Rovers require knowledge of terrain to plan trajectories that maximize safety and efficiency. Terrain type classification relies on input from human operators or machine learning-based image classification algorithms. However, high level terrain classification is typically not sufficient to prevent incidents such as rovers becoming unexpectedly stuck in a sand trap; in these situations, online rover-terrain interaction data can be leveraged to accurately predict future dynamics and prevent further damage to the rover. This paper presents a meta-learning-based approach to adapt probabilistic predictions of rover dynamics by augmenting a nominal model affine in parameters with a Bayesian regression algorithm (P-ALPaCA). A regularization scheme is introduced to encourage orthogonality of nominal and learned features, leading to interpretable probabilistic estimates of terrain parameters in varying terrain conditions.

Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint via Lagrangian relaxation, transforming it into a regularization term in the objective function. A particularly challenging class includes the zero-norm function, which promotes sparsity in statistical parameter estimation. Most existing exact methods for solving these problems introduce binary variables and artificial bounds to reformulate them as higher-dimensional mixed-integer programs, solvable by standard solvers. Other exact approaches exploit specific structural properties of the objective, making them difficult to generalize across different problem types. Alternative methods employ nonconvex penalties with favorable statistical characteristics, but these are typically addressed using heuristic or local optimization techniques due to their structural complexity. In this paper, we propose a novel graph-based method to globally solve optimization problems involving generalized norm-bounding constraints. Our approach encompasses standard $\ell_p$-norms for $p \in [0, \infty)$ and nonconvex penalties such as SCAD and MCP. We leverage decision diagrams to construct strong convex relaxations directly in the original variable space, eliminating the need for auxiliary variables or artificial bounds. Integrated into a spatial branch-and-cut framework, our method guarantees convergence to the global optimum. We demonstrate its effectiveness through preliminary computational experiments on benchmark sparse linear regression problems involving complex nonconvex penalties, which are not tractable using existing global optimization techniques.

Given the increasing complexity of omics datasets, a key challenge is not only improving classification performance but also enhancing the transparency and reliability of model decisions. Effective model performance and feature selection are fundamental for explainability and reliability. In many cases, high dimensional omics datasets suffer from limited number of samples due to clinical constraints, patient conditions, phenotypes rarity and others conditions. Current omics based classification models often suffer from narrow interpretability, making it difficult to discern meaningful insights where trust and reproducibility are critical. This study presents a machine learning based classification framework that integrates feature selection with data augmentation techniques to achieve high standard classification accuracy while ensuring better interpretability. Using the publicly available dataset (E MTAB 8026), we explore a bootstrap analysis in six binary classification scenarios to evaluate the proposed model's behaviour. We show that the proposed pipeline yields cross validated perfomance on small dataset that is conserved when the trained classifier is applied to a larger test set. Our findings emphasize the fundamental balance between accuracy and feature selection, highlighting the positive effect of introducing synthetic data for better generalization, even in scenarios with very limited samples availability.

Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial inference (EFI). In the proposed method, deep neural networks are used to model the treatment and control effect functions, while an additional neural network is employed to estimate their parameters. The universal approximation capability of deep neural networks ensures the broad applicability of this method. Numerical results highlight the superior performance of the proposed Double-NN method compared to the conformal quantile regression (CQR) method in individual treatment effect estimation. From the perspective of statistical inference, this work advances the theory and methodology for statistical inference of large models. Specifically, it is theoretically proven that the proposed method permits the model size to increase with the sample size $n$ at a rate of $O(n^ζ)$ for some $0 \leq ζ<1$, while still maintaining proper quantification of uncertainty in the model parameters. This result marks a significant improvement compared to the range $0\leq ζ< \frac{1}{2}$ required by the classical central limit theorem. Furthermore, this work provides a rigorous framework for quantifying the uncertainty of deep neural networks under the neural scaling law, representing a substantial contribution to the statistical understanding of large-scale neural network models.

Population pharmacokinetic (PopPK) modelling is a fundamental tool for understanding drug behaviour across diverse patient populations and enabling personalized dosing strategies to improve therapeutic outcomes. A key challenge in PopPK analysis lies in identifying and modelling covariates that influence drug absorption, as these relationships are often complex and nonlinear. Traditional methods may fail to capture hidden patterns within the data. In this study, we propose a data-driven, model-free framework that integrates Variational Autoencoders (VAEs) deep learning model and LASSO regression to uncover key covariates from simulated tacrolimus pharmacokinetic (PK) profiles. The VAE compresses high-dimensional PK signals into a structured latent space, achieving accurate reconstruction with a mean absolute percentage error (MAPE) of 2.26%. LASSO regression is then applied to map patient-specific covariates to the latent space, enabling sparse feature selection through L1 regularization. This approach consistently identifies clinically relevant covariates for tacrolimus including SNP, age, albumin, and hemoglobin which are retained across the tested regularization strength levels, while effectively discarding non-informative features. The proposed VAE-LASSO methodology offers a scalable, interpretable, and fully data-driven solution for covariate selection, with promising applications in drug development and precision pharmacotherapy.

A fundamental challenge in the cognitive sciences is discovering the dynamics that govern behaviour. Take the example of spoken language, which is characterised by a highly variable and complex set of physical movements that map onto the small set of cognitive units that comprise language. What are the fundamental dynamical principles behind the movements that structure speech production? In this study, we discover models in the form of symbolic equations that govern articulatory gestures during speech. A sparse symbolic regression algorithm is used to discover models from kinematic data on the tongue and lips. We explore these candidate models using analytical techniques and numerical simulations, and find that a second-order linear model achieves high levels of accuracy, but a nonlinear force is required to properly model articulatory dynamics in approximately one third of cases. This supports the proposal that an autonomous, nonlinear, second-order differential equation is a viable dynamical law for articulatory gestures in speech. We conclude by identifying future opportunities and obstacles in data-driven model discovery and outline prospects for discovering the dynamical principles that govern language, brain and behaviour.

In particular, Theorem 5 applies when null A δ = { δ }, i.e., when θ null A is just a standard, non-robust, solution. This is different from [56], whose main result is only applicable to solutions satisfying the infinitely many constraints f (θ, δ) 0, δ A δ i, i = 1,...,N, where A δ i is tuned to the Wasserstein bound. As previously noted, R plays the role of a tunable parameter, and the result in Theorem 5 holds for any choice of the value ofR . As a consequence, the user can play with R to optimize the bound on Risk ( θ null A) given in Theorem 5. As R increases, s A, null A (and, thereby, ε (s A, null A)) tends to increase while µ/R diminishes. While the best compromise is difficult to foresee, one can experimentally try various choices R 1 < R 2 < < R i < R h and select the one giving the best result. The corresponding confidence level can be bounded as follows: P Nnull D: Risk (θ null A) > ε (s A, null A,i) + µ R i for at least one i { 1,...h } null h null i =1P Nnull D: Risk (θ null A) > ε (s A, null A,i) + µ R i null h null i =1β = hβ, 29 from which P Nnull D: Risk ( θ null A) ε ( s A, null A,i) + µ R i for all i = 1,...h null 1 hβ.

Selecting high-quality candidates from large datasets is critical in applications such as drug discovery, precision medicine, and alignment of large language models (LLMs). While Conformal Selection (CS) provides rigorous uncertainty quantification, it is limited to univariate responses and scalar criteria. To address this issue, we propose Multivariate Conformal Selection (mCS), a generalization of CS designed for multivariate response settings. Our method introduces regional monotonicity and employs multivariate nonconformity scores to construct conformal p-values, enabling finite-sample False Discovery Rate (FDR) control. We present two variants: mCS-dist, using distance-based scores, and mCS-learn, which learns optimal scores via differentiable optimization. Experiments on simulated and real-world datasets demonstrate that mCS significantly improves selection power while maintaining FDR control, establishing it as a robust framework for multivariate selection tasks.

Appropriate modelling of extreme skew surges is crucial, particularly for coastal risk management. Our study focuses on modelling extreme skew surges along the French Atlantic coast, with a particular emphasis on investigating the extremal dependence structure between stations. We employ the peak-over-threshold framework, where a multivariate extreme event is defined whenever at least one location records a large value, though not necessarily all stations simultaneously. A novel method for determining an appropriate level (threshold) above which observations can be classified as extreme is proposed. Two complementary approaches are explored. First, the multivariate generalized Pareto distribution is employed to model extremes, leveraging its properties to derive a generative model that predicts extreme skew surges at one station based on observed extremes at nearby stations. Second, a novel extreme regression framework is assessed for point predictions. This specific regression framework enables accurate point predictions using only the "angle" of input variables, i.e. input variables divided by their norms. The ultimate objective is to reconstruct historical skew surge time series at stations with limited data. This is achieved by integrating extreme skew surge data from stations with longer records, such as Brest and Saint-Nazaire, which provide over 150 years of observations.

In recent years, two parallel research trends have emerged in machine learning, yet their intersections remain largely unexplored. On one hand, there has been a significant increase in literature focused on Individual Treatment Effect (ITE) modeling, particularly targeting the Conditional Average Treatment Effect (CATE) using meta-learner techniques. These approaches often aim to identify causal effects from observational data. On the other hand, the field of Explainable Machine Learning (XML) has gained traction, with various approaches developed to explain complex models and make their predictions more interpretable. A prominent technique in this area is Shapley Additive Explanations (SHAP), which has become mainstream in data science for analyzing supervised learning models. However, there has been limited exploration of SHAP application in identifying predictive biomarkers through CATE models, a crucial aspect in pharmaceutical precision medicine. We address inherent challenges associated with the SHAP concept in multi-stage CATE strategies and introduce a surrogate estimation approach that is agnostic to the choice of CATE strategy, effectively reducing computational burdens in high-dimensional data. Using this approach, we conduct simulation benchmarking to evaluate the ability to accurately identify biomarkers using SHAP values derived from various CATE meta-learners and Causal Forest.