Large language models (LLMs) have demonstrated remarkable capabilities across various tasks. However, these models could offer biased, hallucinated, or non-factual responses camouflaged by their fluency and realistic appearance. Uncertainty estimation is the key method to address this challenge. While research efforts in uncertainty estimation are ramping up, there is a lack of comprehensive and dedicated surveys on LLM uncertainty estimation. This survey presents four major avenues of LLM uncertainty estimation. Furthermore, we perform extensive experimental evaluations across multiple methods and datasets. At last, we provide critical and promising future directions for LLM uncertainty estimation.

The integration of network information and node attribute information has recently gained significant attention in the community detection literature. In this work, we consider community detection in the Contextual Labeled Stochastic Block Model (CLSBM), where the network follows an LSBM and node attributes follow a Gaussian Mixture Model (GMM). Our primary focus is the misclassification rate, which measures the expected number of nodes misclassified by community detection algorithms. We first establish a lower bound on the optimal misclassification rate that holds for any algorithm. When we specialize our setting to the LSBM (which preserves only network information) or the GMM (which preserves only node attribute information), our lower bound recovers prior results. Moreover, we present an efficient spectral-based algorithm tailored for the CLSBM and derive an upper bound on its misclassification rate. Although the algorithm does not attain the lower bound, it serves as a reliable starting point for designing more accurate community detection algorithms (as many algorithms use spectral method as an initial step, followed by refinement procedures to enhance accuracy).

Recent advances in Large Language Models (LLMs) have showcased their remarkable reasoning capabilities, making them influential across various fields. However, in robotics, their use has primarily been limited to manipulation planning tasks due to their inherent textual output. This paper addresses this limitation by investigating the potential of adopting the reasoning ability of LLMs for generating numerical predictions in robotics tasks, specifically for robotic grasping. We propose Reasoning Tuning, a novel method that integrates a reasoning phase before prediction during training, leveraging the extensive prior knowledge and advanced reasoning abilities of LLMs. This approach enables LLMs, notably with multi-modal capabilities, to generate accurate numerical outputs like grasp poses that are context-aware and adaptable through conversations. Additionally, we present the Reasoning Tuning VLM Grasp dataset, carefully curated to facilitate the adaptation of LLMs to robotic grasping. Extensive validation on both grasping datasets and real-world experiments underscores the adaptability of multi-modal LLMs for numerical prediction tasks in robotics. This not only expands their applicability but also bridges the gap between text-based planning and direct robot control, thereby maximizing the potential of LLMs in robotics.

Federated learning has recently garnered significant attention, especially within the domain of supervised learning. However, despite the abundance of unlabeled data on end-users, unsupervised learning problems such as clustering in the federated setting remain underexplored. In this paper, we investigate the federated clustering problem, with a focus on federated k-means. We outline the challenge posed by its non-convex objective and data heterogeneity in the federated framework. To tackle these challenges, we adopt a new perspective by studying the structures of local solutions in k-means and propose a one-shot algorithm called FeCA (Federated Centroid Aggregation). FeCA adaptively refines local solutions on clients, then aggregates these refined solutions to recover the global solution of the entire dataset in a single round. We empirically demonstrate the robustness of FeCA under various federated scenarios on both synthetic and real-world data. Additionally, we extend FeCA to representation learning and present DeepFeCA, which combines Deep-Cluster and FeCA for unsupervised feature learning in the federated setting.

Accurate segmentation of tools in robot-assisted surgery is critical for machine perception, as it facilitates numerous downstream tasks including augmented reality feedback. While current feed-forward neural network-based methods exhibit excellent segmentation performance under ideal conditions, these models have proven susceptible to even minor corruptions, significantly impairing the model's performance. This vulnerability is especially problematic in surgical settings where predictions might be used to inform high-stakes decisions. To better understand model behavior under non-adversarial corruptions, prior work has explored introducing artificial corruptions, like Gaussian noise or contrast perturbation to test set images, to assess model robustness. However, these corruptions are either not photo-realistic or model/task agnostic. Thus, these investigations provide limited insights into model deterioration under realistic surgical corruptions. To address this limitation, we introduce the SegSTRONG-C challenge that aims to promote the development of algorithms robust to unforeseen but plausible image corruptions of surgery, like smoke, bleeding, and low brightness. We collect and release corruption-free mock endoscopic video sequences for the challenge participants to train their algorithms and benchmark them on video sequences with photo-realistic non-adversarial corruptions for a binary robot tool segmentation task. This new benchmark will allow us to carefully study neural network robustness to non-adversarial corruptions of surgery, thus constituting an important first step towards more robust models for surgical computer vision. In this paper, we describe the data collection and annotation protocol, baseline evaluations of established segmentation models, and data augmentation-based techniques to enhance model robustness.

Deep neural networks (DNNs) have demonstrated remarkable empirical performance in large-scale supervised learning problems, particularly in scenarios where both the sample size $n$ and the dimension of covariates $p$ are large. This study delves into the application of DNNs across a wide spectrum of intricate causal inference tasks, where direct estimation falls short and necessitates multi-stage learning. Examples include estimating the conditional average treatment effect and dynamic treatment effect. In this framework, DNNs are constructed sequentially, with subsequent stages building upon preceding ones. To mitigate the impact of estimation errors from early stages on subsequent ones, we integrate DNNs in a doubly robust manner. In contrast to previous research, our study offers theoretical assurances regarding the effectiveness of DNNs in settings where the dimensionality $p$ expands with the sample size. These findings are significant independently and extend to degenerate single-stage learning problems.

While random forests are commonly used for regression problems, existing methods often lack adaptability in complex situations or lose optimality under simple, smooth scenarios. In this study, we introduce the adaptive split balancing forest (ASBF), capable of learning tree representations from data while simultaneously achieving minimax optimality under the Lipschitz class. To exploit higher-order smoothness levels, we further propose a localized version that attains the minimax rate under the H\"older class $\mathcal{H}^{q,\beta}$ for any $q\in\mathbb{N}$ and $\beta\in(0,1]$. Rather than relying on the widely-used random feature selection, we consider a balanced modification to existing approaches. Our results indicate that an over-reliance on auxiliary randomness may compromise the approximation power of tree models, leading to suboptimal results. Conversely, a less random, more balanced approach demonstrates optimality. Additionally, we establish uniform upper bounds and explore the application of random forests in average treatment effect estimation problems. Through simulation studies and real-data applications, we demonstrate the superior empirical performance of the proposed methods over existing random forests.

Vintage factor analysis is one important type of factor analysis that aims to first find a low-dimensional representation of the original data, and then to seek a rotation such that the rotated low-dimensional representation is scientifically meaningful. Perhaps the most widely used vintage factor analysis is the Principal Component Analysis (PCA) followed by the varimax rotation. Despite its popularity, little theoretical guarantee can be provided mainly because varimax rotation requires to solve a non-convex optimization over the set of orthogonal matrices. In this paper, we propose a deflation varimax procedure that solves each row of an orthogonal matrix sequentially. In addition to its net computational gain and flexibility, we are able to fully establish theoretical guarantees for the proposed procedure in a broad context. Adopting this new varimax approach as the second step after PCA, we further analyze this two step procedure under a general class of factor models. Our results show that it estimates the factor loading matrix in the optimal rate when the signal-to-noise-ratio (SNR) is moderate or large. In the low SNR regime, we offer possible improvement over using PCA and the deflation procedure when the additive noise under the factor model is structured. The modified procedure is shown to be optimal in all SNR regimes. Our theory is valid for finite sample and allows the number of the latent factors to grow with the sample size as well as the ambient dimension to grow with, or even exceed, the sample size. Extensive simulation and real data analysis further corroborate our theoretical findings.

Statistical inference and estimation for causal relationships has a long tradition and has attracted significant attention as the emerging of large and complex datasets and the need for new statistical tools to handle such challenging datasets. In many applications, data is collected dynamically over time, and individuals are exposed to treatments at multiple stages. Typical examples include mobile health datasets, electronic health records, and many other biomedical studies and political science datasets. This work considers statistical inference of causal effects for longitudinal and observational data with high-dimensional covariates (confounders). We aim to establish valid statistical inference for dynamic treatment effects under possible model misspecifications. For the sake of simplicity, we consider dynamic settings with two exposure times. Suppose that we collect independent and identically distributed (i.i.d.) samples S: (W

This paper proposes a confidence interval construction for heterogeneous treatment effects in the context of multi-stage experiments with $N$ samples and high-dimensional, $d$, confounders. Our focus is on the case of $d\gg N$, but the results obtained also apply to low-dimensional cases. We showcase that the bias of regularized estimation, unavoidable in high-dimensional covariate spaces, is mitigated with a simple double-robust score. In this way, no additional bias removal is necessary, and we obtain root-$N$ inference results while allowing multi-stage interdependency of the treatments and covariates. Memoryless property is also not assumed; treatment can possibly depend on all previous treatment assignments and all previous multi-stage confounders. Our results rely on certain sparsity assumptions of the underlying dependencies. We discover new product rate conditions necessary for robust inference with dynamic treatments.