Recent advances in large-scale models, including deep neural networks and large language models, have substantially improved performance across a wide range of learning tasks. The widespread availability of such pre-trained models creates new opportunities for data-efficient statistical learning, provided they can be effectively integrated into downstream tasks. Motivated by this setting, we study few-shot personalization, where a pre-trained black-box model is adapted to a target domain using a limited number of samples. We develop a theoretical framework for few-shot personalization in nonparametric regression and propose algorithms that can incorporate a black-box pre-trained model into the regression procedure. We establish the minimax optimal rate for the personalization problem and show that the proposed method attains this rate. Our results clarify the statistical benefits of leveraging pre-trained models under sample scarcity and provide robustness guarantees when the pre-trained model is not informative. We illustrate the finite-sample performance of the methods through simulations and an application to the California housing dataset with several pre-trained models.

In reinforcement learning, the softmax parametrization is the standard approach for policies over discrete action spaces. However, it fails to capture the order relationship between actions. Motivated by a real-world industrial problem, we propose a novel policy parametrization based on ordinal regression models adapted to the reinforcement learning setting. Our approach addresses practical challenges, and numerical experiments demonstrate its effectiveness in real applications and in continuous action tasks, where discretizing the action space and applying the ordinal policy yields competitive performance.

Stress haunts people in modern society, which may cause severe health issues if left unattended. With social media becoming an integral part of daily life, leveraging social media to detect stress has gained increasing attention. While the majority of the work focuses on classifying stress states and stress categories, this study introduce a new task aimed at estimating more specific stressors (like exam, writing paper, etc.) through users' posts on social media. Unfortunately, the diversity of stressors with many different classes but a few examples per class, combined with the consistent arising of new stressors over time, hinders the machine understanding of stressors. To this end, we cast the stressor estimation problem within a practical scenario few-shot learning setting, and propose a novel meta-learning based stressor estimation framework that is enhanced by a meta-knowledge inheritance mechanism. This model can not only learn generic stressor context through meta-learning, but also has a good generalization ability to estimate new stressors with little labeled data. A fundamental breakthrough in our approach lies in the inclusion of the meta-knowledge inheritance mechanism, which equips our model with the ability to prevent catastrophic forgetting when adapting to new stressors. The experimental results show that our model achieves state-of-the-art performance compared with the baselines. Additionally, we construct a social media-based stressor estimation dataset that can help train artificial intelligence models to facilitate human well-being. The dataset is now public at \href{https://www.kaggle.com/datasets/xinwangcs/stressor-cause-of-mental-health-problem-dataset}{\underline{Kaggle}} and \href{https://huggingface.co/datasets/XinWangcs/Stressor}{\underline{Hugging Face}}.

We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a specific choice of step size, followed by standard KDE with a modified bandwidth. The step size and modified bandwidth are chosen to remove the leading order bias in the KDE. Our experiments on synthetic tasks in 1D, 2D and on MNIST, demonstrate that our proposed SD-KDE method significantly reduces the mean integrated squared error compared to the standard Silverman KDE, even with noisy estimates in the score function. These results underscore the potential of integrating score-based corrections into nonparametric density estimation.

The EU Artificial Intelligence Act (AI Act) came into force in the European Union (EU) on 1 August 2024. It is a key piece of legislation both for the citizens at the heart of AI technologies and for the industry active in the internal market. The AI Act imposes progressive compliance on organisations - both private and public - involved in the global value chain of AI systems and models marketed and used in the EU. While the Act is unprecedented on an international scale in terms of its horizontal and binding regulatory scope, its global appeal in support of trustworthy AI is one of its major challenges.

Dynamic density estimation is ubiquitous in many applications, including computer vision and signal processing. One popular method to tackle this problem is the "sliding window" kernel density estimator. There exist various implementations of this method that use heuristically defined weight sequences for the observed data. The weight sequence, however, is a key aspect of the estimator affecting the tracking performance significantly. In this work, we study the exact mean integrated squared error (MISE) of "sliding window" Gaussian Kernel Density Estimators for evolving Gaussian densities. We provide a principled guide for choosing the optimal weight sequence by theoretically characterizing the exact MISE, which can be formulated as constrained quadratic programming. We present empirical evidence with synthetic datasets to show that our weighting scheme indeed improves the tracking performance compared to heuristic approaches.

This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The subsamples and their constituting data points are regarded as $\it{chromosome}$ and $\it{gene}$, respectively, in the terminology of genetic algorithm. Second, each pair of subsamples breeds two new subsamples, where each data point faces either $\it{crossover}$, $\it{mutation}$, or $\it{reproduction}$ with a certain probability. The dominant subsamples in terms of fitness values are inherited by the next generation. This process is repeated generation by generation and brings the sparse representation of kernel density estimator in its completion. We confirmed from simulation studies that the resulting estimator can perform better than other well-known density estimators.

This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original data. The resulting estimator brings us data-adaptive weighting parameters and bandwidth matrices, and realizes a sparse representation of kernel density estimation. We develop the non-asymptotic error bound of estimator obtained via the proposed stagewise minimization algorithm. It is confirmed from simulation studies that the proposed estimator performs competitive to or sometime better than other well-known density estimators.

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs). These elements enable an adaptive and hierarchical discretization of the sample space with small or large elements in regions with smoothly or highly variable densities, respectively. The novel refinement strategy that we propose is based on statistical goodness-of-fit and pair-wise (as an approximation to mutual) independence tests that evaluate the local approximation of the distribution in terms of DEs. The capabilities of our new method are inspected based on several examples of different dimensionality and successfully compared with other state-of-the-art density estimators.