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The challenge of noisy multi-objective optimization lies in the constant trade-off between exploring new decision points and improving the precision of known points through resampling. This decision should take into account both the variability of the objective functions and the current estimate of a point in relation to the Pareto front. Since the amount and distribution of noise are generally unknown, it is desirable for a decision function to be highly adaptive to the properties of the optimization problem. This paper presents a resampling decision function that incorporates the stochastic nature of the optimization problem by using bootstrapping and the probability of dominance. The distribution-free estimation of the probability of dominance is achieved using bootstrap estimates of the means. To make the procedure applicable even with very few observations, we transfer the distribution observed at other decision points. The efficiency of this resampling approach is demonstrated by applying it in the NSGA-II algorithm with a sequential resampling procedure under multiple noise variations.

We study the asymptotic generalization of an overparameterized linear model for multiclass classification under the Gaussian covariates bi-level model introduced in Subramanian et al.~'22, where the number of data points, features, and classes all grow together. We fully resolve the conjecture posed in Subramanian et al.~'22, matching the predicted regimes for generalization. Furthermore, our new lower bounds are akin to an information-theoretic strong converse: they establish that the misclassification rate goes to 0 or 1 asymptotically. One surprising consequence of our tight results is that the min-norm interpolating classifier can be asymptotically suboptimal relative to noninterpolating classifiers in the regime where the min-norm interpolating regressor is known to be optimal. The key to our tight analysis is a new variant of the Hanson-Wright inequality which is broadly useful for multiclass problems with sparse labels. As an application, we show that the same type of analysis can be used to analyze the related multilabel classification problem under the same bi-level ensemble.

We consider in this work an inverse acoustic scattering problem when only phaseless data is available. The inverse problem is highly nonlinear and ill-posed due to the lack of the phase information. Solving inverse scattering problems with phaseless data is important in applications as the collection of physically acceptable phased data is usually difficult and expensive. A novel direct sampling method (DSM) will be developed to effectively estimate the locations and geometric shapes of the unknown scatterers from phaseless data generated by a very limited number of incident waves. With a careful theoretical analysis of the behavior of the index function and some representative numerical examples, the new DSM is shown to be computationally efficient, easy to implement, robust to large noise, and does not require any prior knowledge of the unknown scatterers. Furthermore, to fully exploit the index functions obtained from the DSM, we also propose to integrate the DSM with a deep learning technique (DSM-DL) to achieve high-quality reconstructions. Several challenging and representative numerical experiments are carried out to demonstrate the accuracy and robustness of reconstructions by DSM-DL. The DSM-DL networks trained by phased data are further theoretically and numerically shown to be able to solve problems with phaseless data. Additionally, our numerical experiments also show the DSM-DL can solve inverse scattering problems with mixed types of scatterers, which renders its applications in many important practical scenarios.

Neural amortized Bayesian inference (ABI) can solve probabilistic inverse problems orders of magnitude faster than classical methods. However, neural ABI is not yet sufficiently robust for widespread and safe applicability. In particular, when performing inference on observations outside of the scope of the simulated data seen during training, for example, because of model misspecification, the posterior approximations are likely to become highly biased. Due to the bad pre-asymptotic behavior of current neural posterior estimators in the out-of-simulation regime, the resulting estimation biases cannot be fixed in acceptable time by just simulating more training data. In this proof-of-concept paper, we propose a semi-supervised approach that enables training not only on (labeled) simulated data generated from the model, but also on unlabeled data originating from any source, including real-world data. To achieve the latter, we exploit Bayesian self-consistency properties that can be transformed into strictly proper losses without requiring knowledge of true parameter values, that is, without requiring data labels. The results of our initial experiments show remarkable improvements in the robustness of ABI on out-of-simulation data. Even if the observed data is far away from both labeled and unlabeled training data, inference remains highly accurate. If our findings also generalize to other scenarios and model classes, we believe that our new method represents a major breakthrough in neural ABI.

Human values and their measurement are long-standing interdisciplinary inquiry. Recent advances in AI have sparked renewed interest in this area, with large language models (LLMs) emerging as both tools and subjects of value measurement. This work introduces Generative Psychometrics for Values (GPV), an LLM-based, data-driven value measurement paradigm, theoretically grounded in text-revealed selective perceptions. The core idea is to dynamically parse unstructured texts into perceptions akin to static stimuli in traditional psychometrics, measure the value orientations they reveal, and aggregate the results. Applying GPV to human-authored blogs, we demonstrate its stability, validity, and superiority over prior psychological tools. Then, extending GPV to LLM value measurement, we advance the current art with 1) a psychometric methodology that measures LLM values based on their scalable and free-form outputs, enabling context-specific measurement; 2) a comparative analysis of measurement paradigms, indicating response biases of prior methods; and 3) an attempt to bridge LLM values and their safety, revealing the predictive power of different value systems and the impacts of various values on LLM safety. Through interdisciplinary efforts, we aim to leverage AI for next-generation psychometrics and psychometrics for value-aligned AI.

In complex scenarios where typical pick-and-place techniques are insufficient, often non-prehensile manipulation can ensure that a robot is able to fulfill its task. However, non-prehensile manipulation is challenging due to its underactuated nature with hybrid-dynamics, where a robot needs to reason about an object's long-term behavior and contact-switching, while being robust to contact uncertainty. The presence of clutter in the workspace further complicates this task, introducing the need to include more advanced spatial analysis to avoid unwanted collisions. Building upon prior work on reinforcement learning with multimodal categorical exploration for planar pushing, we propose to incorporate location-based attention to enable robust manipulation in cluttered scenes. Unlike previous approaches addressing this obstacle avoiding pushing task, our framework requires no predefined global paths and considers the desired target orientation of the manipulated object. Experimental results in simulation as well as with a real KUKA iiwa robot arm demonstrate that our learned policy manipulates objects successfully while avoiding collisions through complex obstacle configurations, including dynamic obstacles, to reach the desired target pose.

Pose estimation is a crucial problem in simultaneous localization and mapping (SLAM). However, developing a robust and consistent state estimator remains a significant challenge, as the traditional extended Kalman filter (EKF) struggles to handle the model nonlinearity, especially for inertial measurement unit (IMU) and light detection and ranging (LiDAR). To provide a consistent and efficient solution of pose estimation, we propose Eq-LIO, a robust state estimator for tightly coupled LIO systems based on an equivariant filter (EqF). Compared with the invariant Kalman filter based on the $\SE_2(3)$ group structure, the EqF uses the symmetry of the semi-direct product group to couple the system state including IMU bias, navigation state and LiDAR extrinsic calibration state, thereby suppressing linearization error and improving the behavior of the estimator in the event of unexpected state changes. The proposed Eq-LIO owns natural consistency and higher robustness, which is theoretically proven with mathematical derivation and experimentally verified through a series of tests on both public and private datasets.

The success of AI models relies on the availability of large, diverse, and high-quality datasets, which can be challenging to obtain due to data scarcity, privacy concerns, and high costs. Synthetic data has emerged as a promising solution by generating artificial data that mimics real-world patterns. This paper provides an overview of synthetic data research, discussing its applications, challenges, and future directions. We present empirical evidence from prior art to demonstrate its effectiveness and highlight the importance of ensuring its factuality, fidelity, and unbiasedness. We emphasize the need for responsible use of synthetic data to build more powerful, inclusive, and trustworthy language models.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.