The deployment of large language models (LLMs) in diverse applications requires a thorough understanding of their decision-making strategies and behavioral patterns. As a supplement to a recent study on the behavioral Turing test, this paper presents a comprehensive analysis of five leading LLM-based chatbot families as they navigate a series of behavioral economics games. By benchmarking these AI chatbots, we aim to uncover and document both common and distinct behavioral patterns across a range of scenarios. The findings provide valuable insights into the strategic preferences of each LLM, highlighting potential implications for their deployment in critical decision-making roles.

Point Cloud Interpolation confronts challenges from point sparsity, complex spatiotemporal dynamics, and the difficulty of deriving complete 3D point clouds from sparse temporal information. This paper presents NeuroGauss4D-PCI, which excels at modeling complex non-rigid deformations across varied dynamic scenes. The method begins with an iterative Gaussian cloud soft clustering module, offering structured temporal point cloud representations. The proposed temporal radial basis function Gaussian residual utilizes Gaussian parameter interpolation over time, enabling smooth parameter transitions and capturing temporal residuals of Gaussian distributions. Additionally, a 4D Gaussian deformation field tracks the evolution of these parameters, creating continuous spatiotemporal deformation fields. A 4D neural field transforms low-dimensional spatiotemporal coordinates ($x,y,z,t$) into a high-dimensional latent space. Finally, we adaptively and efficiently fuse the latent features from neural fields and the geometric features from Gaussian deformation fields. NeuroGauss4D-PCI outperforms existing methods in point cloud frame interpolation, delivering leading performance on both object-level (DHB) and large-scale autonomous driving datasets (NL-Drive), with scalability to auto-labeling and point cloud densification tasks. The source code is released at https://github.com/jiangchaokang/NeuroGauss4D-PCI.

Monocular depth estimation is an ill-posed problem as the same 2D image can be projected from infinite 3D scenes. Although the leading algorithms in this field have reported significant improvement, they are essentially geared to the particular compound of pictorial observations and camera parameters (i.e., intrinsics and extrinsics), strongly limiting their generalizability in real-world scenarios. To cope with this challenge, this paper proposes a novel ground embedding module to decouple camera parameters from pictorial cues, thus promoting the generalization capability. Given camera parameters, the proposed module generates the ground depth, which is stacked with the input image and referenced in the final depth prediction. A ground attention is designed in the module to optimally combine ground depth with residual depth. Our ground embedding is highly flexible and lightweight, leading to a plug-in module that is amenable to be integrated into various depth estimation networks. Experiments reveal that our approach achieves the state-of-the-art results on popular benchmarks, and more importantly, renders significant generalization improvement on a wide range of cross-domain tests.

Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss of CCA by the excess prediction loss defined through a prediction-after-dimension-reduction framework. Such framework suggests viewing CCA estimation as estimating the subspaces spanned by the canonical variates. Interestedly, the proposed error metrics derived from the excess prediction loss turn out to be closely related to the principal angles between the subspaces spanned by the population and sample canonical variates respectively. We characterize the non-asymptotic minimax rates under the proposed metrics, especially the dependency of the minimax rates on the key quantities including the dimensions, the condition number of the covariance matrices, the canonical correlations and the eigen-gap, with minimal assumptions on the joint covariance matrix. To the best of our knowledge, this is the first finite sample result that captures the effect of the canonical correlations on the minimax rates.

Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their close connection to generalized linear models, it is also natural to incorporate covariate information in them. The current paper presents two universal fitting algorithms for networks with edge covariates: one based on nuclear norm penalization and the other based on projected gradient descent. Both algorithms are motivated by maximizing likelihood for a special class of inner-product models while working simultaneously for a wide range of different latent space models, such as distance models, which allow latent vectors to affect edge formation in flexible ways. These fitting methods, especially the one based on projected gradient descent, are fast and scalable to large networks. We obtain their rates of convergence for both inner-product models and beyond. The effectiveness of the modeling approach and fitting algorithms is demonstrated on five real world network datasets for different statistical tasks, including community detection with and without edge covariates, and network assisted learning.

Canonical Correlation Analysis (CCA) is a widely used spectral technique for finding correlation structures in multi-view datasets. In this paper, we tackle the problem of large scale CCA, where classical algorithms, usually requiring computing the product of two huge matrices and huge matrix decomposition, are computationally and storage expensive. We recast CCA from a novel perspective and propose a scalable and memory efficient Augmented Approximate Gradient (AppGrad) scheme for finding top $k$ dimensional canonical subspace which only involves large matrix multiplying a thin matrix of width $k$ and small matrix decomposition of dimension $k\times k$. Further, AppGrad achieves optimal storage complexity $O(k(p_1+p_2))$, compared with classical algorithms which usually require $O(p_1^2+p_2^2)$ space to store two dense whitening matrices. The proposed scheme naturally generalizes to stochastic optimization regime, especially efficient for huge datasets where batch algorithms are prohibitive. The online property of stochastic AppGrad is also well suited to the streaming scenario, where data comes sequentially. To the best of our knowledge, it is the first stochastic algorithm for CCA. Experiments on four real data sets are provided to show the effectiveness of the proposed methods.