithms are adopted in various fields for solving regression problems with high accuracy and low computational cost. Still, information on which tree-based ensemble algorithm to select for correcting satellite precipitation products for the contiguous United States (US) at the daily time scale is missing from the literature. In this study, we worked towards filling this methodological gap by conducting an extensive comparison between three algorithms of the category of interest, specifically between random forests, gradient boosting machines (gbm) and extreme gradient boosting (XGBoost). We used daily data from the PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) and the IMERG (Integrated Multi-satellitE Retrievals for GPM) gridded datasets. We also used earth-observed precipitation data from the Global Historical Climatology Network daily (GHCNd) database. The experiments referred to the entire contiguous US and additionally included the application of the linear regression algorithm for benchmarking purposes. The results suggest that XGBoost is the best-performing tree-based ensemble algorithm among those compared...