We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved locations, subject to additive noise. This leads us away from the standard assumption of i.i.d. data to a setting in which the $n$ covariate vectors are exchangeable but not independent in general. Under an assumption of independence across dimensions, $4$-th order moment, and other regularity conditions, we obtain probabilistic bounds on a notion of predictive excess risk adapted to our random functional covariate setting, making use of recent results of Barzilai and Shamir. We derive convergence rates in regimes where $p$ grows suitably fast relative to $n$, illustrating interplay between ingredients of the model in determining convergence behaviour and the role of additive covariate noise in benign-overfitting.

Multidimensional data is often associated with uncertainties that are not well-described by normal distributions. In this work, we describe how such distributions can be projected to a low-dimensional space using uncertainty-aware principal component analysis (UAPCA). We propose to model multidimensional distributions using Gaussian mixture models (GMMs) and derive the projection from a general formulation that allows projecting arbitrary probability density functions. The low-dimensional projections of the densities exhibit more details about the distributions and represent them more faithfully compared to UAPCA mappings. Further, we support including user-defined weights between the different distributions, which allows for varying the importance of the multidimensional distributions. We evaluate our approach by comparing the distributions in low-dimensional space obtained by our method and UAPCA to those obtained by sample-based projections.

Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to generate high-fidelity synthetic data. Specifically, we draw multiple pseudo-data sets from a diffusion model fitted to the original data, apply any off-the-shelf selector (e.g., lasso or SCAD), and store the resulting inclusion indicators and coefficients. Aggregating across replicas produces a stable subset of predictors with calibrated stability scores for variable selection. Theoretically, we show that the proposed method is selection consistent under mild assumptions. Because the generative model imports knowledge from large pre-trained weights, the procedure naturally benefits from transfer learning, boosting power when the observed sample is small or noisy. We also extend the framework of aggregating synthetic data to other model selection problems, including graphical model selection, and statistical inference that supports valid confidence intervals and hypothesis tests. Extensive simulations show consistent gains over the lasso, stability selection, and knockoff baselines, especially when predictors are strongly correlated, achieving higher true-positive rates and lower false-discovery proportions. By coupling diffusion-based data augmentation with principled aggregation, our method advances variable selection methodology and broadens the toolkit for interpretable, statistically rigorous analysis in complex scientific applications.

Imbalanced distribution learning is a common and significant challenge in predictive modeling, often reducing the performance of standard algorithms. Although various approaches address this issue, most are tailored to classification problems, with a limited focus on regression. This paper introduces a novel method to improve learning on tabular data within the Imbalanced Regression (IR) framework, which is a critical problem. We propose using Variational Autoencoders (VAEs) to model and define a latent representation of data distributions. However, VAEs can be inefficient with imbalanced data like other standard approaches. To address this, we develop an innovative data generation method that combines a disentangled VAE with a Smoothed Bootstrap applied in the latent space. We evaluate the efficiency of this method through numerical comparisons with competitors on benchmark datasets for IR.

Modelling of human preferences is an important step in modern post-training pipelines for AI alignment. One popular approach of building such models of human preference is assuming that human preference rankings assume a Plackett-Luce (Plackett, 1975; Luce et al., 1959) distribution. In this monograph, I draw a somewhat remarkable connection of the popular statistical model for estimating lifetimes, the Cox Proportional Hazard model (Cox, 1972) to the Plackett-Luce model and then consequently to algorithms such as Direct Preference Optimization, a popular algorithm for aligning modern Artifical Intelligence (Ouyang et al., 2022). To the best of my knowledge, at the time of writing the connection between the Proportional Hazards model and the Plackett-Luce is relatively little known, and the subsequent connections to the AI alignment algorithms such as'Direct Preference Optimization ' (Rafailov et al., 2023) are not well appreciated. I believe that explcitly stating this connection will help the AI research community build on existing research in semi-parametric statistics to build better models of human preference.

Existing research on single-machine scheduling is largely focused on exact algorithms, which perform well on typical instances but can significantly deteriorate on certain regions of the problem space. In contrast, data-driven approaches provide strong and scalable performance when tailored to the structure of specific datasets. Leveraging this idea, we focus on a single-machine scheduling problem where each job is defined by its weight, duration, due date, and deadline, aiming to minimize the total weight of tardy jobs. We introduce a novel data-driven scheduling heuristic that combines machine learning with problem-specific characteristics, ensuring feasible solutions, which is a common challenge for ML-based algorithms. Experimental results demonstrate that our approach significantly outperforms the state-of-the-art in terms of optimality gap, number of optimal solutions, and adaptability across varied data scenarios, highlighting its flexibility for practical applications. In addition, we conduct a systematic exploration of ML models, addressing a common gap in similar studies by offering a detailed model selection process and providing insights into why the chosen model is the best fit.

Federated Learning (FL) can be vulnerable to attacks, such as model poisoning, where adversaries send malicious local weights to compromise the global model. Federated Unlearning (FU) is emerging as a solution to address such vulnerabilities by selectively removing the influence of detected malicious contributors on the global model without complete retraining. However, unlike typical FU scenarios where clients are trusted and cooperative, applying FU with malicious and possibly colluding clients is challenging because their collaboration in unlearning their data cannot be assumed. This work presents FedUP, a lightweight FU algorithm designed to efficiently mitigate malicious clients' influence by pruning specific connections within the attacked model. Our approach achieves efficiency by relying only on clients' weights from the last training round before unlearning to identify which connections to inhibit. Isolating malicious influence is non-trivial due to overlapping updates from benign and malicious clients. FedUP addresses this by carefully selecting and zeroing the highest magnitude weights that diverge the most between the latest updates from benign and malicious clients while preserving benign information. FedUP is evaluated under a strong adversarial threat model, where up to 50%-1 of the clients could be malicious and have full knowledge of the aggregation process. We demonstrate the effectiveness, robustness, and efficiency of our solution through experiments across IID and Non-IID data, under label-flipping and backdoor attacks, and by comparing it with state-of-the-art (SOTA) FU solutions. In all scenarios, FedUP reduces malicious influence, lowering accuracy on malicious data to match that of a model retrained from scratch while preserving performance on benign data. FedUP achieves effective unlearning while consistently being faster and saving storage compared to the SOTA.

Due to regulations like the Right to be Forgotten, there is growing demand for removing training data and its influence from models. Since full retraining is costly, various machine unlearning methods have been proposed. In this paper, we firstly present an efficient knowledge graph (KG) unlearning algorithm. We remark that KG unlearning is nontrivial due to the distinctive structure of KG and the semantic relations between entities. Also, unlearning by estimating the influence of removed components incurs significant computational overhead when applied to large-scale knowledge graphs. To this end, we define an influence function for KG unlearning and propose to approximate the model's sensitivity without expensive computation of first-order and second-order derivatives for parameter updates. Specifically, we use Taylor expansion to estimate the parameter changes caused by data removal. Given that the first-order gradients and second-order derivatives dominate the computational load, we use the Fisher matrices and zeroth-order optimization to approximate the inverse-Hessian vector product without constructing the computational graphs. Our experimental results demonstrate that the proposed method outperforms other state-of-the-art graph unlearning baselines significantly in terms of unlearning efficiency and unlearning quality. Our code is released at https://github.com/NKUShaw/ZOWFKGIF.

Speaker de-identification aims to conceal a speaker's identity while preserving intelligibility of the underlying speech. We introduce a benchmark that quantifies residual identity leakage with three complementary error rates: equal error rate, cumulative match characteristic hit rate, and embedding-space similarity measured via canonical correlation analysis and Procrustes analysis. Evaluation results reveal that all state-of-the-art speaker de-identification systems leak identity information. The highest performing system in our evaluation performs only slightly better than random guessing, while the lowest performing system achieves a 45% hit rate within the top 50 candidates based on CMC. These findings highlight persistent privacy risks in current speaker de-identification technologies.

A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced and showed to have the potential for studying finite topological spaces, such as a dataset. It is a new method from the general topology perspective. A typed topological space is a topological space whose open sets are assigned types. Topological concepts and methods can be redefined using open sets of certain types. In this article, we develop a special set of types and its related typed topology on a dataset $X$. Using it, we can investigate the inner structure of $X$. In particular, $R^2$ has a natural quotient space, in which $X$ is organized into tracks, and each track is split into components. Those components are in a order. Further, they can be represented by an integer sequence. Components crossing tracks form branches, and the relationship can be well represented by a type of pseudotree (called typed-II pseudotree). Such structures provide a platform for new algorithms for problems such as calculating convex hull, holes, clustering and anomaly detection.