We study the question of volume optimality in split conformal regression, a topic still poorly understood in comparison to coverage control. Using the fact that the calibration step can be seen as an empirical volume minimization problem, we first derive a finite-sample upper-bound on the excess volume loss of the interval returned by the classical split method. This important quantity measures the difference in length between the interval obtained with the split method and the shortest oracle prediction interval. Then, we introduce EffOrt, a methodology that modifies the learning step so that the base prediction function is selected in order to minimize the length of the returned intervals. In particular, our theoretical analysis of the excess volume loss of the prediction sets produced by EffOrt reveals the links between the learning and calibration steps, and notably the impact of the choice of the function class of the base predictor. We also introduce Ad-EffOrt, an extension of the previous method, which produces intervals whose size adapts to the value of the covariate. Finally, we evaluate the empirical performance and the robustness of our methodologies.

There are many examples in which the statistical units of interest are samples of a continuous time categorical random process, that is to say a continuous time stochastic process taking values in a finite state space. Without loosing any information, we associate to each state a binary random function, taking values in $\{0,1\}$, and turn the problem of statistical modeling of a categorical process into a multivariate functional data analysis issue. The (multivariate) covariance operator has nice interpretations in terms of departure from independence of the joint probabilities and the multivariate functional principal components are simple to interpret. Under the weak hypothesis assuming only continuity in probability of the $0-1$ trajectories, it is simple to build consistent estimators of the covariance kernel and perform multivariate functional principal components analysis. The sample paths being piecewise constant, with a finite number of jumps, this a rare case in functional data analysis in which the trajectories can be observed exhaustively. The approach is illustrated on a data set of sensory perceptions, considering different gustometer-controlled stimuli experiments. We show how it can be easily extended to analyze experiments, such as temporal check-all-that-apply, in which two states or more can be observed at the same time.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Ordinal variables, such as on the Likert scale, are common in applied research. Yet, existing methods for causal inference tend to target nominal or continuous data. When applied to ordinal data, this fails to account for the inherent ordering or imposes well-defined relative magnitudes. Hence, there is a need for specialised methods to compute interventional effects between ordinal variables while accounting for their ordinality. One potential framework is to presume a latent Gaussian Directed Acyclic Graph (DAG) model: that the ordinal variables originate from marginally discretizing a set of Gaussian variables whose latent covariance matrix is constrained to satisfy the conditional independencies inherent in a DAG. Conditioned on a given latent covariance matrix and discretisation thresholds, we derive a closed-form function for ordinal causal effects in terms of interventional distributions in the latent space. Our causal estimation combines naturally with algorithms to learn the latent DAG and its parameters, like the Ordinal Structural EM algorithm. Simulations demonstrate the applicability of the proposed approach in estimating ordinal causal effects both for known and unknown structures of the latent graph. As an illustration of a real-world use case, the method is applied to survey data of 408 patients from a study on the functional relationships between symptoms of obsessive-compulsive disorder and depression.

Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such as generalized additive models and hierarchical forecasting. In this paper, we propose a unified framework for integrating and combining linear constraints in time series forecasting. Within this framework, we show that the exact minimizer of the constrained empirical risk can be computed efficiently using linear algebra alone. This approach allows for highly scalable implementations optimized for GPUs. We validate the proposed methodology through extensive benchmarking on real-world tasks, including electricity demand forecasting and tourism forecasting, achieving state-of-the-art performance.

Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately, the usual Bayesian computations can be quite challenging and expensive. Here we start with a recently proposed empirical Bayes solution, with strong theoretical convergence properties, and develop a novel and computationally efficient variational approximation thereof. One such novelty is that we develop this approximation directly for the marginal distribution on the model space, rather than on the regression coefficients themselves. We demonstrate the method's strong performance in simulations, and prove that our variational approximation inherits the strong selection consistency property satisfied by the posterior distribution that it is approximating.

The challenge arises from heteroscedasticity, which implies that the covariance is sample dependent and is often unknown. Consequently, recent methods learn the covariance through unsupervised frameworks, which unfortunately yield a trade-off between computational complexity and accuracy. While this trade-off could be alleviated through supervision, obtaining labels for the covariance is non-trivial. Here, we study self-supervised covariance estimation in deep heteroscedastic regression. We address two questions: (1) How should we supervise the covariance assuming ground truth is available? We address (1) by analysing two popular measures: the KL Divergence and the 2-Wasserstein distance. Subsequently, we derive an upper bound on the 2-Wasserstein distance between normal distributions with non-commutative covariances that is stable to optimize. We address (2) through a simple neighborhood based heuristic algorithm which results in surprisingly effective pseudo-labels for the covariance. Our experiments over a wide range of synthetic and real datasets demonstrate that the proposed 2-Wasserstein bound coupled with pseudo-label annotations results in a computationally cheaper yet accurate deep heteroscedastic regression. The target distribution is typically used for downstream tasks such as uncertainty estimation, correlation analysis, sampling, and in bayesian frameworks. The key challenge in deep heteroscedastic regression lies in estimating heteroscedasticity, which implies that the variance of the target is input dependent and variable. Moreover, unlike the mean, the covariance lacks direct supervision and needs to be inferred. The standard approach without the ground-truth covariance relies on optimizing the negative loglikelihood to jointly learn the mean and covariance (Dorta et al., 2018).

Analyzing development projects is crucial for understanding donors aid strategies, recipients priorities, and to assess development finance capacity to adress development issues by on-the-ground actions. In this area, the Organisation for Economic Co-operation and Developments (OECD) Creditor Reporting System (CRS) dataset is a reference data source. This dataset provides a vast collection of project narratives from various sectors (approximately 5 million projects). While the OECD CRS provides a rich source of information on development strategies, it falls short in informing project purposes due to its reporting process based on donors self-declared main objectives and pre-defined industrial sectors. This research employs a novel approach that combines Machine Learning (ML) techniques, specifically Natural Language Processing (NLP), an innovative Python topic modeling technique called BERTopic, to categorise (cluster) and label development projects based on their narrative descriptions. By revealing existing yet hidden topics of development finance, this application of artificial intelligence enables a better understanding of donor priorities and overall development funding and provides methods to analyse public and private projects narratives.

Predicting drug-gene associations is crucial for drug development and disease treatment. While graph neural networks (GNN) have shown effectiveness in this task, they face challenges with data sparsity and efficient contrastive learning implementation. We introduce a graph diffusion network for drug-gene prediction (GDNDGP), a framework that addresses these limitations through two key innovations. First, it employs meta-path-based homogeneous graph learning to capture drug-drug and gene-gene relationships, ensuring similar entities share embedding spaces. Second, it incorporates a parallel diffusion network that generates hard negative samples during training, eliminating the need for exhaustive negative sample retrieval. Our model achieves superior performance on the DGIdb 4.0 dataset and demonstrates strong generalization capability on tripartite drug-gene-disease networks. Results show significant improvements over existing methods in drug-gene prediction tasks, particularly in handling complex heterogeneous relationships. The source code is publicly available at https://github.com/csjywu1/GDNDGP.

Prostate cancer (Pca) continues to be a leading cause of cancer-related mortality in men, and the limitations in precision of traditional diagnostic methods such as the Digital Rectal Exam (DRE), Prostate-Specific Antigen (PSA) testing, and biopsies underscore the critical importance of accurate staging detection in enhancing treatment outcomes and improving patient prognosis. This study leverages machine learning and deep learning approaches, along with feature selection and extraction methods, to enhance PCa pathological staging predictions using RNA sequencing data from The Cancer Genome Atlas (TCGA). Gene expression profiles from 486 tumors were analyzed using advanced algorithms, including Random Forest (RF), Logistic Regression (LR), Extreme Gradient Boosting (XGB), and Support Vector Machine (SVM). The performance of the study is measured with respect to the F1-score, as well as precision and recall, all of which are calculated as weighted averages. The results reveal that the highest test F1-score, approximately 83%, was achieved by the Random Forest algorithm, followed by Logistic Regression at 80%, while both Extreme Gradient Boosting (XGB) and Support Vector Machine (SVM) scored around 79%. Furthermore, deep learning models with data augmentation achieved an accuracy of 71. 23%, while PCA-based dimensionality reduction reached an accuracy of 69.86%. This research highlights the potential of AI-driven approaches in clinical oncology, paving the way for more reliable diagnostic tools that can ultimately improve patient outcomes.