arXiv subjects

Xuan Wu

Publications and source records attributed to Xuan Wu.

At least 55 records · Page 3Linked to original sources

arXiv2024

An Onboard Framework for Staircases Modeling Based on Point Clouds

The detection of traversable regions on staircases and the physical modeling constitutes pivotal aspects of the mobility of legged robots. This paper presents an onboard framework tailored to the detection of traversable regions and the modeling of physical attributes of staircases by point cloud data. To mitigate the influence of illumination variations and the overfitting due to the dataset diversity, a series of data augmentations are introduced to enhance the training of the fundamental network. A curvature suppression cross-entropy(CSCE) loss is proposed to reduce the ambiguity of prediction on the boundary between traversable and non-traversable regions. Moreover, a measurement correction based on the pose estimation of stairs is introduced to calibrate the output of raw modeling that is influenced by tilted perspectives. Lastly, we collect a dataset pertaining to staircases and introduce new evaluation criteria. Through a series of rigorous experiments conducted on this dataset, we substantiate the superior accuracy and generalization capabilities of our proposed method. Codes, models, and datasets will be available at https://github.com/szturobotics/Stair-detection-and-modeling-project.

cs.RO↗

arXiv2024

A Gaussian Process Based Method with Deep Kernel Learning for Pricing High-dimensional American Options

In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes to address the challenges traditionally associated with GPR. These challenges include its diminished reliability in high-dimensional scenarios and the excessive computational costs associated with processing extensive numbers of simulated paths Our findings indicate that the proposed method surpasses the performance of the least squares Monte Carlo method in high-dimensional scenarios, particularly when the underlying assets are modeled by Merton's jump diffusion model. Moreover, our approach does not exhibit a significant increase in computational time as the number of dimensions grows. Consequently, this method emerges as a potential tool for alleviating the challenges posed by the curse of dimensionality.

q-fin.CP↗

arXiv2024

On Optimal Coreset Construction for Euclidean $(k,z)$-Clustering

Constructing small-sized coresets for various clustering problems in different metric spaces has attracted significant attention for the past decade. A central problem in the coreset literature is to understand what is the best possible coreset size for $(k,z)$-clustering in Euclidean space. While there has been significant progress in the problem, there is still a gap between the state-of-the-art upper and lower bounds. For instance, the best known upper bound for $k$-means ($z=2$) is $\min \{O(k^{3/2} \varepsilon^{-2}),O(k \varepsilon^{-4})\}$ [1,2], while the best known lower bound is $Ω(k\varepsilon^{-2})$ [1]. In this paper, we make significant progress on both upper and lower bounds. For a large range of parameters (i.e., $\varepsilon, k$), we have a complete understanding of the optimal coreset size. In particular, we obtain the following results: (1) We present a new coreset lower bound $Ω(k \varepsilon^{-z-2})$ for Euclidean $(k,z)$-clustering when $\varepsilon \geq Ω(k^{-1/(z+2)})$. In view of the prior upper bound $\tilde{O}_z(k \varepsilon^{-z-2})$ [1], the bound is optimal. The new lower bound also implies improved lower bounds for $(k,z)$-clustering in doubling metrics. (2) For the upper bound, we provide efficient coreset construction algorithms for $(k,z)$-clustering with improved or optimal coreset sizes in several metric spaces. In particular, we provide an $\tilde{O}_z(k^{\frac{2z+2}{z+2}} \varepsilon^{-2})$-sized coreset, with a unfied analysis, for $(k,z)$-clustering for all $z\geq 1$ in Euclidean space. [1] Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC'22. [2] Cohen-Addad, Larsen, Saulpic, Schwiegelshohn, Sheikh-Omar, NeurIPS'22.

cs.DS↗

arXiv2024

Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient

Diffusion models (DMs) are a type of generative model that has a huge impact on image synthesis and beyond. They achieve state-of-the-art generation results in various generative tasks. A great diversity of conditioning inputs, such as text or bounding boxes, are accessible to control the generation. In this work, we propose a conditioning mechanism utilizing Gaussian mixture models (GMMs) as feature conditioning to guide the denoising process. Based on set theory, we provide a comprehensive theoretical analysis that shows that conditional latent distribution based on features and classes is significantly different, so that conditional latent distribution on features produces fewer defect generations than conditioning on classes. Two diffusion models conditioned on the Gaussian mixture model are trained separately for comparison. Experiments support our findings. A novel gradient function called the negative Gaussian mixture gradient (NGMG) is proposed and applied in diffusion model training with an additional classifier. Training stability has improved. We also theoretically prove that NGMG shares the same benefit as the Earth Mover distance (Wasserstein) as a more sensible cost function when learning distributions supported by low-dimensional manifolds.

cs.LG↗

arXiv2024

Distilling Autoregressive Models to Obtain High-Performance Non-Autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed

Neural construction models have shown promising performance for Vehicle Routing Problems (VRPs) by adopting either the Autoregressive (AR) or Non-Autoregressive (NAR) learning approach. While AR models produce high-quality solutions, they generally have a high inference latency due to their sequential generation nature. Conversely, NAR models generate solutions in parallel with a low inference latency but generally exhibit inferior performance. In this paper, we propose a generic Guided Non-Autoregressive Knowledge Distillation (GNARKD) method to obtain high-performance NAR models having a low inference latency. GNARKD removes the constraint of sequential generation in AR models while preserving the learned pivotal components in the network architecture to obtain the corresponding NAR models through knowledge distillation. We evaluate GNARKD by applying it to three widely adopted AR models to obtain NAR VRP solvers for both synthesized and real-world instances. The experimental results demonstrate that GNARKD significantly reduces the inference time (4-5 times faster) with acceptable performance drop (2-3\%). To the best of our knowledge, this study is first-of-its-kind to obtain NAR VRP solvers from AR ones through knowledge distillation.

cs.LG↗

arXiv2023

Incorporating Surprisingly Popular Algorithm and Euclidean Distance-based Adaptive Topology into PSO

While many Particle Swarm Optimization (PSO) algorithms only use fitness to assess the performance of particles, in this work, we adopt Surprisingly Popular Algorithm (SPA) as a complementary metric in addition to fitness. Consequently, particles that are not widely known also have the opportunity to be selected as the learning exemplars. In addition, we propose a Euclidean distance-based adaptive topology to cooperate with SPA, where each particle only connects to k number of particles with the shortest Euclidean distance during each iteration. We also introduce the adaptive topology into heterogeneous populations to better solve large-scale problems. Specifically, the exploration sub-population better preserves the diversity of the population while the exploitation sub-population achieves fast convergence. Therefore, large-scale problems can be solved in a collaborative manner to elevate the overall performance. To evaluate the performance of our method, we conduct extensive experiments on various optimization problems, including three benchmark suites and two real-world optimization problems. The results demonstrate that our Euclidean distance-based adaptive topology outperforms the other widely adopted topologies and further suggest that our method performs significantly better than state-of-the-art PSO variants on small, medium, and large-scale problems.

cs.NE↗

arXiv2023

An Efficient 1 Iteration Learning Algorithm for Gaussian Mixture Model And Gaussian Mixture Embedding For Neural Network

We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves the accuracy and only take 1 iteration for learning. We theoretically proof that this new algorithm is guarantee to converge regardless the parameters initialisation. We compare our GMM expansion method with classic probability layers in neural network leads to demonstrably better capability to overcome data uncertainty and inverse problem. Finally, we test GMM based generator which shows a potential to build further application that able to utilized distribution random sampling for stochastic variation as well as variation control.

cs.LG↗

arXiv2023

Improved Coresets for Clustering with Capacity and Fairness Constraints

We study coresets for clustering with capacity and fairness constraints. Our main result is a near-linear time algorithm to construct $\tilde{O}(k^2\varepsilon^{-2z-2})$-sized $\varepsilon$-coresets for capacitated $(k,z)$-clustering which improves a recent $\tilde{O}(k^3\varepsilon^{-3z-2})$ bound by [BCAJ+22, HJLW23]. As a corollary, we also save a factor of $k \varepsilon^{-z}$ on the coreset size for fair $(k,z)$-clustering compared to them. We fundamentally improve the hierarchical uniform sampling framework of [BCAJ+22] by adaptively selecting sample size on each ring instance, proportional to its clustering cost to an optimal solution. Our analysis relies on a key geometric observation that reduces the number of total ``effective centers" from [BCAJ+22]'s $\tilde{O}(k^2\varepsilon^{-z})$ to merely $O(k\log \varepsilon^{-1})$ by being able to ``ignore'' all center points that are too far or too close to the ring center.

cs.DS↗

arXiv2023

Youku-mPLUG: A 10 Million Large-scale Chinese Video-Language Dataset for Pre-training and Benchmarks

To promote the development of Vision-Language Pre-training (VLP) and multimodal Large Language Model (LLM) in the Chinese community, we firstly release the largest public Chinese high-quality video-language dataset named Youku-mPLUG, which is collected from Youku, a well-known Chinese video-sharing website, with strict criteria of safety, diversity, and quality. Youku-mPLUG contains 10 million Chinese video-text pairs filtered from 400 million raw videos across a wide range of 45 diverse categories for large-scale pre-training. In addition, to facilitate a comprehensive evaluation of video-language models, we carefully build the largest human-annotated Chinese benchmarks covering three popular video-language tasks of cross-modal retrieval, video captioning, and video category classification. Youku-mPLUG can enable researchers to conduct more in-depth multimodal research and develop better applications in the future. Furthermore, we release popular video-language pre-training models, ALPRO and mPLUG-2, and our proposed modularized decoder-only model mPLUG-video pre-trained on Youku-mPLUG. Experiments show that models pre-trained on Youku-mPLUG gain up to 23.1% improvement in video category classification. Besides, mPLUG-video achieves a new state-of-the-art result on these benchmarks with 80.5% top-1 accuracy in video category classification and 68.9 CIDEr score in video captioning, respectively. Finally, we scale up mPLUG-video based on the frozen Bloomz with only 1.7% trainable parameters as Chinese multimodal LLM, and demonstrate impressive instruction and video understanding ability. The zero-shot instruction understanding experiment indicates that pretraining with Youku-mPLUG can enhance the ability to comprehend overall and detailed visual semantics, recognize scene text, and leverage open-domain knowledge.

cs.CV↗

arXiv2023

On Coresets for Clustering in Small Dimensional Euclidean Spaces

We consider the problem of constructing small coresets for $k$-Median in Euclidean spaces. Given a large set of data points $P\subset \mathbb{R}^d$, a coreset is a much smaller set $S\subset \mathbb{R}^d$, so that the $k$-Median costs of any $k$ centers w.r.t. $P$ and $S$ are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small $d$ is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for $k$-Median in small dimensions. For small $d$, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small $d$. In particular, we completely settle the coreset size bound for $1$-d $k$-Median (up to log factors). Interestingly, our results imply a strong separation between $1$-d $1$-Median and $1$-d $2$-Median. As far as we know, this is the first such separation between $k=1$ and $k=2$ in any dimension.

cs.DS↗

arXiv2022

Shape-Aware Fine-Grained Classification of Erythroid Cells

Fine-grained classification and counting of bone marrow erythroid cells are vital for evaluating the health status and formulating therapeutic schedules for leukemia or hematopathy. Due to the subtle visual differences between different types of erythroid cells, it is challenging to apply existing image-based deep learning models for fine-grained erythroid cell classification. Moreover, there is no large open-source datasets on erythroid cells to support the model training. In this paper, we introduce BMEC (Bone Morrow Erythroid Cells), the first large fine-grained image dataset of erythroid cells, to facilitate more deep learning research on erythroid cells. BMEC contains 5,666 images of individual erythroid cells, each of which is extracted from the bone marrow erythroid cell smears and professionally annotated to one of the four types of erythroid cells. To distinguish the erythroid cells, one key indicator is the cell shape which is closely related to the cell growth and maturation. Therefore, we design a novel shape-aware image classification network for fine-grained erythroid cell classification. The shape feature is extracted from the shape mask image and aggregated to the raw image feature with a shape attention module. With the shape-attended image feature, our network achieved superior classification performance (81.12\% top-1 accuracy) on the BMEC dataset comparing to the baseline methods. Ablation studies also demonstrate the effectiveness of incorporating the shape information for the fine-grained cell classification. To further verify the generalizability of our method, we tested our network on two additional public white blood cells (WBC) datasets and the results show our shape-aware method can generally outperform recent state-of-the-art works on classifying the WBC. The code and BMEC dataset can be found on https://github.com/wangye8899/BMEC.

cs.CV↗

arXiv2022

Coresets for Clustering in Graphs of Bounded Treewidth

We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path metric of edge-weighted graphs. Such clustering problems are essential to data analysis and used for example in road networks and data visualization. A coreset is a compact summary of the data that approximately preserves the clustering objective for every possible center set, and it offers significant efficiency improvements in terms of running time, storage, and communication, including in streaming and distributed settings. Our main result is a near-linear time construction of a coreset for k-Median in a general graph $G$, with size $O_{ε, k}(\mathrm{tw}(G))$ where $\mathrm{tw}(G)$ is the treewidth of $G$, and we complement the construction with a nearly-tight size lower bound. The construction is based on the framework of Feldman and Langberg [STOC 2011], and our main technical contribution, as required by this framework, is a uniform bound of $O(\mathrm{tw}(G))$ on the shattering dimension under any point weights. We validate our coreset on real-world road networks, and our scalable algorithm constructs tiny coresets with high accuracy, which translates to a massive speedup of existing approximation algorithms such as local search for graph k-Median.

cs.DS↗

arXiv2022

Differentiable Fuzzy $\mathcal{ALC}$: A Neural-Symbolic Representation Language for Symbol Grounding

Neural-symbolic computing aims at integrating robust neural learning and sound symbolic reasoning into a single framework, so as to leverage the complementary strengths of both of these, seemingly unrelated (maybe even contradictory) AI paradigms. The central challenge in neural-symbolic computing is to unify the formulation of neural learning and symbolic reasoning into a single framework with common semantics, that is, to seek a joint representation between a neural model and a logical theory that can support the basic grounding learned by the neural model and also stick to the semantics of the logical theory. In this paper, we propose differentiable fuzzy $\mathcal{ALC}$ (DF-$\mathcal{ALC}$) for this role, as a neural-symbolic representation language with the desired semantics. DF-$\mathcal{ALC}$ unifies the description logic $\mathcal{ALC}$ and neural models for symbol grounding; in particular, it infuses an $\mathcal{ALC}$ knowledge base into neural models through differentiable concept and role embeddings. We define a hierarchical loss to the constraint that the grounding learned by neural models must be semantically consistent with $\mathcal{ALC}$ knowledge bases. And we find that capturing the semantics in grounding solely by maximizing satisfiability cannot revise grounding rationally. We further define a rule-based loss for DF adapting to symbol grounding problems. The experiment results show that DF-$\mathcal{ALC}$ with rule-based loss can improve the performance of image object detectors in an unsupervised learning way, even in low-resource situations.

cs.AI↗

arXiv2022

Near-optimal Coresets for Robust Clustering

We consider robust clustering problems in $\mathbb{R}^d$, specifically $k$-clustering problems (e.g., $k$-Median and $k$-Means with $m$ outliers, where the cost for a given center set $C \subset \mathbb{R}^d$ aggregates the distances from $C$ to all but the furthest $m$ data points, instead of all points as in classical clustering. We focus on the $ε$-coreset for robust clustering, a small proxy of the dataset that preserves the clustering cost within $ε$-relative error for all center sets. Our main result is an $ε$-coreset of size $O(m + \mathrm{poly}(k ε^{-1}))$ that can be constructed in near-linear time. This significantly improves previous results, which either suffers an exponential dependence on $(m + k)$ [Feldman and Schulman, SODA'12], or has a weaker bi-criteria guarantee [Huang et al., FOCS'18]. Furthermore, we show this dependence in $m$ is nearly-optimal, and the fact that it is isolated from other factors may be crucial for dealing with large number of outliers. We construct our coresets by adapting to the outlier setting a recent framework [Braverman et al., FOCS'22] which was designed for capacity-constrained clustering, overcoming a new challenge that the participating terms in the cost, particularly the excluded $m$ outlier points, are dependent on the center set $C$. We validate our coresets on various datasets, and we observe a superior size-accuracy tradeoff compared with popular baselines including uniform sampling and sensitivity sampling. We also achieve a significant speedup of existing approximation algorithms for robust clustering using our coresets.

cs.DS↗

arXiv2022

The Bessel Line Ensemble

In this paper, we construct the Bessel line ensemble, a countable collection of continuous random curves. This line ensemble is stationary under horizontal shifts with the Bessel point process as its one-time marginal. Its finite dimensional distributions are given by the extended Bessel kernel. Furthermore, it enjoys a novel resampling invariance with respect to non-intersecting squared Bessel bridges. The Bessel line ensemble is constructed by extracting the hard edge scaling limit of a collection of independent squared Bessel processes starting at the origin and never being conditioned to intersect. This process is also known as the Dyson Bessel process, and it arises as the evolution of the eigenvalues of the Laguerre unitary ensemble with i.i.d. complex Brownian entries.

math.PR↗

arXiv2022

The Power of Uniform Sampling for Coresets

Motivated by practical generalizations of the classic $k$-median and $k$-means objectives, such as clustering with size constraints, fair clustering, and Wasserstein barycenter, we introduce a meta-theorem for designing coresets for constrained-clustering problems. The meta-theorem reduces the task of coreset construction to one on a bounded number of ring instances with a much-relaxed additive error. This reduction enables us to construct coresets using uniform sampling, in contrast to the widely-used importance sampling, and consequently we can easily handle constrained objectives. Notably and perhaps surprisingly, this simpler sampling scheme can yield coresets whose size is independent of $n$, the number of input points. Our technique yields smaller coresets, and sometimes the first coresets, for a large number of constrained clustering problems, including capacitated clustering, fair clustering, Euclidean Wasserstein barycenter, clustering in minor-excluded graph, and polygon clustering under Fréchet and Hausdorff distance. Finally, our technique yields also smaller coresets for $1$-median in low-dimensional Euclidean spaces, specifically of size $\tilde{O}(\varepsilon^{-1.5})$ in $\mathbb{R}^2$ and $\tilde{O}(\varepsilon^{-1.6})$ in $\mathbb{R}^3$.

cs.DS↗

arXiv2022

Brownian regularity for the KPZ line ensemble

This paper seeks a quantitative comparison between the curves in the KPZ line ensemble [CH16] and a standard Brownian bridge under the $t^{1/3}$ vertical and $t^{2/3}$ horizontal scaling. The estimate we obtained is parallel to the one established in [Ham1], where the Airy line ensemble was studied. Our main tool is the soft Brownian Gibbs property enjoyed by the KPZ line ensemble. In view of the Gibbs property, the KPZ line ensemble differs from the Airy line ensemble mainly due to the intersecting nature of its curves, which results in the main technical difficulty in this paper. We develop a resampling framework, the soft jump ensemble, to tackle this difficulty. Our method is highly inspired by the jump ensemble technique developed in [Ham1].

math.PR↗

arXiv2022

New Coresets for Projective Clustering and Applications

$(j,k)$-projective clustering is the natural generalization of the family of $k$-clustering and $j$-subspace clustering problems. Given a set of points $P$ in $\mathbb{R}^d$, the goal is to find $k$ flats of dimension $j$, i.e., affine subspaces, that best fit $P$ under a given distance measure. In this paper, we propose the first algorithm that returns an $L_\infty$ coreset of size polynomial in $d$. Moreover, we give the first strong coreset construction for general $M$-estimator regression. Specifically, we show that our construction provides efficient coreset constructions for Cauchy, Welsch, Huber, Geman-McClure, Tukey, $L_1-L_2$, and Fair regression, as well as general concave and power-bounded loss functions. Finally, we provide experimental results based on real-world datasets, showing the efficacy of our approach.

cs.LG↗