The third inequality follows from identifying that for a given λ, the best policy may be defined pointwise as the argument of the maximum written in the expectation. Thus, only the middle equality () deserves a proof. We obtain it by applying a general theorem of strong duality (which requires feasibility for slightly smaller cost constraints). We restate a result extracted from the monograph by Luenberger [1969]. It relies on the dual functional φ, whose expression we recall below.

This work presents general upper and lower bounds on the Kullback-Leibler (KL) divergence of coreset approximations that reflect the full range of applicability of Bayesian coresets.

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization parameters of Ridge regression, LASSO, and the ElasticNet across multiple problem instances, a setting that encompasses both cross-validation and multi-task hyperparameter optimization. We obtain a novel structural result for the ElasticNet which characterizes the loss as a function of the tuning parameters as a piecewise-rational function with algebraic boundaries. We use this to bound the structural complexity of the regularized loss functions and show generalization guarantees for tuning the ElasticNet regression coefficients in the statistical setting. We also consider the more challenging online learning setting, where we show vanishing average expected regret relative to the optimal parameter pair.

Simulation-based inference (SBI) is constantly in search of more expressive and efficient algorithms to accurately infer the parameters of complex simulation models. In line with this goal, we present consistency models for posterior estimation (CMPE), a new conditional sampler for SBI that inherits the advantages of recent unconstrained architectures and overcomes their sampling inefficiency at inference time. CMPE essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be flexibly tailored to the structure of the estimation problem. We provide hyperparameters and default architectures that support consistency training over a wide range of different dimensions, including low-dimensional ones which are important in SBI workflows but were previously difficult to tackle even with unconditional consistency models. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on hard low-dimensional benchmarks, but also achieves competitive performance with much faster sampling speed on two realistic estimation problems with high data and/or parameter dimensions.

The Area Under the ROC Curve (AUC) is a well-known metric for evaluating instance-level long-tail learning problems. In the past two decades, many AUC optimization methods have been proposed to improve model performance under long-tail distributions. In this paper, we explore AUC optimization methods in the context of pixel-level long-tail semantic segmentation, a much more complicated scenario. This task introduces two major challenges for AUC optimization techniques. On one hand, AUC optimization in a pixel-level task involves complex coupling across loss terms, with structured inner-image and pairwise inter-image dependencies, complicating theoretical analysis. On the other hand, we find that mini-batch estimation of AUC loss in this case requires a larger batch size, resulting in an unaffordable space complexity.

We utilize an open and widely used data format, i.e., JSON format, for the MEQA dataset. A sample within the dataset, accompanied by the data format explanation, is shown in Listing 1. " context ": " Roadside IED kills Russian major general [...] ", # The context of the question " question ": " Who died before AI - monitor reported it online?", " What event contains Al - Monitor is the communicator? " What event is after #1 has a victim? " Who died in the #2? major general, local commander, lieutenant general " The dataset and source code for the MEQA dataset have been released to GitHub: https:// github.com/du-nlp-lab/MEQA.

Existing benchmarks for multi-hop question answering (QA) primarily evaluate models based on their ability to reason about entities and the relationships between them. However, there's a lack of insight into how these models perform in terms of both events and entities.