We introduce the Multiple Quantile Graphical Model (MQGM), which extends the neighborhood selection approach of Meinshausen and Bühlmann for learning sparse graphical models. The latter is defined by the basic subproblem of modeling the conditional mean of one variable as a sparse function of all others. Our approach models a set of conditional quantiles of one variable as a sparse function of all others, and hence offers a much richer, more expressive class of conditional distribution estimates. We establish that, under suitable regularity conditions, the MQGM identifies the exact conditional independencies with probability tending to one as the problem size grows, even outside of the usual homoskedastic Gaussian data model. We develop an efficient algorithm for fitting the MQGM using the alternating direction method of multipliers. We also describe a strategy for sampling from the joint distribution that underlies the MQGM estimate. Lastly, we present detailed experiments that demonstrate the flexibility and effectiveness of the MQGM in modeling hetereoskedastic non-Gaussian data.

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension is also presented. Experiments on synthetic and real data show that HOLRR computes accurate solutions while being computationally very competitive.

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretation and can improve the accuracy of the predictive models. The method, which is a recursive extension of maxima hunting (MH), performs variable selection by identifying the maxima of a relevance function, which measures the strength of the correlation of the predictor functional variable with the class label. At each stage, the information associated with the selected variable is removed by subtracting the conditional expectation of the process. The results of an extensive empirical evaluation are used to illustrate that, in the problems investigated, RMH has comparable or higher predictive accuracy than standard dimensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.

We present an effective method for supervised feature construction. The main goal of the approach is to construct a feature representation for which a set of linear hypotheses is of sufficient capacity - large enough to contain a satisfactory solution to the considered problem and small enough to allow good generalization from a small number of training examples. We achieve this goal with a greedy procedure that constructs features by empirically fitting squared error residuals. The proposed constructive procedure is consistent and can output a rich set of features. The effectiveness of the approach is evaluated empirically by fitting a linear ridge regression model in the constructed feature space and our empirical results indicate a superior performance of our approach over competing methods.

The right ventricular (RV) function deterioration strongly predicts clinical outcomes in numerous circumstances. To boost the clinical deployment of ensemble regression methods that quantify RV volumes using tabular data from the widely available two-dimensional echocardiography (2DE), we propose to complement the volume predictions with uncertainty scores. To this end, we employ an instance-based method which uses the learned tree structure to identify the nearest training samples to a target instance and then uses a number of distribution types to more flexibly model the output. The probabilistic and point-prediction performances of the proposed framework are evaluated on a relatively small-scale dataset, comprising 100 end-diastolic and end-systolic RV volumes. The reference values for point performance were obtained from MRI. The results demonstrate that our flexible approach yields improved probabilistic and point performances over other state-of-the-art methods. The appropriateness of the proposed framework is showcased by providing exemplar cases. The estimated uncertainty embodies both aleatoric and epistemic types. This work aligns with trustworthy artificial intelligence since it can be used to enhance the decision-making process and reduce risks. The feature importance scores of our framework can be exploited to reduce the number of required 2DE views which could enhance the proposed pipeline's clinical application.

Time-to-event analysis is a branch of statistics that has increased in popularity during the last decades due to its many application fields, such as predictive maintenance, customer churn prediction and population lifetime estimation. In this paper, we review and compare the performance of several prediction models for time-to-event analysis. These consist of semi-parametric and parametric statistical models, in addition to machine learning approaches. Our study is carried out on three datasets and evaluated in two different scores (the integrated Brier score and concordance index). Moreover, we show how ensemble methods, which surprisingly have not yet been much studied in time-to-event analysis, can improve the prediction accuracy and enhance the robustness of the prediction performance. We conclude the analysis with a simulation experiment in which we evaluate the factors influencing the performance ranking of the methods using both scores. Keywords: Ensemble methods, time-to-event analysis, integrated Brier score, concordance index.

This paper describes how to analyze the influence of Earth system variables on the errors when providing temperature forecasts. The initial framework to get the data has been based on previous research work, which resulted in a very interesting discovery. However, the aforementioned study only worked on individual correlations of the variables with respect to the error. This research work is going to re-use the main ideas but introduce three main novelties: (1) applying a data science approach by a few representative locations; (2) taking advantage of the rankings created by Spearman correlation but enriching them with other metrics looking for a more robust ranking of the variables; (3) evaluation of the methodology by learning random forest models for regression with the distinct experimental variations. The main contribution is the framework that shows how to convert correlations into rankings and combine them into an aggregate ranking. We have carried out experiments on five chosen locations to analyze the behavior of this ranking-based methodology. The results show that the specific performance is dependent on the location and season, which is expected, and that this selection technique works properly with Random Forest models but can also improve simpler regression models such as Bayesian Ridge. This work also contributes with an extensive analysis of the results. We can conclude that this selection based on the top-k ranked variables seems promising for this real problem, and it could also be applied in other domains.

Yield forecasting, the science of predicting agricultural productivity before the crop harvest occurs, helps a wide range of stakeholders make better decisions around agricultural planning. This study aims to investigate whether machine learning-based yield prediction models can capably predict Kharif season rice yields at the district level in India several months before the rice harvest takes place. The methodology involved training 19 machine learning models such as CatBoost, LightGBM, Orthogonal Matching Pursuit, and Extremely Randomized Trees on 20 years of climate, satellite, and rice yield data across 247 of Indian rice-producing districts. In addition to model-building, a dynamic dashboard was built understand how the reliability of rice yield predictions varies across districts. The results of the proof-of-concept machine learning pipeline demonstrated that rice yields can be predicted with a reasonable degree of accuracy, with out-of-sample R2, MAE, and MAPE performance of up to 0.82, 0.29, and 0.16 respectively. These results outperformed test set performance reported in related literature on rice yield modeling in other contexts and countries. In addition, SHAP value analysis was conducted to infer both the importance and directional impact of the climate and remote sensing variables included in the model. Important features driving rice yields included temperature, soil water volume, and leaf area index. In particular, higher temperatures in August correlate with increased rice yields, particularly when the leaf area index in August is also high. Building on the results, a proof-of-concept dashboard was developed to allow users to easily explore which districts may experience a rise or fall in yield relative to the previous year.

The increasing usage of machine learning models in consequential decision-making processes has spurred research into the fairness of these systems. While significant work has been done to study group fairness in the in-processing and post-processing setting, there has been little that theoretically connects these results to the pre-processing domain. This paper proposes that achieving group fairness in downstream models can be formulated as finding the optimal design matrix in which to modify a response variable in a Randomized Response framework. We show that measures of group fairness can be directly controlled for with optimal model utility, proposing a pre-processing algorithm called FairRR that yields excellent downstream model utility and fairness.

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but fail to consider the optimization property of the learned model. As empirically shown in recent work, the sharpness of learned minima influences OOD generalization. To bridge this gap between optimization and OOD generalization, we study the effect of sharpness on how a model tolerates data change in domain shift which is usually captured by "robustness" in generalization. In this paper, we give a rigorous connection between sharpness and robustness, which gives better OOD guarantees for robust algorithms. It also provides a theoretical backing for "flat minima leads to better OOD generalization". Overall, we propose a sharpness-based OOD generalization bound by taking robustness into consideration, resulting in a tighter bound than non-robust guarantees. Our findings are supported by the experiments on a ridge regression model, as well as the experiments on deep learning classification tasks.