LCAQ sensors have been shown to play a critical role in the establishment of dense, expansive air-quality monitoring networks and combating elevated pollution levels. The calibration of LCAQ sensors against regulatory-grade monitors is an expensive, laborious and time-consuming process, especially when a large number of sensors are to be deployed in a geographically diverse layout. In this work, we present the RESPIRE technique to calibrate LCAQ sensors to detect ambient CO (Carbon Monoxide) levels. RESPIRE offers specific advantages over baseline calibration methods popular in literature, such as improved prediction in cross-site, cross-season, and cross-sensor settings. RESPIRE offers a training algorithm that is provably resistant to outliers and an explainable model with the ability to flag instances of model overfitting. Empirical results are presented based on data collected during an extensive deployment spanning four sites, two seasons and six sensor packages.

Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study presents the state-of-the-art of these approaches and compares them using various simulation models. The compared methods include the distance-based approaches k-prototypes, PDQ, and convex k-means, and the probabilistic methods KAy-means for MIxed LArge data (KAMILA), the mixture of Bayesian networks (MBNs), and latent class model (LCM). The aim is to provide insights into the behavior of different methods across a wide range of scenarios by varying some experimental factors such as the number of clusters, cluster overlap, sample size, dimension, proportion of continuous variables in the dataset, and clusters' distribution. The degree of cluster overlap and the proportion of continuous variables in the dataset and the sample size have a significant impact on the observed performances. When strong interactions exist between variables alongside an explicit dependence on cluster membership, none of the evaluated methods demonstrated satisfactory performance. In our experiments KAMILA, LCM, and k-prototypes exhibited the best performance, with respect to the adjusted rand index (ARI). All the methods are available in R.

This study investigates the limitations of applying Markov Chain Monte Carlo (MCMC) methods to arbitrary objective functions, focusing on a two-block MCMC framework which alternates between Metropolis-Hastings and Gibbs sampling. While such approaches are often considered advantageous for enabling data-driven regularization, we show that their performance critically depends on the sharpness of the employed likelihood form. By introducing a sharpness parameter and exploring alternative likelihood formulations proportional to the target objective function, we demonstrate how likelihood curvature governs both in-sample performance and the degree of regularization inferred by the training data. Empirical applications are conducted on reinforcement learning tasks: including a navigation problem and the game of tic-tac-toe. The study concludes with a separate analysis examining the implications of extreme likelihood sharpness on arbitrary objective functions stemming from the classic game of blackjack, where the first block of the two-block MCMC framework is replaced with an iterative optimization step. The resulting hybrid approach achieves performance nearly identical to the original MCMC framework, indicating that excessive likelihood sharpness effectively collapses posterior mass onto a single dominant mode.

Deep neural networks are prone to learning shortcuts, spurious and easily learned correlations in training data that cause severe failures in out-of-distribution (OOD) generalization. A dominant line of work seeks robustness by learning a robust representation, often explicitly partitioning the latent space into core and spurious components; this approach can be complex, brittle, and difficult to scale. W e take a different approach: instead of a robust representation, we learn a robust function. W e present a simple and effective training method that renders the classifier functionally invariant to shortcut signals. Our method operates within a disentangled latent space, which is essential as it isolates spurious and core features into distinct dimensions. This separation enables the identification of candidate shortcut features by their strong correlation with the label, used as a proxy for semantic simplicity. The classifier is then desensitized to these features by injecting targeted, anisotropic latent noise during training. W e analyze this as targeted Jacobian regularization, which forces the classifier to ignore spurious features and rely on more complex, core semantic signals. The result is state-of-the-art OOD performance on established shortcut learning benchmarks.

Abstract--Recent work has demonstrated the utility of Random Forest (RF) proximities for various supervised machine learning tasks, including outlier detection, missing data imputation, and visualization. However, the utility of the RF proximities depends upon the success of the RF model, which itself is not the ideal model in all contexts. RF proximities have recently been extended to time series by means of the distance-based Proximity Forest (PF) model, among others, affording time series analysis with the benefits of RF proximities. In this work, we introduce the generalized PF model, thereby extending RF proximities to all contexts in which supervised distance-based machine learning can occur . Additionally, we introduce a variant of the PF model for regression tasks. We also introduce the notion of using the generalized PF model as a meta-learning framework, extending supervised imputation capability to any pre-trained classifier . We experimentally demonstrate the unique advantages of the generalized PF model compared with both the RF model and the k-nearest neighbors model.

Existing methods are either: (i) DNN-based, which are inherently coupled with network-specific parameters, inevitably introducing architectural bias and compromising generalization; or (ii) DNN-free, which utilize heuristics that lack rigorous theoretical guarantees for stability and accuracy. Neither approach explicitly constrains distributional equivalence of the representative subsets, largely because continuous distribution matching is broadly considered inapplicable to discrete dataset sampling. Furthermore, prevalent distribution metrics (e.g., MSE, KL, MMD, and CE) are often incapable of accurately capturing higher-order moments differences. These deficiencies lead to suboptimal coreset performance, preventing the selected coreset from being truly equivalent to the original dataset. W e propose F AST (Frequency-domain Aligned Sampling via T opology), the first DNN-free distribution-matching coreset selection framework that formulates coreset selection task as a graph-constrained optimization problem grounded in spectral graph theory and employs the Characteristic Function Distance (CFD) to capture full distributional information (i.e., all moments and intrinsic correlations) in the frequency domain. W e further discover that naive CFD suffers from a "vanishing phase gradient" issue in medium and high-frequency regions; to address this, we introduce an Attenuated Phase-Decoupled CFD.

Corrupted training data are ubiquitous. Corrective Machine Unlearning (CMU) seeks to remove the influence of such corruption post-training. Prior CMU typically assumes access to identified corrupted training samples (a "forget set"). However, in many real-world scenarios the training data are no longer accessible. We formalize source-free CMU, where the original training data are unavailable and, consequently, no forget set of identified corrupted training samples can be specified. Instead, we assume a small proxy (surrogate) set of corrupted samples that reflect the suspected corruption type without needing to be the original training samples. In this stricter setting, methods relying on forget set are ineffective or narrow in scope. We introduce Corrective Unlearning in Task Space (CUTS), a lightweight weight space correction method guided by the proxy set using task arithmetic principles. CUTS treats the clean and the corruption signal as distinct tasks. Specifically, we briefly fine-tune the corrupted model on the proxy to amplify the corruption mechanism in the weight space, compute the difference between the corrupted and fine-tuned weights as a proxy task vector, and subtract a calibrated multiple of this vector to cancel the corruption. Without access to clean data or a forget set, CUTS recovers a large fraction of the lost utility under label noise and, for backdoor triggers, nearly eliminates the attack with minimal damage to utility, outperforming state-of-the-art specialized CMU methods in source-free setting.

Dependent data underlies many statistical studies in the social and health sciences, which often involve sensitive or private information. Differential privacy (DP) and in particular \textit{user-level} DP provide a natural formalization of privacy requirements for processing dependent data where each individual provides multiple observations to the dataset. However, dependence introduced, e.g., through repeated measurements challenges the existing statistical theory under DP-constraints. In \iid{} settings, noisy Winsorized mean estimators have been shown to be minimax optimal for standard (\textit{item-level}) and \textit{user-level} DP estimation of a mean $μ\in \R^d$. Yet, their behavior on potentially dependent observations has not previously been studied. We fill this gap and show that Winsorized mean estimators can also be used under dependence for bounded and unbounded data, and can lead to asymptotic and finite sample guarantees that resemble their \iid{} counterparts under a weak notion of dependence. For this, we formalize dependence via log-Sobolev inequalities on the joint distribution of observations. This enables us to adapt the stable histogram by Karwa and Vadhan (2018) to a non-\iid{} setting, which we then use to estimate the private projection intervals of the Winsorized estimator. The resulting guarantees for our item-level mean estimator extend to \textit{user-level} mean estimation and transfer to the local model via a randomized response histogram. Using the mean estimators as building blocks, we provide extensions to random effects models, longitudinal linear regression and nonparametric regression. Therefore, our work constitutes a first step towards a systematic study of DP for dependent data.

The Heckman selection model is one of the most well-renounced econometric models in the analysis of data with sample selection. This model is designed to rectify sample selection biases based on the assumption of bivariate normal error terms. However, real data diverge from this assumption in the presence of heavy tails and/or atypical observations. Recently, this assumption has been relaxed via a more flexible Student's t-distribution, which has appealing statistical properties. This paper introduces a novel Heckman selection model using a bivariate contaminated normal distribution for the error terms. We present an efficient ECM algorithm for parameter estimation with closed-form expressions at the E-step based on truncated multinormal distribution formulas. The identifiability of the proposed model is also discussed, and its properties have been examined. Through simulation studies, we compare our proposed model with the normal and Student's t counterparts and investigate the finite-sample properties and the variation in missing rate. Results obtained from two real data analyses showcase the usefulness and effectiveness of our model. The proposed algorithms are implemented in the R package HeckmanEM.

Asynchronous federated learning (FL) has recently gained attention for its enhanced efficiency and scalability, enabling local clients to send model updates to the server at their own pace without waiting for slower participants. However, such a design encounters significant challenges, such as the risk of outdated updates from straggler clients degrading the overall model performance and the potential bias introduced by faster clients dominating the learning process, especially under heterogeneous data distributions. Existing methods typically address only one of these issues, creating a conflict where mitigating the impact of outdated updates can exacerbate the bias created by faster clients, and vice versa. To address these challenges, we propose FedEcho, a novel framework that incorporates uncertainty-aware distillation to enhance the asynchronous FL performances under large asynchronous delays and data heterogeneity. Specifically, uncertainty-aware distillation enables the server to assess the reliability of predictions made by straggler clients, dynamically adjusting the influence of these predictions based on their estimated uncertainty. By prioritizing more certain predictions while still leveraging the diverse information from all clients, FedEcho effectively mitigates the negative impacts of outdated updates and data heterogeneity. Through extensive experiments, we demonstrate that FedEcho consistently outperforms existing asynchronous federated learning baselines, achieving robust performance without requiring access to private client data.