We address data-driven learning of the infinitesimal generator of stochastic diffusion processes, essential for understanding numerical simulations of natural and physical systems.

We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high dimensions, such as neural networks and decision trees. Our main theoretical result characterizes and establishes the convergence of our estimator to the true conditional density in the data limit. We develop condensité, a method that implements this approach. We demonstrate the benefit of the auxiliary samples on synthetic data and showcase that condensité can achieve good out-of-the-box results. We evaluate our method on a large population survey dataset and on a satellite imaging dataset. In both cases, we find that condensité matches or outperforms the state of the art and yields conditional densities in line with established findings in the literature on each dataset. Our contribution opens up new possibilities for regression-based conditional density estimation and the empirical results indicate strong promise for applied research.

We investigate the fundamental problem of leveraging offline data to accelerate online reinforcement learning - a direction with strong potential but limited theoretical grounding. Our study centers on how to learn and apply value envelopes within this context. To this end, we introduce a principled two-stage framework: the first stage uses offline data to derive upper and lower bounds on value functions, while the second incorporates these learned bounds into online algorithms. Our method extends prior work by decoupling the upper and lower bounds, enabling more flexible and tighter approximations. In contrast to approaches that rely on fixed shaping functions, our envelopes are data-driven and explicitly modeled as random variables, with a filtration argument ensuring independence across phases. The analysis establishes high-probability regret bounds determined by two interpretable quantities, thereby providing a formal bridge between offline pre-training and online fine-tuning. Empirical results on tabular MDPs demonstrate substantial regret reductions compared with both UCBVI and prior methods.

WFCRL also offers turbine load observations that will allow to optimize the farm performance while limiting turbine structural damages.

This paper introduces a comprehensive open-source framework for developing correlation kernels, with a particular focus on user-defined and composition of kernels for surrogate modeling. By advancing kernel-based modeling techniques, we incorporate frequency-aware elements that effectively capture complex mechanical behaviors and timefrequency dynamics intrinsic to aircraft systems. Traditional kernel functions, often limited to exponential-based methods, are extended to include a wider range of kernels such as exponential squared sine and rational quadratic kernels, along with their respective firstand second-order derivatives. The proposed methodologies are first validated on a sinus cardinal test case and then applied to forecasting Mauna-Loa Carbon Dioxide (CO 2 ) concentrations and airline passenger traffic. All these advancements are integrated into the open-source Surrogate Modeling Toolbox (SMT 2.0), providing a versatile platform for both standard and customizable kernel configurations. Furthermore, the framework enables the combination of various kernels to leverage their unique strengths into composite models tailored to specific problems. The resulting framework offers a flexible toolset for engineers and researchers, paving the way for numerous future applications in metamodeling for complex, frequency-sensitive domains.

This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix of the data. The corresponding graph learning problem then scales to the squares of the number of variables (nodes), which is usually problematic at large dimension. To tackle this issue, we propose a graph learning framework that leverages a low-rank factorization of the conditional correlation matrix. In order to solve for the resulting optimization problems, we derive tools required to apply Riemannian optimization techniques for this particular structure. The proposal is then particularized to a low-rank constrained counterpart of the GLasso algorithm, i.e., the penalized maximum likelihood estimation of a Gaussian graphical model. Experiments on synthetic and real data evidence that a very efficient dimension-versus-performance trade-off can be achieved with this approach.

Characterizing changes in inter-joint coordination presents significant challenges, as it necessitates the examination of relationships between multiple degrees of freedom during movements and their temporal evolution. Existing metrics are inadequate in providing physiologically coherent results that document both the temporal and spatial aspects of inter-joint coordination. In this article, we introduce two novel metrics to enhance the analysis of inter-joint coordination. The first metric, Joint Contribution Variation based on Principal Component Analysis (JcvPCA), evaluates the variation in each joint's contribution during series of movements. The second metric, Joint Synchronization Variation based on Continuous Relative Phase (JsvCRP), measures the variation in temporal synchronization among joints between two movement datasets. We begin by presenting each metric and explaining their derivation. We then demonstrate the application of these metrics using simulated and experimental datasets involving identical movement tasks performed with distinct coordination strategies. The results show that these metrics can successfully differentiate between unique coordination strategies, providing meaningful insights into joint collaboration during movement. These metrics hold significant potential for fields such as ergonomics and clinical rehabilitation, where a precise understanding of the evolution of inter-joint coordination strategies is crucial. Potential applications include evaluating the effects of upper limb exoskeletons in industrial settings or monitoring the progress of patients undergoing neurological rehabilitation.

This paper introduces MIX, a multi-task deep learning approach to solve open-ended question-answering. First, we design our system as a multi-stage pipeline of 3 building blocks: a BM25-based Retriever to reduce the search space, a RoBERTa-based Scorer, and an Extractor to rank retrieved paragraphs and extract relevant text spans, respectively. Eventually, we further improve the computational efficiency of our system to deal with the scalability challenge: thanks to multi-task learning, we parallelize the close tasks solved by the Scorer and the Extractor. Our system is on par with state-of-the-art performances on the squad-open benchmark while being simpler conceptually.