In this paper, we consider the uncertainty quantification problem for regression models. Specifically, we consider an individual calibration objective for characterizing the quantiles of the prediction model. While such an objective is well-motivated from downstream tasks such as newsvendor cost, the existing methods have been largely heuristic and lack of statistical guarantee in terms of individual calibration. We show via simple examples that the existing methods focusing on population-level calibration guarantees such as average calibration or sharpness can lead to harmful and unexpected results. We propose simple nonparametric calibration methods that are agnostic of the underlying prediction model and enjoy both computational efficiency and statistical consistency. Our approach enables a better understanding of the possibility of individual calibration, and we establish matching upper and lower bounds for the calibration error of our proposed methods. Technically, our analysis combines the nonparametric analysis with a covering number argument for parametric analysis, which advances the existing theoretical analyses in the literature of nonparametric density estimation and quantile bandit problems. Importantly, the nonparametric perspective sheds new theoretical insights into regression calibration in terms of the curse of dimensionality and reconciles the existing results on the impossibility of individual calibration. To our knowledge, we make the first effort to reach both individual calibration and finite-sample guarantee with minimal assumptions in terms of conformal prediction. Numerical experiments show the advantage of such a simple approach under various metrics, and also under covariates shift. We hope our work provides a simple benchmark and a starting point of theoretical ground for future research on regression calibration.

In causal inference about two treatments, Conditional Average Treatment Effects (CATEs) play an important role as a quantity representing an individualized causal effect, defined as a difference between the expected outcomes of the two treatments conditioned on covariates. This study assumes two linear regression models between a potential outcome and covariates of the two treatments and defines CATEs as a difference between the linear regression models. Then, we propose a method for consistently estimating CATEs even under high-dimensional and non-sparse parameters. In our study, we demonstrate that desirable theoretical properties, such as consistency, remain attainable even without assuming sparsity explicitly if we assume a weaker assumption called implicit sparsity originating from the definition of CATEs. In this assumption, we suppose that parameters of linear models in potential outcomes can be divided into treatment-specific and common parameters, where the treatment-specific parameters take difference values between each linear regression model, while the common parameters remain identical. Thus, in a difference between two linear regression models, the common parameters disappear, leaving only differences in the treatment-specific parameters. Consequently, the non-zero parameters in CATEs correspond to the differences in the treatment-specific parameters. Leveraging this assumption, we develop a Lasso regression method specialized for CATE estimation and present that the estimator is consistent. Finally, we confirm the soundness of the proposed method by simulation studies.

Manifold visualisation techniques are commonly used to visualise high-dimensional datasets in physical sciences. In this paper we apply a recently introduced manifold visualisation method, called Slise, on datasets from physics and chemistry. Slisemap combines manifold visualisation with explainable artificial intelligence. Explainable artificial intelligence is used to investigate the decision processes of black box machine learning models and complex simulators. With Slisemap we find an embedding such that data items with similar local explanations are grouped together. Hence, Slisemap gives us an overview of the different behaviours of a black box model. This makes Slisemap into a supervised manifold visualisation method, where the patterns in the embedding reflect a target property. In this paper we show how Slisemap can be used and evaluated on physical data and that Slisemap is helpful in finding meaningful information on classification and regression models trained on these datasets.

Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and noiseless covariate data. In this paper, we present a novel estimation method that tackles these limitations by leveraging the low-rank structure inherent in the covariate matrix. Our proposed framework combines the concepts of global Fr\'echet regression and principal component regression, aiming to improve the efficiency and accuracy of the regression estimator. By incorporating the low-rank structure, our method enables more effective modeling and estimation, particularly in high-dimensional and errors-in-variables regression settings. We provide a theoretical analysis of the proposed estimator's large-sample properties, including a comprehensive rate analysis of bias, variance, and additional variations due to measurement errors. Furthermore, our numerical experiments provide empirical evidence that supports the theoretical findings, demonstrating the superior performance of our approach. Overall, this work introduces a promising framework for regression analysis of non-Euclidean variables, effectively addressing the challenges associated with limited and noisy covariate data, with potential applications in diverse fields.

Feature attribution is a fundamental task in both machine learning and data analysis, which involves determining the contribution of individual features or variables to a model's output. This process helps identify the most important features for predicting an outcome. The history of feature attribution methods can be traced back to General Additive Models (GAMs), which extend linear regression models by incorporating non-linear relationships between dependent and independent variables. In recent years, gradient-based methods and surrogate models have been applied to unravel complex Artificial Intelligence (AI) systems, but these methods have limitations. GAMs tend to achieve lower accuracy, gradient-based methods can be difficult to interpret, and surrogate models often suffer from stability and fidelity issues. Furthermore, most existing methods do not consider users' contexts, which can significantly influence their preferences. To address these limitations and advance the current state-of-the-art, we define a novel feature attribution framework called Context-Aware Feature Attribution Through Argumentation (CA-FATA). Our framework harnesses the power of argumentation by treating each feature as an argument that can either support, attack or neutralize a prediction. Additionally, CA-FATA formulates feature attribution as an argumentation procedure, and each computation has explicit semantics, which makes it inherently interpretable. CA-FATA also easily integrates side information, such as users' contexts, resulting in more accurate predictions.

Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that the model is well-specified, an assumption that is violated in most practical applications, since the required knowledge is rarely available. As a result, the produced uncertainty estimates can become very misleading; for example the prediction intervals (PIs) produced for the 95\% confidence level may cover much less than 95\% of the true labels. To address this issue, this paper introduces an extension of GPR based on a Machine Learning framework called, Conformal Prediction (CP). This extension guarantees the production of PIs with the required coverage even when the model is completely misspecified. The proposed approach combines the advantages of GPR with the valid coverage guarantee of CP, while the performed experimental results demonstrate its superiority over existing methods.

The aim of this study is to analyze the effect of serum metabolites on diabetic nephropathy (DN) and predict the prevalence of DN through a machine learning approach. The dataset consists of 548 patients from April 2018 to April 2019 in Second Affiliated Hospital of Dalian Medical University (SAHDMU). We select the optimal 38 features through a Least absolute shrinkage and selection operator (LASSO) regression model and a 10-fold cross-validation. We compare four machine learning algorithms, including eXtreme Gradient Boosting (XGB), random forest, decision tree and logistic regression, by AUC-ROC curves, decision curves, calibration curves. We quantify feature importance and interaction effects in the optimal predictive model by Shapley Additive exPlanations (SHAP) method. The XGB model has the best performance to screen for DN with the highest AUC value of 0.966. The XGB model also gains more clinical net benefits than others and the fitting degree is better. In addition, there are significant interactions between serum metabolites and duration of diabetes. We develop a predictive model by XGB algorithm to screen for DN. C2, C5DC, Tyr, Ser, Met, C24, C4DC, and Cys have great contribution in the model, and can possibly be biomarkers for DN.

As the importance of eco-friendly transportation increases, providing an efficient approach for marine vessel operation is essential. Methods for status monitoring with consideration to the weather condition and forecasting with the use of in-service data from ships requires accurate and complete models for predicting the energy efficiency of a ship. The models need to effectively process all the operational data in real-time. This paper presents models that can predict fuel consumption using in-service data collected from a passenger ship. Statistical and domain-knowledge methods were used to select the proper input variables for the models. These methods prevent over-fitting, missing data, and multicollinearity while providing practical applicability. Prediction models that were investigated include multiple linear regression (MLR), decision tree approach (DT), an artificial neural network (ANN), and ensemble methods. The best predictive performance was from a model developed using the XGboost technique which is a boosting ensemble approach. \rvv{Our code is available on GitHub at \url{https://github.com/pagand/model_optimze_vessel/tree/OE} for future research.

Modeling groundwater levels continuously across California's Central Valley (CV) hydrological system is challenging due to low-quality well data which is sparsely and noisily sampled across time and space. A novel machine learning method is proposed for modeling groundwater levels by learning from a 3D lithological texture model of the CV aquifer. The proposed formulation performs multivariate regression by combining Gaussian processes (GP) and deep neural networks (DNN). Proposed hierarchical modeling approach constitutes training the DNN to learn a lithologically informed latent space where non-parametric regression with GP is performed. The methodology is applied for modeling groundwater levels across the CV during 2015 - 2020. We demonstrate the efficacy of GP-DNN regression for modeling non-stationary features in the well data with fast and reliable uncertainty quantification. Our results indicate that the 2017 and 2019 wet years in California were largely ineffective in replenishing the groundwater loss caused during previous drought years.

Conformal inference provides a general distribution-free method to rigorously calibrate the output of any machine learning algorithm for novelty detection. While this approach has many strengths, it has the limitation of being randomized, in the sense that it may lead to different results when analyzing twice the same data, and this can hinder the interpretation of any findings. We propose to make conformal inferences more stable by leveraging suitable conformal e-values instead of p-values to quantify statistical significance. This solution allows the evidence gathered from multiple analyses of the same data to be aggregated effectively while provably controlling the false discovery rate. Further, we show that the proposed method can reduce randomness without much loss of power compared to standard conformal inference, partly thanks to an innovative way of weighting conformal e-values based on additional side information carefully extracted from the same data. Simulations with synthetic and real data confirm this solution can be effective at eliminating random noise in the inferences obtained with state-of-the-art alternative techniques, sometimes also leading to higher power.