Maintaining predictive accuracy in non-stationary environments requires online model selection to adapt autonomously to unknown distribution shifts. However, existing tuning-free algorithms face a fundamental trade-off between robustness and agility. Specifically, to ensure dynamic regret bounds, they must restrict learning rates to small constants (e.g., $O(1)$). This restriction inevitably causes significant adaptation lag during abrupt changes. To resolve this, we propose a novel optimistic online mirror descent that utilizes safeguarded large learning rates up to $Θ(T)$, where $T$ is the number of rounds. Our key technical contribution is a post-hoc penalty mechanism that dynamically monitors unstable updates and excludes learning rates incurring excessive regret, eliminating the need for restrictive a priori constraints. We show that the cumulative penalty remains $O(\log T)$, allowing our algorithm to match near-optimal worst-case guarantees while achieving superior rates in benign cases. Empirical evaluations on synthetic and eleven diverse real-world datasets demonstrate that our approach reduces the adaptation lag from hundreds of rounds to a few rounds, consistently outperforming tuning-free baselines.

Low-light, long-exposure defocus deblurring remains a challenging problem due to the simultaneous presence of severe blur and complex biased noise. Existing methods typically rely on simplified noise assumptions, which limits their effectiveness under realistic imaging conditions. In this work, we propose Physen-Noise2Noise, a self-supervised deblurring framework guided by the physical model of defocus imaging, which leverages noisy multi-frame observations without requiring clean reference images. Unlike conventional Noise2Noise-based approaches that assume zero-mean noise, we derive a frequency-domain constraint inherent to the defocus imaging process and incorporate it into the learning framework via a learnable noise bias parameter. In addition, a multi-frame noisy initialization strategy is introduced to suppress complex biased noise prior to deblurring, providing a more stable starting point for reconstruction. This formulation explicitly models biased noise and enables joint bias correction and high-frequency detail recovery during training. Furthermore, we develop a pretrain-finetune variant to enhance robustness and generalization under challenging noise conditions. Extensive experiments on both simulation and real-world datasets demonstrate that the proposed method consistently outperforms state-of-the-art self-supervised approaches for defocus deblurring in the presence of complex biased noise.

In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs ($\text{DAGs}$). However, dependency structures can vary across subjects, and ignoring this structural heterogeneity introduces bias and obscures subpopulation-specific dependencies. To address this, we propose Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM), a unified framework built upon Structural Equation Modeling (SEM) that jointly learns cluster assignments and cluster-specific dependency structures. We encode acyclicity via a smooth constraint and integrate a groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on their structural similarity. This yields a nonconvex optimization problem that incorporates sparsity, acyclicity, and structural consensus constraints. We address the nonconvexity by using the augmented Lagrangian method and solve it with an adapted version of the Alternating Direction Method of Multipliers (ADMM) for difference-of-convex programs. For certain graph structures, such as upper triangular adjacency matrices, our algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Experiments demonstrate that our method recovers cluster-specific causal dependency structures with a high true positive rate and a low false discovery rate. This capability enables the robust discovery of heterogeneous dependencies across subjects where the subpopulation label is unknown.

Capped-usage SaaS products -- LLM subscriptions such as Claude Code and ChatGPT, cloud platforms such as Vercel and Cloudflare Workers, corporate benefit platforms, identity-verification services with liability transfer -- share a structural signature with insurance products: a fixed premium decoupled from realized consumption, stochastic per-user demand with heavy-tailed severity, a non-fungible cap that resets on a fixed schedule, and a portfolio-level exposure that requires reserve adequacy under tail risk. We argue that this is not an analogy. It is the same operational problem actuarial science has been tooled for decades to address, restated with new dependent variables (tokens, bandwidth bytes, function-invocations, gym check-ins) in place of medical claims. This paper proposes a modeling framework for capped-usage SaaS pricing built from frequency-severity decomposition, premium calculation principles, and Monte Carlo reserve adequacy. We map the framework to publicly observable subscription tiers in two domains (LLM services and cloud platforms), ground it in canonical health-insurance economics (Arrow 1963; Pauly 1968; Manning et al. 1987; Brot-Goldberg et al. 2017), and demonstrate divergence from traditional unit economics through a worked example. The contribution is operational rather than theoretical: not a new theorem, but vocabulary and tools currently absent from cs.LG/stat.ML practice.

This article proposes an inferential framework for comparing predictor importance in classification problems with categorical response variables. The approach is based on the categorical Gini correlation (CGC) proposed by Dang et al. (2020), a measure of dependence between numerical predictors and categorical outcomes. Predictor importance is evaluated by testing differences in CGCs across competing predictor groups. The proposed methodology accommodates predictors of arbitrary and unequal dimensions and allows for dependence between predictor groups. Asymptotic normality of the test statistic is established under both the null and alternative hypotheses, and the resulting test is shown to be consistent. In addition to deriving the asymptotic distribution, a nonparametric bootstrap procedure is developed as an alternative approach to inference. Simulation studies, along with applications to breast cancer and human activity recognition datasets, demonstrate the effectiveness of the proposed framework.

Subgroup analyses within randomized controlled trials are often underpowered due to limited sample sizes. We address this challenge by leveraging trial participants outside the subgroup of interest to augment estimation within the subgroup. Specifically, we study two Targeted Maximum Likelihood Estimators (TMLEs) that borrow information from non-subgroup participants within the same trial: a TMLE with pooled regression (TMLE-PR) and an Adaptive Targeted Maximum Likelihood Estimator (A-TMLE). Both estimators enable information sharing without relying on any external real-world data, thereby capitalizing on key strengths of the trial: most importantly, the protection against bias afforded by the randomized treatment, but also harmonized data collection, and consistent treatment and outcome definitions. The general strategy proposed here directly advances the priorities of key regulatory agencies, including the FDA, by improving the precision of subgroup-specific treatment effect estimates without introducing external sources of bias, thereby facilitating rigorous inference to support equitable labeling, access, and post-market evaluation. In a case study based on analysis of data from a cardiovascular outcome trial (LEADER, NCT01179048), we estimate the risk reduction of major adverse cardiac events (MACE) under liraglutide treatment among Black and Asian subgroups -- each comprising less than 10\% of the trial population -- using the proposed estimators that borrow information from the remainder of the trial. Using A-TMLE, in particular, we find estimated absolute MACE risk reductions of 1.6, 1.5, and 1.5 percentage points among Asian participants and 2.1, 2.0, and 2.1 percentage points among Black participants at 365, 540, and 730 days, respectively, with 95\% confidence intervals excluding the null at each time point.

Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate location-adaptive kernels. In this work, we introduce pre-training, a key idea behind many cutting-edge AI technologies, to the context of non-parametric density estimation. By establishing a pre-trained neural network that can recommend an appropriate location-adaptive kernel for each sample point, efficient density estimation with adaptive kernels is achieved in high dimensions. A wide range of numerical experiments show that this strategy is highly effective for improving density-estimation accuracy, when the target distribution is close to the distribution family for pre-training. When the target distribution is substantially different from the pre-training distribution family, the benefit from the proposed pre-training strategy may be diluted, but can be reactivated by an additional fine-tuning procedure.

This paper introduces an algorithm-agnostic approach to feature-based time series clustering via amortized neural inference. By training neural networks to approximate the optimal partitioning rule from simulated data, the proposed framework reduces reliance on conventional clustering methods, such as $K$-means, $K$-medoids, or hierarchical clustering, and their associated objective functions and heuristics. Leveraging statistical features, such as autocorrelations and quantile autocorrelations, the approach learns a data-driven affinity structure from which clustering partitions can be recovered, without requiring explicit prior specification of cluster shapes or structures. In addition, one version of the method can automatically determine the number of clusters, avoiding ad-hoc selection procedures. Comprehensive empirical studies show that the proposed framework achieves competitive or superior clustering accuracy relative to traditional methods, even in challenging scenarios where competing techniques are provided with the true number of clusters. An application to financial time series of stock returns illustrates its practical utility. By reducing the need for algorithm selection and calibration, the proposed framework opens new possibilities for automated, adaptive, and data-driven clustering of temporal data across scientific and industrial domains.

We propose a data augmentation method for offline reinforcement learning, motivated by active positioning problems. Particularly, our approach enables the training of off-policy models from a limited number of suboptimal trajectories. We introduce a trajectory-based augmentation technique that exploits task structure and the geometric relationship between rewards, value functions, and mathematical properties of logging policies. During data collection, our augmentation supports suboptimal logging policies, leading to higher data quality and improved offline reinforcement learning performance. We provide theoretical justification for these strategies and validate them empirically across positioning tasks of varying dimensionality and under partial observability.

Designing the sensing architecture for large-scale spatio-temporal systems is hard when accuracy requirements are specified but sensor models are uncertain or unavailable. Classical design treats sensor placement and estimation sequentially, requiring valid forward models for each sensing modality. This paper inverts the design flow: given an error budget, synthesize the measurement likelihood that enforces it while injecting minimal information beyond the dynamical prior. The likelihood is constructed by constrained optimization: among all posteriors satisfying a prescribed accuracy bound relative to a target, select the one minimizing Kullback-Leibler divergence from the prior. The solution is a maximum-entropy posterior in relative-entropy form, and the induced likelihood is the Radon-Nikodym derivative. The framework accommodates arbitrary discrepancies and is instantiated for Wasserstein distance, maximum mean discrepancy, $f$-divergences, moment constraints, and hybrid metrics. For each, we derive the discrete particle-level problem, analyze its convex or convex-relaxed structure, and present solvers with complexity scaling. A closed-form solution exists for the symmetric exponential-tilt case, and a distillation procedure converts nonparametric likelihood samples into parametric forms. A two-layer sensor design architecture embeds the synthesized likelihood in the recursive predict-update loop, connecting accuracy budgets to physical sensor placement, precision, and configuration. Numerical experiments comparing four metrics on unimodal and multimodal scenarios confirm the accuracy constraints are reliably enforced and reveal how metric choice determines the amount and spatial distribution of injected information.