We investigate algorithmic principles that enable efficient data deletion in ML.

Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for identifying and forecasting Hamiltonian systems directly from data. We present two approaches: a two-step method that reconstructs trajectories before learning the Hamiltonian, and a one-step method that jointly infers both. Across several benchmark systems, including mass-spring dynamics, a nonlinear pendulum, and the Henon-Heiles system, we demonstrate that our framework achieves accurate, data-efficient predictions and outperforms two-step kernel-based baselines, particularly in scarce-data regimes, while preserving the conservation properties of Hamiltonian dynamics. Moreover, our methodology provides theoretical a priori error estimates, ensuring reliability of the learned models. We also provide a more general, problem-agnostic numerical framework that goes beyond Hamiltonian systems and can be used for data-driven learning of arbitrary dynamical systems.

Class Activation Maps (CAMs) are one of the important methods for visualizing regions used by deep learning models. Yet their robustness to different noise remains underexplored. In this work, we evaluate and report the resilience of various CAM methods for different noise perturbations across multiple architectures and datasets. By analyzing the influence of different noise types on CAM explanations, we assess the susceptibility to noise and the extent to which dataset characteristics may impact explanation stability. The findings highlight considerable variability in noise sensitivity for various CAMs. We propose a robustness metric for CAMs that captures two key properties: consistency and responsiveness. Consistency reflects the ability of CAMs to remain stable under input perturbations that do not alter the predicted class, while responsiveness measures the sensitivity of CAMs to changes in the prediction caused by such perturbations. The metric is evaluated empirically across models, different perturbations, and datasets along with complementary statistical tests to exemplify the applicability of our proposed approach.

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit from this development. Difficulties still arise when we can only access summarized data consisting of representative features, summary statistics, and data point counts. Such situations frequently occur primarily due to concerns about confidentiality and management costs associated with spatial data. This study tackles learning and inference using only summarized data within the framework of Gaussian process regression. To address this challenge, we analyze the approximation errors in the marginal likelihood and posterior distribution that arise from utilizing representative features. We also introduce the concept of sample quasi-likelihood, which facilitates learning and inference using only summarized data. Non-Gaussian likelihoods satisfying certain assumptions can be captured by specifying a variance function that characterizes a sample quasi-likelihood function. Theoretical and experimental results demonstrate that the approximation performance is influenced by the granularity of summarized data relative to the length scale of covariance functions. Experiments on a real-world dataset highlight the practicality of our method for spatial modeling.

Policy optimization methods benefit from a simple and tractable policy functional, usually the Gaussian for continuous action spaces. In this paper, we consider a broader policy family that remains tractable: the q-exponential family. This family of policies is flexible, allowing the specification of both heavy-tailed policies (q > 1) and light-tailed policies (q < 1). This paper examines the interplay between q-exponential policies for several actor-critic algorithms conducted on both online and offline problems. We find that heavy-tailed policies are more effective in general and can consistently improve on Gaussian. In particular, we find the Student's t-distribution to be more stable than the Gaussian across settings and that a heavy-tailed q-Gaussian for Tsallis Advantage Weighted Actor-Critic consistently performs well in offline benchmark problems. Our code is available at https://github.com/lingweizhu/qexp.

Reading fluency assessment is a critical component of literacy programmes, serving to guide and monitor early education interventions. Given the resource intensive nature of the exercise when conducted by teachers, the development of automatic tools that can operate on audio recordings of oral reading is attractive as an objective and highly scalable solution. Multiple complex aspects such as accuracy, rate and expressiveness underlie human judgements of reading fluency. In this work, we investigate end-to-end modeling on a training dataset of children's audio recordings of story texts labeled by human experts. The pre-trained wav2vec2.0 model is adopted due its potential to alleviate the challenges from the limited amount of labeled data. We report the performance of a number of system variations on the relevant measures, and also probe the learned embeddings for lexical and acoustic-prosodic features known to be important to the perception of reading fluency.

Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the smoothed classifiers, the fundamental trade-off between accuracy and (adversarial) robustness has been well evidenced in the literature: i.e., increasing the robustness of a classifier for an input can be at the expense of decreased accuracy for some other inputs. In this paper, we propose a simple training method leveraging this trade-off to obtain robust smoothed classifiers, in particular, through a sample-wise control of robustness over the training samples. We make this control feasible by using "accuracy under Gaussian noise" as an easy-to-compute proxy of adversarial robustness for an input. Specifically, we differentiate the training objective depending on this proxy to filter out samples that are unlikely to benefit from the worst-case (adversarial) objective. Our experiments show that the proposed method, despite its simplicity, consistently exhibits improved certified robustness upon state-of-the-art training methods. Somewhat surprisingly, we find these improvements persist even for other notions of robustness, e.g., to various types of common corruptions.

In many high-dimensional prediction or classification tasks, complementary data on the features are available, e.g. prior biological knowledge on (epi)genetic markers. Here we consider tasks with numerical prior information that provide an insight into the importance (weight) and the direction (sign) of the feature effects, e.g. regression coefficients from previous studies. We propose an approach for integrating multiple sources of such prior information into penalised regression. If suitable co-data are available, this improves the predictive performance, as shown by simulation and application. The proposed method is implemented in the R package `transreg' (https://github.com/lcsb-bds/transreg).

Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of these joint quantile regressions, however, is \textit{quantile crossing}, which violates the desirable monotone property of the conditional quantile function. In this work, we propose the Incremental (Spline) Quantile Functions I(S)QF, a flexible and efficient distribution-free quantile estimation framework that resolves quantile crossing with a simple neural network layer. Moreover, I(S)QF inter/extrapolate to predict arbitrary quantile levels that differ from the underlying training ones. Equipped with the analytical evaluation of the continuous ranked probability score of I(S)QF representations, we apply our methods to NN-based times series forecasting cases, where the savings of the expensive re-training costs for non-trained quantile levels is particularly significant. We also provide a generalization error analysis of our proposed approaches under the sequence-to-sequence setting. Lastly, extensive experiments demonstrate the improvement of consistency and accuracy errors over other baselines.

Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the development of active-learning reliability methods. These methods approximate the limit-state function (LSF) using surrogate models trained with a sequentially enriched set of model evaluations. A recently proposed method called stochastic spectral embedding (SSE) aims to improve the local approximation accuracy of global, spectral surrogate modelling techniques by sequentially embedding local residual expansions in subdomains of the input space. In this work we apply SSE to the LSF, giving rise to a stochastic spectral embedding-based reliability (SSER) method. The resulting partition of the input space decomposes the failure probability into a set of easy-to-compute domain-wise failure probabilities. We propose a set of modifications that tailor the algorithm to efficiently solve rare event estimation problems. These modifications include specialized refinement domain selection, partitioning and enrichment strategies. We showcase the algorithm performance on four benchmark problems of various dimensionality and complexity in the LSF.