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.

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.

Given a query from one modality, few-shot cross-modal retrieval (CMR) retrieves semantically similar instances in another modality with the target domain including classes that are disjoint from the source domain. Compared with classical few-shot CMR methods, vision-language pretraining methods like CLIP have shown great few-shot or zero-shot learning performance. However, they still suffer challenges due to (1) the feature degradation encountered in the target domain and (2) the extreme data imbalance. To tackle these issues, we propose FLEX-CLIP, a novel Feature-level Generation Network Enhanced CLIP. FLEX-CLIP includes two training stages. In multimodal feature generation, we propose a composite multimodal VAE-GAN network to capture real feature distribution patterns and generate pseudo samples based on CLIP features, addressing data imbalance. For common space projection, we develop a gate residual network to fuse CLIP features with projected features, reducing feature degradation in X-shot scenarios. Experimental results on four benchmark datasets show a 7%-15% improvement over state-of-the-art methods, with ablation studies demonstrating enhancement of CLIP features.

Accurate lower-limb joint kinematic estimation is critical for applications such as patient monitoring, rehabilitation, and exoskeleton control. While previous studies have employed wearable sensor-based deep learning (DL) models for estimating joint kinematics, these methods often require extensive new datasets to adapt to unseen gait patterns. Meanwhile, researchers in computer vision have advanced human pose estimation models, which are easy to deploy and capable of real-time inference. However, such models are infeasible in scenarios where cameras cannot be used. To address these limitations, we propose a computer vision-based DL adaptation framework for real-time joint kinematic estimation. This framework requires only a small dataset (i.e., 1-2 gait cycles) and does not depend on professional motion capture setups. Using transfer learning, we adapted our temporal convolutional network (TCN) to stiff knee gait data, allowing the model to further reduce root mean square error by 9.7% and 19.9% compared to a TCN trained on only able-bodied and stiff knee datasets, respectively. Our framework demonstrates a potential for smartphone camera-trained DL models to estimate real-time joint kinematics across novel users in clinical populations with applications in wearable robots.

In this work we compare the generative behavior at the next token prediction level in several language models by comparing them to human productions in the cloze task. We find that while large models trained for longer are typically better estimators of human productions, but they reliably under-estimate the probabilities of human responses, over-rank rare responses, under-rank top responses, and produce highly distinct semantic spaces. Altogether, this work demonstrates in a tractable, interpretable domain that LM generations can not be used as replacements of or models of the cloze task.

Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov semigroup. The unbounded nature of IGs complicates traditional methods such as vector-valued regression and Hilbert-Schmidt operator analysis. Existing techniques, including physics-informed kernel regression, are computationally expensive and limited in scope, with no recovery guarantees for transfer operator methods when the time-lag is small. We propose a novel method that leverages the IG's resolvent, characterized by the Laplace transform of transfer operators. This approach is robust to time-lag variations, ensuring accurate eigenvalue learning even for small time-lags. Our statistical analysis applies to a broader class of Markov processes than current methods while reducing computational complexity from quadratic to linear in the state dimension. Finally, we illustrate the behaviour of our method in two experiments.