The geographically weighted regression (GWR) is an essential tool for estimating the spatial variation of relationships between dependent and independent variables in geographical contexts. However, GWR suffers from the problem that classical linear regressions, which compose the GWR model, are more prone to be underfitting, especially for significant volume and complex nonlinear data, causing inferior comparative performance. Nevertheless, some advanced models, such as the decision tree and the support vector machine, can learn features from complex data more effectively while they cannot provide explainable quantification for the spatial variation of localized relationships. To address the above issues, we propose a geographically gradient boosting weighted regression model, GWRBoost, that applies the localized additive model and gradient boosting optimization method to alleviate underfitting problems and retains explainable quantification capability for spatially-varying relationships between geographically located variables. Furthermore, we formulate the computation method of the Akaike information score for the proposed model to conduct the comparative analysis with the classic GWR algorithm. Simulation experiments and the empirical case study are applied to prove the efficient performance and practical value of GWRBoost. The results show that our proposed model can reduce the RMSE by 18.3% in parameter estimation accuracy and AICc by 67.3% in the goodness of fit.

Hydrocarbon prospect risking is a critical application in geophysics predicting well outcomes from a variety of data including geological, geophysical, and other information modalities. Traditional routines require interpreters to go through a long process to arrive at the probability of success of specific outcomes. AI has the capability to automate the process but its adoption has been limited thus far owing to a lack of transparency in the way complicated, black box models generate decisions. We demonstrate how LIME -- a model-agnostic explanation technique -- can be used to inject trust in model decisions by uncovering the model's reasoning process for individual predictions. It generates these explanations by fitting interpretable models in the local neighborhood of specific datapoints being queried. On a dataset of well outcomes and corresponding geophysical attribute data, we show how LIME can induce trust in model's decisions by revealing the decision-making process to be aligned to domain knowledge. Further, it has the potential to debug mispredictions made due to anomalous patterns in the data or faulty training datasets.

In a high dimensional linear predictive regression where the number of potential predictors can be larger than the sample size, we consider using LASSO, a popular L1-penalized regression method, to estimate the sparse coefficients when many unit root regressors are present. Consistency of LASSO relies on two building blocks: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix of the regressors. In our setting where unit root regressors are driven by temporal dependent non-Gaussian innovations, we establish original probabilistic bounds for these two building blocks. The bounds imply that the rates of convergence of LASSO are different from those in the familiar cross sectional case. In practical applications given a mixture of stationary and nonstationary predictors, asymptotic guarantee of LASSO is preserved if all predictors are scale-standardized. In an empirical example of forecasting the unemployment rate with many macroeconomic time series, strong performance is delivered by LASSO when the initial specification is guided by macroeconomic domain expertise.

Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and responses $\mathcal{Y}$ are both high-dimensional tensors. By demonstrating that the general inner product or the contracted product on a unit rank tensor can be decomposed into standard inner products and outer products, the problem can be simply transformed into a tensor to scalar regression followed by a tensor decomposition. So we propose a fast solution based on stagewise search composed by contraction part and generation part which are optimized alternatively. We successfully demonstrate our method can out perform current methods in terms of accuracy and predictors selection by effectively incorporating the structural information.

In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common outcome. In many scientific contexts it is exactly these tail events that researchers are most interested in anticipating, so that adequate measures can be taken to prevent or attenuate a major impact on society. Despite such efforts, we have yet to provide definite answers to crucial issues in evaluating predictive solutions in domains such as weather, pollution, health. In this paper, we deal with two encapsulated problems simultaneously. First, assessing the performance of regression models when non-uniform preferences apply - not all values are equally relevant concerning the accuracy of their prediction, and there's a particular interest in the most extreme values. Second, assessing the robustness of models when dealing with uncertainty regarding the actual underlying distribution of values relevant for such problems. We show how different levels of relevance associated with target values may impact experimental conclusions, and demonstrate the practical utility of the proposed methods.

Risk management in many environmental settings requires an understanding of the mechanisms that drive extreme events. Useful metrics for quantifying such risk are extreme quantiles of response variables conditioned on predictor variables that describe, e.g., climate, biosphere and environmental states. Typically these quantiles lie outside the range of observable data and so, for estimation, require specification of parametric extreme value models within a regression framework. Classical approaches in this context utilise linear or additive relationships between predictor and response variables and suffer in either their predictive capabilities or computational efficiency; moreover, their simplicity is unlikely to capture the truly complex structures that lead to the creation of extreme wildfires. In this paper, we propose a new methodological framework for performing extreme quantile regression using artificial neutral networks, which are able to capture complex non-linear relationships and scale well to high-dimensional data. The ``black box" nature of neural networks means that they lack the desirable trait of interpretability often favoured by practitioners; thus, we unify linear, and additive, regression methodology with deep learning to create partially-interpretable neural networks that can be used for statistical inference but retain high prediction accuracy. To complement this methodology, we further propose a novel point process model for extreme values which overcomes the finite lower-endpoint problem associated with the generalised extreme value class of distributions. Efficacy of our unified framework is illustrated on U.S. wildfire data with a high-dimensional predictor set and we illustrate vast improvements in predictive performance over linear and spline-based regression techniques.

In time series forecasting, decomposition-based algorithms break aggregate data into meaningful components and are therefore appreciated for their particular advantages in interpretability. Recent algorithms often combine machine learning (hereafter ML) methodology with decomposition to improve prediction accuracy. However, incorporating ML is generally considered to sacrifice interpretability inevitably. In addition, existing hybrid algorithms usually rely on theoretical models with statistical assumptions and focus only on the accuracy of aggregate predictions, and thus suffer from accuracy problems, especially in component estimates. In response to the above issues, this research explores the possibility of improving accuracy without losing interpretability in time series forecasting. We first quantitatively define interpretability for data-driven forecasts and systematically review the existing forecasting algorithms from the perspective of interpretability. Accordingly, we propose the W-R algorithm, a hybrid algorithm that combines decomposition and ML from a novel perspective. Specifically, the W-R algorithm replaces the standard additive combination function with a weighted variant and uses ML to modify the estimates of all components simultaneously. We mathematically analyze the theoretical basis of the algorithm and validate its performance through extensive numerical experiments. In general, the W-R algorithm outperforms all decomposition-based and ML benchmarks. Based on P50_QL, the algorithm relatively improves by 8.76% in accuracy on the practical sales forecasts of JD.com and 77.99% on a public dataset of electricity loads. This research offers an innovative perspective to combine the statistical and ML algorithms, and JD.com has implemented the W-R algorithm to make accurate sales predictions and guide its marketing activities.

In our first case study, predicting house prices, you will create models that predict a continuous value (price) from input features (square footage, number of bedrooms and bathrooms,...). This is just one of the many places where regression can be applied. Other applications range from predicting health outcomes in medicine, stock prices in finance, and power usage in high-performance computing, to analyzing which regulators are important for gene expression. In this course, you will explore regularized linear regression models for the task of prediction and feature selection. You will be able to handle very large sets of features and select between models of various complexity.

The theoretical advances on the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to improve the forecasts made by deterministic physical models. Numerous state-of-the-art statistical postprocessing techniques are based on distributional regression evaluated with the Continuous Ranked Probability Score (CRPS). However, theoretical properties of such evaluation with the CRPS have solely considered the unconditional framework (i.e. without covariates) and infinite sample sizes. We extend these results and study the rate of convergence in terms of CRPS of distributional regression methods. We find the optimal minimax rate of convergence for a given class of distributions and show that the k-nearest neighbor method and the kernel method reach this optimal minimax rate.

Federated learning (FL) is an emerging machine learning paradigm, in which clients jointly learn a model with the help of a cloud server. A fundamental challenge of FL is that the clients are often heterogeneous, e.g., they have different computing powers, and thus the clients may send model updates to the server with substantially different delays. Asynchronous FL aims to address this challenge by enabling the server to update the model once any client's model update reaches it without waiting for other clients' model updates. However, like synchronous FL, asynchronous FL is also vulnerable to poisoning attacks, in which malicious clients manipulate the model via poisoning their local data and/or model updates sent to the server. Byzantine-robust FL aims to defend against poisoning attacks. In particular, Byzantine-robust FL can learn an accurate model even if some clients are malicious and have Byzantine behaviors. However, most existing studies on Byzantine-robust FL focused on synchronous FL, leaving asynchronous FL largely unexplored. In this work, we bridge this gap by proposing AFLGuard, a Byzantine-robust asynchronous FL method. We show that, both theoretically and empirically, AFLGuard is robust against various existing and adaptive poisoning attacks (both untargeted and targeted). Moreover, AFLGuard outperforms existing Byzantine-robust asynchronous FL methods.