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arXiv:2509.05724v1 Announce Type: new Abstract: Recent advances in neural density estimation have enabled powerful simulation-based inference (SBI) methods that can flexibly approximate Bayesian inference for intractable stochastic models. Although these methods have demonstrated reliable posterior estimation when the simulator accurately represents the underlying data generative process (GDP), recent work has shown that they perform poorly in the presence of model misspecification. This poses a significant problem for their use on real-world problems, due to simulators always misrepresenting the true DGP to a certain degree. In this paper, we introduce robust variational neural posterior estimation (RVNP), a method which addresses the problem of misspecification in amortised SBI by bridging the simulation-to-reality gap using variational inference and error modelling. We test RVNP on multiple benchmark tasks, including using real data from astronomy, and show that it can recover robust posterior inference in a data-driven manner without adopting tunable hyperparameters or priors governing the misspecification.

arXiv:2509.05766v1 Announce Type: cross Abstract: Anomaly detection underpins critical applications from network security and intrusion detection to fraud prevention, where recognizing aberrant patterns rapidly is indispensable. Progress in this area is routinely impeded by two obstacles: extreme class imbalance and the curse of dimensionality. To combat the former, we previously introduced Precision-Recall Curve (PRC) classification trees and their ensemble extension, the PRC Random Forest (PRC-RF). Building on that foundation, we now propose a hybrid framework that integrates PRC-RF with autoencoders, unsupervised machine learning methods that learn compact latent representations, to confront both challenges simultaneously. Extensive experiments across diverse benchmark datasets demonstrate that the resulting Autoencoder-PRC-RF model achieves superior accuracy, scalability, and interpretability relative to prior methods, affirming its potential for high-stakes anomaly-detection tasks.

arXiv:2408.09718v2 Announce Type: replace Abstract: Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational data do not support them. This issue is especially critical in scientific fields involving highly noisy observations, such as cryo-electron microscopy. This study investigates confirmation bias in Gaussian mixture models. We consider the following experiment: A team of scientists assumes they are analyzing data drawn from a Gaussian mixture model with known signals (hypotheses) as centroids. However, in reality, the observations consist entirely of noise without any informative structure. The researchers use a single iteration of the K-means or expectation-maximization algorithms, two popular algorithms to estimate the centroids. Despite the observations being pure noise, we show that these algorithms yield biased estimates that resemble the initial hypotheses, contradicting the unbiased expectation that averaging these noise observations would converge to zero. Namely, the algorithms generate estimates that mirror the postulated model, although the hypotheses (the presumed centroids of the Gaussian mixture) are not evident in the observations. Specifically, among other results, we prove a positive correlation between the estimates produced by the algorithms and the corresponding hypotheses. We also derive explicit closed-form expressions of the estimates for a finite and infinite number of hypotheses. This study underscores the risks of confirmation bias in low signal-to-noise environments, provides insights into potential pitfalls in scientific methodologies, and highlights the importance of prudent data interpretation.

arXiv:2509.05778v1 Announce Type: cross Abstract: Out-of-distribution (OOD) detection plays a key role in enhancing the robustness of artificial intelligence systems by identifying inputs that differ significantly from the training distribution, thereby preventing unreliable predictions and enabling appropriate fallback mechanisms. Developing reliable OOD detection methods is a significant challenge, and rigorous evaluation of these techniques is essential for ensuring their effectiveness, as it allows researchers to assess their performance under diverse conditions and to identify potential limitations or failure modes. Cross-validation (CV) has proven to be a highly effective tool for providing a reasonable estimate of the performance of a learning algorithm. Although OOD scenarios exhibit particular characteristics, an appropriate adaptation of CV can lead to a suitable evaluation framework for this setting. This work proposes a dual CV framework for robust evaluation of OOD detection models, aimed at improving the reliability of their assessment. The proposed evaluation framework aims to effectively integrate in-distribution (ID) and OOD data while accounting for their differing characteristics. To achieve this, ID data are partitioned using a conventional approach, whereas OOD data are divided by grouping samples based on their classes. Furthermore, we analyze the context of data with class hierarchy to propose a data splitting that considers the entire class hierarchy to obtain fair ID-OOD partitions to apply the proposed evaluation framework. This framework is called Dual Cross-Validation for Robust Out-of-Distribution Detection (DCV-ROOD). To test the validity of the evaluation framework, we selected a set of state-of-the-art OOD detection methods, both with and without outlier exposure. The results show that the method achieves very fast convergence to the true performance.

arXiv:2412.07081v2 Announce Type: replace Abstract: An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers.

arXiv:2509.05864v1 Announce Type: cross Abstract: A/B testing is a widely adopted methodology for estimating conditional average treatment effects (CATEs) in both clinical trials and online platforms. While most existing research has focused primarily on maximizing estimation accuracy, practical applications must also account for additional objectives-most notably welfare or revenue loss. In many settings, it is critical to administer treatments that improve patient outcomes or to implement plans that generate greater revenue from customers. Within a machine learning framework, such objectives are naturally captured through the notion of cumulative regret. In this paper, we investigate the fundamental trade-off between social welfare loss and statistical accuracy in (adaptive) experiments with heterogeneous treatment effects. We establish matching upper and lower bounds for the resulting multi-objective optimization problem and employ the concept of Pareto optimality to characterize the necessary and sufficient conditions for optimal experimental designs. Beyond estimating CATEs, practitioners often aim to deploy treatment policies that maximize welfare across the entire population. We demonstrate that our Pareto-optimal adaptive design achieves optimal post-experiment welfare, irrespective of the in-experiment trade-off between accuracy and welfare. Furthermore, since clinical and commercial data are often highly sensitive, it is essential to incorporate robust privacy guarantees into any treatment-allocation mechanism. To this end, we develop differentially private algorithms that continue to achieve our established lower bounds, showing that privacy can be attained at negligible cost.

arXiv:2502.13822v2 Announce Type: replace Abstract: We establish novel and general high-dimensional concentration inequalities and Berry-Esseen bounds for vector-valued martingales induced by Markov chains. We apply these results to analyze the performance of the Temporal Difference (TD) learning algorithm with linear function approximations, a widely used method for policy evaluation in Reinforcement Learning (RL), obtaining a sharp high-probability consistency guarantee that matches the asymptotic variance up to logarithmic factors. Furthermore, we establish an $O(T^{-frac{1}{4}}log T)$ distributional convergence rate for the Gaussian approximation of the TD estimator, measured in convex distance. Our martingale bounds are of broad applicability, and our analysis of TD learning provides new insights into statistical inference for RL algorithms, bridging gaps between classical stochastic approximation theory and modern RL applications.

arXiv:2509.05865v1 Announce Type: cross Abstract: Motivated by privacy regulations and the need to mitigate the effects of harmful data, machine unlearning seeks to modify trained models so that they effectively ``forget'' designated data. A key challenge in verifying unlearning is forging -- adversarially crafting data that mimics the gradient of a target point, thereby creating the appearance of unlearning without actually removing information. To capture this phenomenon, we consider the collection of data points whose gradients approximate a target gradient within tolerance $epsilon$ -- which we call an $epsilon$-forging set -- and develop a framework for its analysis. For linear regression and one-layer neural networks, we show that the Lebesgue measure of this set is small. It scales on the order of $epsilon$, and when $epsilon$ is small enough, $epsilon^d$. More generally, under mild regularity assumptions, we prove that the forging set measure decays as $epsilon^{(d-r)/2}$, where $d$ is the data dimension and $r<d$ is the nullity of a variation matrix defined by the model gradients. Extensions to batch SGD and almost-everywhere smooth loss functions yield the same asymptotic scaling. In addition, we establish probability bounds showing that, under non-degenerate data distributions, the likelihood of randomly sampling a forging point is vanishingly small. These results provide evidence that adversarial forging is fundamentally limited and that false unlearning claims can, in principle, be detected.

arXiv:2509.05922v1 Announce Type: cross Abstract: This paper provides robust, new evidence on the causal drivers of market troughs. We demonstrate that conclusions about these triggers are critically sensitive to model specification, moving beyond restrictive linear models with a flexible DML average partial effect causal machine learning framework. Our robust estimates identify the volatility of options-implied risk appetite and market liquidity as key causal drivers, relationships misrepresented or obscured by simpler models. These findings provide high-frequency empirical support for intermediary asset pricing theories. This causal analysis is enabled by a high-performance nowcasting model that accurately identifies capitulation events in real-time.

arXiv:2509.05930v1 Announce Type: cross Abstract: We introduce the Smoothed Online Optimization for Target Tracking (SOOTT) problem, a new framework that integrates three key objectives in online decision-making under uncertainty: (1) tracking cost for following a dynamically moving target, (2) adversarial perturbation cost for withstanding unpredictable disturbances, and (3) switching cost for penalizing abrupt changes in decisions. This formulation captures real-world scenarios such as elastic and inelastic workload scheduling in AI clusters, where operators must balance long-term service-level agreements (e.g., LLM training) against sudden demand spikes (e.g., real-time inference). We first present BEST, a robust algorithm with provable competitive guarantees for SOOTT. To enhance practical performance, we introduce CoRT, a learning-augmented variant that incorporates untrusted black-box predictions (e.g., from ML models) into its decision process. Our theoretical analysis shows that CoRT strictly improves over BEST when predictions are accurate, while maintaining robustness under arbitrary prediction errors. We validate our approach through a case study on workload scheduling, demonstrating that both algorithms effectively balance trajectory tracking, decision smoothness, and resilience to external disturbances.