Independent and identically distributed (i.i.d.) data is essential to many data analysis and modeling techniques. In the medical domain, collecting data from multiple sites or institutions is a common strategy that guarantees sufficient clinical diversity, determined by the decentralized nature of medical data. However, data from various sites are easily biased by the local environment or facilities, thereby violating the i.i.d. rule. A common strategy is to harmonize the site bias while retaining important biological information. The ComBat is among the most popular harmonization approaches and has recently been extended to handle distributed sites. However, when faced with situations involving newly joined sites in training or evaluating data from unknown/unseen sites, ComBat lacks compatibility and requires retraining with data from all the sites. The retraining leads to significant computational and logistic overhead that is usually prohibitive. In this work, we develop a novel Cluster ComBat harmonization algorithm, which leverages cluster patterns of the data in different sites and greatly advances the usability of ComBat harmonization. We use extensive simulation and real medical imaging data from ADNI to demonstrate the superiority of the proposed approach. Our codes are provided in https://github.com/illidanlab/distributed-cluster-harmonization.

Explainable machine learning (XML) has emerged as a major challenge in artificial intelligence (AI). Although black-box models such as Deep Neural Networks and Gradient Boosting often exhibit exceptional predictive accuracy, their lack of interpretability is a notable drawback, particularly in domains requiring transparency and trust. This paper tackles this core AI problem by proposing a novel method to enhance explainability with minimal accuracy loss, using a Mixture of Linear Models (MLM) estimated under the co-supervision of black-box models. We have developed novel methods for estimating MLM by leveraging AI techniques. Specifically, we explore two approaches for partitioning the input space: agglomerative clustering and decision trees. The agglomerative clustering approach provides greater flexibility in model construction, while the decision tree approach further enhances explainability, yielding a decision tree model with linear or logistic regression models at its leaf nodes. Comparative analyses with widely-used and state-of-the-art predictive models demonstrate the effectiveness of our proposed methods. Experimental results show that statistical models can significantly enhance the explainability of AI, thereby broadening their potential for real-world applications. Our findings highlight the critical role that statistical methodologies can play in advancing explainable AI.

In this study, we delve into the realm of meta-learning to combine point base forecasts for probabilistic short-term electricity demand forecasting. Our approach encompasses the utilization of quantile linear regression, quantile regression forest, and post-processing techniques involving residual simulation to generate quantile forecasts. Furthermore, we introduce both global and local variants of meta-learning. In the local-learning mode, the meta-model is trained using patterns most similar to the query pattern. Through extensive experimental studies across 35 forecasting scenarios and employing 16 base forecasting models, our findings underscored the superiority of quantile regression forest over its competitors.

Understanding the business cycle is crucial for building economic stability, guiding business planning, and informing investment decisions. The business cycle refers to the recurring pattern of expansion and contraction in economic activity over time. Economic analysis is inherently complex, incorporating a myriad of factors (such as macroeconomic indicators, political decisions). This complexity makes it challenging to fully account for all variables when determining the current state of the economy and predicting its future trajectory in the upcoming months. The objective of this study is to investigate the capacity of machine learning models in automatically analyzing the state of the economic, with the goal of forecasting business phases (expansion, slowdown, recession and recovery) in the United States and the EuroZone. We compared three different machine learning approaches to classify the phases of the business cycle, and among them, the Multinomial Logistic Regression (MLR) achieved the best results. Specifically, MLR got the best results by achieving the accuracy of 65.25% (Top1) and 84.74% (Top2) for the EuroZone and 75% (Top1) and 92.14% (Top2) for the United States. These results demonstrate the potential of machine learning techniques to predict business cycles accurately, which can aid in making informed decisions in the fields of economics and finance.

The data augmentation (DA) algorithms are popular Markov chain Monte Carlo (MCMC) algorithms often used for sampling from intractable probability distributions. This review article comprehensively surveys DA MCMC algorithms, highlighting their theoretical foundations, methodological implementations, and diverse applications in frequentist and Bayesian statistics. The article discusses tools for studying the convergence properties of DA algorithms. Furthermore, it contains various strategies for accelerating the speed of convergence of the DA algorithms, different extensions of DA algorithms and outlines promising directions for future research. This paper aims to serve as a resource for researchers and practitioners seeking to leverage data augmentation techniques in MCMC algorithms by providing key insights and synthesizing recent developments.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

As a widely employed statistical method across various domains, regression analysis predicts or models the relationship between independent and dependent variables [1]. To accommodate data of diverse scales and characteristics, numerous regression methods have been developed, resulting in favorable practical outcomes [2,3]. Despite their success, ongoing efforts aim to devise more efficient algorithms to enhance both accuracy and interpretability. Technological advancements in various industries have led to increasingly complex, high-dimensional, and structured datasets. These datasets often contain information from diverse domains such as spatial, imagery, and spectral data. Such data should be analyzed as a unified and structured entity rather than as a mere collection of data points.

We consider correlated \emph{factor} regression models (FRM) and analyze the performance of classical ridge interpolators. Utilizing powerful \emph{Random Duality Theory} (RDT) mathematical engine, we obtain \emph{precise} closed form characterizations of the underlying optimization problems and all associated optimizing quantities. In particular, we provide \emph{excess prediction risk} characterizations that clearly show the dependence on all key model parameters, covariance matrices, loadings, and dimensions. As a function of the over-parametrization ratio, the generalized least squares (GLS) risk also exhibits the well known \emph{double-descent} (non-monotonic) behavior. Similarly to the classical linear regression models (LRM), we demonstrate that such FRM phenomenon can be smoothened out by the optimally tuned ridge regularization. The theoretical results are supplemented by numerical simulations and an excellent agrement between the two is observed. Moreover, we note that ``ridge smootenhing'' is often of limited effect already for over-parametrization ratios above $5$ and of virtually no effect for those above $10$. This solidifies the notion that one of the recently most popular neural networks paradigms -- \emph{zero-training (interpolating) generalizes well} -- enjoys wider applicability, including the one within the FRM estimation/prediction context.

Single-cell datasets often lack individual cell labels, making it challenging to identify cells associated with disease. To address this, we introduce Mixture Modeling for Multiple Instance Learning (MMIL), an expectation maximization method that enables the training and calibration of cell-level classifiers using patient-level labels. Our approach can be used to train e.g. lasso logistic regression models, gradient boosted trees, and neural networks. When applied to clinically-annotated, primary patient samples in Acute Myeloid Leukemia (AML) and Acute Lymphoblastic Leukemia (ALL), our method accurately identifies cancer cells, generalizes across tissues and treatment timepoints, and selects biologically relevant features. In addition, MMIL is capable of incorporating cell labels into model training when they are known, providing a powerful framework for leveraging both labeled and unlabeled data simultaneously. Mixture Modeling for MIL offers a novel approach for cell classification, with significant potential to advance disease understanding and management, especially in scenarios with unknown gold-standard labels and high dimensionality.

Multi-task learning (MTL) is a powerful machine learning paradigm designed to leverage shared knowledge across tasks to improve generalization and performance. Previous works have proposed approaches to MTL that can be divided into feature learning, focused on the identification of a common feature representation, and task clustering, where similar tasks are grouped together. In this paper, we propose an MTL approach at the intersection between task clustering and feature transformation based on a two-phase iterative aggregation of targets and features. First, we propose a bias-variance analysis for regression models with additive Gaussian noise, where we provide a general expression of the asymptotic bias and variance of a task, considering a linear regression trained on aggregated input features and an aggregated target. Then, we exploit this analysis to provide a two-phase MTL algorithm (NonLinCTFA). Firstly, this method partitions the tasks into clusters and aggregates each obtained group of targets with their mean. Then, for each aggregated task, it aggregates subsets of features with their mean in a dimensionality reduction fashion. In both phases, a key aspect is to preserve the interpretability of the reduced targets and features through the aggregation with the mean, which is further motivated by applications to Earth science. Finally, we validate the algorithms on synthetic data, showing the effect of different parameters and real-world datasets, exploring the validity of the proposed methodology on classical datasets, recent baselines, and Earth science applications.