Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices.

We thank the reviewers for their constructive suggestions. A summary of the added discussion is provided point-by-point below. Reviewer 1: How much more work is needed versus linear regression. The technical details are thus different (and more involved) here. We have included these derivations for completeness.

By combining robust regression and prior information, we develop an effective robust regression method that can resist adaptive adversarial attacks. Due to the widespread existence of noise and data corruption, it is necessary to recover the true regression parameters when a certain proportion of the response variables have been corrupted. Methods to overcome this problem often involve robust least-squares regression. However, few methods achieve good performance when dealing with severe adaptive adversarial attacks. Based on the combination of prior information and robust regression via hard thresholding from [ 1 ], this paper proposes an algorithm that improves the breakdown point when facing adaptive adversarial attacks. Furthermore, to improve the robustness and reduce the estimation error caused by the inclusion of a prior, the idea of Bayesian reweighting is used to construct a more robust algorithm. We prove the theoretical convergence of proposed algorithms under mild conditions. Extensive experiments show that, under different dataset attacks, our algorithms achieve state-of-the-art results compared with other benchmark algorithms, demonstrating the robustness of the proposed approach.

By combining robust regression and prior information, we develop an effective robust regression method that can resist adaptive adversarial attacks. Due to the widespread existence of noise and data corruption, it is necessary to recover the true regression parameters when a certain proportion of the response variables have been corrupted. Methods to overcome this problem often involve robust least-squares regression. However, few methods achieve good performance when dealing with severe adaptive adversarial attacks. Based on the combination of prior information and robust regression via hard thresholding from [ 1 ], this paper proposes an algorithm that improves the breakdown point when facing adaptive adversarial attacks. Furthermore, to improve the robustness and reduce the estimation error caused by the inclusion of a prior, the idea of Bayesian reweighting is used to construct a more robust algorithm. We prove the theoretical convergence of proposed algorithms under mild conditions. Extensive experiments show that, under different dataset attacks, our algorithms achieve state-of-the-art results compared with other benchmark algorithms, demonstrating the robustness of the proposed approach.

In this paper, we show that distri-butionally robust logistic regression with mixed ( i.e., numerical and categorical) features, despite amounting to an optimization problem of exponential size, admits a polynomial-time solution scheme.

In this work, we argue that the order of play in strategic classification is fundamentally determined by the relative frequencies at which the decision-maker and the agents adapt to each other's actions.

This constant can sometimes be prohibitively large. We show that this approach has advantages in auto-tuning to the ill-posedness of the problem. Darolles et al. [ 2011 ] consider the closed form solution to the minimization problem, which takes the Darolles et al. [ 2011 ] take the latter approach to estimation by first estimating the conditional operators The crucial assumption in this line of work (see e.g. Hall et al. [ 2005 ], Darolles et al. [ 2011 ]) is what Our estimator adapts to these two quantities and automatically and optimally balances them, by imposing an RKHS norm penalty. Our work on sparse linear hypotheses provides a minimax formulation alternative to the Dantzig selector.

Additive models have attracted much attention for high-dimensional regression estimation and variable selection. However, the existing models are usually limited to the single-task learning framework under the mean squared error (MSE) criterion, where the utilization of variable structure depends heavily on a priori knowledge among variables. For high-dimensional observations in real environment, e.g., Coronal Mass Ejections (CMEs) data, the learning performance of previous methods may be degraded seriously due to the complex non-Gaussian noise and the insufficiency of a prior knowledge on variable structure.

Estimating treatment effects (TE) from observational data is a critical yet complex task in many fields, from healthcare and economics to public policy. While recent advances in machine learning and causal inference have produced powerful estimation techniques, their adoption remains limited due to the need for deep expertise in causal assumptions, adjustment strategies, and model selection. In this paper, we introduce CATE-B, an open-source co-pilot system that uses large language models (LLMs) within an agentic framework to guide users through the end-to-end process of treatment effect estimation. CATE-B assists in (i) constructing a structural causal model via causal discovery and LLM-based edge orientation, (ii) identifying robust adjustment sets through a novel Minimal Uncertainty Adjustment Set criterion, and (iii) selecting appropriate regression methods tailored to the causal structure and dataset characteristics. To encourage reproducibility and evaluation, we release a suite of benchmark tasks spanning diverse domains and causal complexities. By combining causal inference with intelligent, interactive assistance, CATE-B lowers the barrier to rigorous causal analysis and lays the foundation for a new class of benchmarks in automated treatment effect estimation.