Extreme rays of the (N,k)(N, k)-Schur Cone

We discuss several partial results towards proving Dennis White's conjecture on the extreme rays of the $(N,2)$-Schur cone. We are interested in which vectors are extreme in the cone generated by all products of Schur functions of partitions with $k$ or fewer parts. For the case where $k =2$, White conjectured that the extreme rays are obtained by excluding a certain family of "bad pairs," and proved a special case of the conjecture using Farkas' Lemma. We present an alternate proof of the special case, in addition to showing more infinite families of extreme rays and reducing White's conjecture to two simpler conjectures.Comment: This paper has been withdrawn by the authors due to a misinterpretation of the generalized Littlewood-Richardson rule in several proof

Credit Fraud Risk Detection Based on XGBoost-LR Hybrid Model

For a long time, the credit business has been the main business of banks and financial institutions. With the rapid growth of business scale, how to use models to detect fraud risk quickly and automatically is a hot research direction. Logistic regression has become the most widely used risk assessment model in the industry due to its good robustness and strong interpretability, but it relies on differentiated features and feature combinations. XGBoost is a powerful and convenient algorithm for feature transformation. Therefore, in this paper, XGBOOST can be used to effectively perform the advantages of feature combination, and a XGBoost-LR hybrid model is constructed. Firstly, use the data to train a XGBoost model, then give the samples in the training data to the XGBoost model to get the leaves nodes of the sample, and then use the leaves nodes after one-hot encoding as a feature to train an LR model. Using the German credit data set published by UCI to verify this model and compare AUC values with other models. The results show that this hybrid model can effectively improve the accuracy of model prediction and has a good application value

ShiftDDPMs: Exploring Conditional Diffusion Models by Shifting Diffusion Trajectories

Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed forward process and learn its reverse process to generate samples from noise in a denoising way. For conditional DDPMs, most existing practices relate conditions only to the reverse process and fit it to the reversal of unconditional forward process. We find this will limit the condition modeling and generation in a small time window. In this paper, we propose a novel and flexible conditional diffusion model by introducing conditions into the forward process. We utilize extra latent space to allocate an exclusive diffusion trajectory for each condition based on some shifting rules, which will disperse condition modeling to all timesteps and improve the learning capacity of model. We formulate our method, which we call \textbf{ShiftDDPMs}, and provide a unified point of view on existing related methods. Extensive qualitative and quantitative experiments on image synthesis demonstrate the feasibility and effectiveness of ShiftDDPMs.Comment: Accepted by AAAI 2023 Conferenc

Exploring Active 3D Object Detection from a Generalization Perspective

To alleviate the high annotation cost in LiDAR-based 3D object detection, active learning is a promising solution that learns to select only a small portion of unlabeled data to annotate, without compromising model performance. Our empirical study, however, suggests that mainstream uncertainty-based and diversity-based active learning policies are not effective when applied in the 3D detection task, as they fail to balance the trade-off between point cloud informativeness and box-level annotation costs. To overcome this limitation, we jointly investigate three novel criteria in our framework Crb for point cloud acquisition - label conciseness}, feature representativeness and geometric balance, which hierarchically filters out the point clouds of redundant 3D bounding box labels, latent features and geometric characteristics (e.g., point cloud density) from the unlabeled sample pool and greedily selects informative ones with fewer objects to annotate. Our theoretical analysis demonstrates that the proposed criteria align the marginal distributions of the selected subset and the prior distributions of the unseen test set, and minimizes the upper bound of the generalization error. To validate the effectiveness and applicability of \textsc{Crb}, we conduct extensive experiments on the two benchmark 3D object detection datasets of KITTI and Waymo and examine both one-stage (\textit{i.e.}, \textsc{Second}) and two-stage 3D detectors (i.e., Pv-rcnn). Experiments evidence that the proposed approach outperforms existing active learning strategies and achieves fully supervised performance requiring $1\%$ and $8\%$ annotations of bounding boxes and point clouds, respectively. Source code: https://github.com/Luoyadan/CRB-active-3Ddet.Comment: To appear in ICLR 202