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Robert Reed, Luca Laurenti, Morteza Lahijanian

Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains. Such applications have two key features: (i) they require rigorous error quantification, and (ii) the noise is often bounded and non-Gaussian due to, e.g., physical constraints. While error bounds for applying GPR in the presence of non-Gaussian noise exist, they tend to be overly restrictive and conservative in practice. In this paper, we provide novel error bounds for GPR under bounded support noise. Specifically, by relying on concentration inequalities and assuming that the latent function has low complexity in the reproducing kernel Hilbert space (RKHS) corresponding to the GP kernel, we derive both probabilistic and deterministic bounds on the error of the GPR. We show that these errors are substantially tighter than existing state-of-the-art bounds and are particularly well-suited for GPR with neural network kernels, i.e., Deep Kernel Learning (DKL). Furthermore, motivated by applications in safety-critical domains, we illustrate how these bounds can be combined with stochastic barrier functions to successfully quantify the safety probability of an unknown dynamical system from finite data. We validate the efficacy of our approach through several benchmarks and comparisons against existing bounds. The results show that our bounds are consistently smaller, and that DKLs can produce error bounds tighter than sample noise, significantly improving the safety probability of control systems.

Rajalaxmi Rajagopalan, Yu-Lin Wei, Romit Roy Choudhury

Black box optimization (BBO) focuses on optimizing unknown functions in high-dimensional spaces. In many applications, sampling the unknown function is expensive, imposing a tight sample budget.Ongoing work is making progress on reducing the sample budget by learning the shape/structure of the function, known as kernel learning. We propose a new method to learn the kernel of a Gaussian Process. Our idea is to create a continuous kernel space in the latent space of a variational autoencoder, and run an auxiliary optimization to identify the best kernel. Results show that the proposed method, Kernel Optimized Blackbox Optimization (KOBO), outperforms state of the art by estimating the optimal at considerably lower sample budgets. Results hold not only across synthetic benchmark functions but also in real applications. We show that a hearing aid may be personalized with fewer audio queries to the user, or a generative model could converge to desirable images from limited user ratings.

Minh-Duc Nguyen, Phuong Mai Dinh, Quang-Huy Nguyen, Long P. Hoang, Dung D. Le

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

Nobuo Namura, Sho Takemori

Real-world optimization problems often involve complex objective functions with costly evaluations. While Bayesian optimization (BO) with Gaussian processes is effective for these challenges, it suffers in high-dimensional spaces due to performance degradation from limited function evaluations. To overcome this, simplification techniques like dimensionality reduction have been employed, yet they often rely on assumptions about the problem characteristics, potentially underperforming when these assumptions do not hold. Trust-region-based methods, which avoid such assumptions, focus on local search but risk stagnation in local optima. In this study, we propose a novel acquisition function, regional expected improvement (REI), designed to enhance trust-region-based BO in medium to high-dimensional settings. REI identifies regions likely to contain the global optimum, improving performance without relying on specific problem characteristics. We provide a theoretical proof that REI effectively identifies optimal trust regions and empirically demonstrate that incorporating REI into trust-region-based BO outperforms conventional BO and other high-dimensional BO methods in medium to high-dimensional real-world problems.

Giorgio Morales, John W. Sheppard

Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and time-consuming. This paper presents an adaptive sampling approach designed to reduce epistemic uncertainty in predictive models. Our primary contribution is the development of a metric that estimates potential epistemic uncertainty leveraging prediction interval-generation neural networks. This estimation relies on the distance between the predicted upper and lower bounds and the observed data at the tested positions and their neighboring points. Our second contribution is the proposal of a batch sampling strategy based on Gaussian processes (GPs). A GP is used as a surrogate model of the networks trained at each iteration of the adaptive sampling process. Using this GP, we design an acquisition function that selects a combination of sampling locations to maximize the reduction of epistemic uncertainty across the domain. We test our approach on three unidimensional synthetic problems and a multi-dimensional dataset based on an agricultural field for selecting experimental fertilizer rates. The results demonstrate that our method consistently converges faster to minimum epistemic uncertainty levels compared to Normalizing Flows Ensembles, MC-Dropout, and simple GPs.

Jiaxing Li, Wei Liu, Chao Xue, Yibing Zhan, Xiaoxing Wang, Weifeng Liu, Dacheng Tao

Bayesian Optimization (BO) is a sample-efficient black-box optimizer commonly used in search spaces where hyperparameters are independent. However, in many practical AutoML scenarios, there will be dependencies among hyperparameters, forming a conditional search space, which can be partitioned into structurally distinct subspaces. The structure and dimensionality of hyperparameter configurations vary across these subspaces, challenging the application of BO. Some previous BO works have proposed solutions to develop multiple Gaussian Process models in these subspaces. However, these approaches tend to be inefficient as they require a substantial number of observations to guarantee each GP's performance and cannot capture relationships between hyperparameters across different subspaces. To address these issues, this paper proposes a novel approach to model the response surfaces of all subspaces in one, which can model the relationships between hyperparameters elegantly via a self-attention mechanism. Concretely, we design a structure-aware hyperparameter embedding to preserve the structural information. Then, we introduce an attention-based deep feature extractor, capable of projecting configurations with different structures from various subspaces into a unified feature space, where the response surfaces can be formulated using a single standard Gaussian Process. The empirical results on a simulation function, various real-world tasks, and HPO-B benchmark demonstrate that our proposed approach improves the efficacy and efficiency of BO within conditional search spaces.

Yuanhao Lai, Pengfei Zheng, Chenpeng Ji, Cheng Qiu, Tingkai Wang, Songhan Zhang, Zhengang Wang, Yunfei Du

Bayesian optimization (BO) is a key technique for solving black-box optimization problems. This study extends the scope of BO from conventional applications (e.g., AutoML and robotics learning) to automated tuning of software systems. Despite GP (Gaussian Process) implementing a foundation formalism for exploitation and exploration in BO, its limited predictive power and unrealistic assumptions (e.g., continuity and Gaussianity) can severely affect its effectiveness and efficiency in tuning complex software systems. To overcome these limitations, we propose a BO framework CoffeeBoost, which implements exploitation and exploration with a GBDT-native distribution-free probabilistic surrogate model. CoffeeBoost constructs surrogate models via stochastic gradient boosting ensembles (SGBE) and quantifies probabilistic distributions via distribution-free conformal predictive systems. Moreover, CoffeeBoost leverages the residual paths in SGBE to improve the local adaptiveness of the resulting predictive distributions in a GBDT-native manner. Across eight auto-tuning benchmarks for database management systems (DBMS), we evaluate CoffeeBoost and show its superior learnability and optimizability against existing GP-based and tree-ensemble-based BO schemes. Detailed analysis further shows CoffeeBoost's predictive distributions excel in both coverage and tightness.

Huiqun Huang, Sihong He, Fei Miao

Trajectory prediction models that can infer both future trajectories and their associated uncertainties of the target vehicles is crucial for safe and robust navigation and path planning of autonomous vehicles. However, the majority of existing trajectory prediction models have neither considered reducing the uncertainty as one objective during the training stage nor provided reliable uncertainty quantification during inference stage, especially under potential distribution shift. Therefore, in this paper, we propose the Conformal Uncertainty Quantification under Distribution Shift framework, CUQDS, to quantify the uncertainty of the predicted trajectories of existing trajectory prediction models under potential data distribution shift, while improving the prediction accuracy of the models and reducing the estimated uncertainty during the training stage. Specifically, CUQDS includes 1) a learning-based Gaussian process regression module that models the output distribution of the base model (any existing trajectory prediction neural networks) and reduces the estimated uncertainty by an additional loss term, and 2) a statistical-based Conformal P control module to calibrate the estimated uncertainty from the Gaussian process regression module in an online setting under potential distribution shift between training and testing data. Experimental results on various state-of-the-art methods using benchmark motion forecasting datasets demonstrate the effectiveness of our proposed design.

Tilman Hoffbauer, Holger H. Hoos, Jakob Bossek

Time series forecasting requires reliable uncertainty estimates. Gaussian process regression provides a powerful framework for modelling this in a probabilistic fashion. However, its application to large time series is challenging, due to its cubic time complexity and quadratic memory requirement. In this work, we present KernelMatmul, a novel method that accelerates Gaussian process inference and thus facilitates scaling of Gaussian process regression to large, irregularly sampled and multi-output time series. Leveraging conjugate gradients in combination with sparsity approximation, KernelMatmul achieves time and memory complexity linear in the number of samples. We thoroughly benchmark our new method against multiple baselines to demonstrate its benefits and limitations, both in efficiency and accuracy.

Wenwen Gong, Yangliao Geng, Dan Zhang, Yifan Zhu, Xiaolong Xu, Haolong Xiang, Amin Beheshti, Xuyun Zhang, Lianyong Qi

Graph Contrastive Learning (GCL), as a primary paradigm of graph self-supervised learning, spurs a fruitful line of research in tackling the data sparsity issue by maximizing the consistency of user/item embeddings between different augmented views with random perturbations. However, diversity, as a crucial metric for recommendation performance and user satisfaction, has received rather little attention. In fact, there exists a challenging dilemma in balancing accuracy and diversity. To address these issues, we propose a new Graph Contrastive Learning (DivGCL) model for diversifying recommendations. Inspired by the excellence of the determinant point process (DPP), DivGCL adopts a DPP likelihood-based loss function to achieve an ideal trade-off between diversity and accuracy, optimizing it jointly with the advanced Gaussian noise-augmented GCL objective. Extensive experiments on four popular datasets demonstrate that DivGCL surpasses existing approaches in balancing accuracy and diversity, with an improvement of 23.47% at T@20 (abbreviation for trade-off metric) on ML-1M.

Jiaxin Gao, Qinglong Cao, Yuntian Chen

Time series forecasting (TSF) is essential in various domains, and recent advancements in diffusion-based TSF models have shown considerable promise. However, these models typically adopt traditional diffusion patterns, treating TSF as a noise-based conditional generation task. This approach neglects the inherent continuous sequential nature of time series, leading to a fundamental misalignment between diffusion mechanisms and the TSF objective, thereby severely impairing performance. To bridge this misalignment, and inspired by the classic Auto-Regressive Moving Average (ARMA) theory, which views time series as continuous sequential progressions evolving from previous data points, we propose a novel Auto-Regressive Moving Diffusion (ARMD) model to first achieve the continuous sequential diffusion-based TSF. Unlike previous methods that start from white Gaussian noise, our model employs chain-based diffusion with priors, accurately modeling the evolution of time series and leveraging intermediate state information to improve forecasting accuracy and stability. Specifically, our approach reinterprets the diffusion process by considering future series as the initial state and historical series as the final state, with intermediate series generated using a sliding-based technique during the forward process. This design aligns the diffusion model's sampling procedure with the forecasting objective, resulting in an unconditional, continuous sequential diffusion TSF model. Extensive experiments conducted on seven widely used datasets demonstrate that our model achieves state-of-the-art performance, significantly outperforming existing diffusion-based TSF models.

Junwei Cheng, Chaobo He, Pengxing Feng, Weixiong Liu, Kunlin Han, Yong Tang

Variational autoencoder performs well in community detection on static networks, but it is difficult to directly extend to continuous dynamic networks. The main reason is that traditional methods mainly rely on adjacency structures to complete the inference and generation processes. However, continuous dynamic networks cannot be described by this structure because the inherent timeliness and causality information of the network would be lost. To address this issue, we propose a novel variational autoencoder, CT-VAE, for community detection in continuous dynamic networks, along with its scalable variant, CT-CAVAE. By conceptualizing node interactions as event streams and adopting the Hawkes process to capture temporal dynamics and causality, and incorporating them into the inference process, CT-VAE can effectively extend the traditional inference approach to continuous dynamic networks. Additionally, in the generation phase, CT-VAE combines pseudo-labeling and compact constraint strategies to facilitate the reconstruction process of non-adjacent structures. For the scalable variant, CT-CAVAE, end-to-end community detection is achieved by cleverly combining Gaussian mixture distribution. Extensive experimental results demonstrate that the proposed CT-VAE and CT-CAVAE achieve more favorable performance compared with the state-of-the-art baselines.

Xingyu Zhu, Xiapu Luo, Xuetao Wei

Recent advancements in text-to-3D generation can generate neural radiance fields (NeRFs) with score distillation sampling, enabling 3D asset creation without real-world data capture. With the rapid advancement in NeRF generation quality, protecting the copyright of the generated NeRF has become increasingly important. While prior works can watermark NeRFs in a post-generation way, they suffer from two vulnerabilities. First, a delay lies between NeRF generation and watermarking because the secret message is embedded into the NeRF model post-generation through fine-tuning. Second, generating a non-watermarked NeRF as an intermediate creates a potential vulnerability for theft. To address both issues, we propose Dreamark to embed a secret message by backdooring the NeRF during NeRF generation. In detail, we first pre-train a watermark decoder. Then, Dreamark generates backdoored NeRFs in a way that the target secret message can be verified by the pre-trained watermark decoder on an arbitrary trigger viewport. We evaluate the generation quality and watermark robustness against image- and model-level attacks. Extensive experiments show that the watermarking process will not degrade the generation quality, and the watermark achieves 90+% accuracy among both image-level attacks (e.g., Gaussian noise) and model-level attacks (e.g., pruning attack).

Xiaohan Zhang, Zhenyu Sun, Yukui Qiu, Junyan Su, Qi Liu

Currently, 3D rendering for large-scale free camera trajectories, namely, arbitrary input camera trajectories, poses significant challenges: 1) The distribution and observation angles of the cameras are irregular, and various types of scenes are included in the free trajectories; 2) Processing the entire point cloud and all images at once for large-scale scenes requires a substantial amount of GPU memory. This paper presents a Toy-GS method for accurately rendering large-scale free camera trajectories. Specifically, we propose an adaptive spatial division approach for free trajectories to divide cameras and the sparse point cloud of the entire scene into various regions according to camera poses. Training each local Gaussian in parallel for each area enables us to concentrate on texture details and minimize GPU memory usage. Next, we use the multi-view constraint and position-aware point adaptive control (PPAC) to improve the rendering quality of texture details. In addition, our regional fusion approach combines local and global Gaussians to enhance rendering quality with an increasing number of divided areas. Extensive experiments have been carried out to confirm the effectiveness and efficiency of Toy-GS, leading to state-of-the-art results on two public large-scale datasets as well as our SCUTic dataset. Our proposal demonstrates an enhancement of 1.19 dB in PSNR and conserves 7 G of GPU memory when compared to various benchmarks.

Wenbo Zhang, Lu Zhang, Ping Hu, Liqian Ma, Yunzhi Zhuge, Huchuan Lu

Injecting semantics into 3D Gaussian Splatting (3DGS) has recently garnered significant attention. While current approaches typically distill 3D semantic features from 2D foundational models (e.g., CLIP and SAM) to facilitate novel view segmentation and semantic understanding, their heavy reliance on 2D supervision can undermine cross-view semantic consistency and necessitate complex data preparation processes, therefore hindering view-consistent scene understanding. In this work, we present FreeGS, an unsupervised semantic-embedded 3DGS framework that achieves view-consistent 3D scene understanding without the need for 2D labels. Instead of directly learning semantic features, we introduce the IDentity-coupled Semantic Field (IDSF) into 3DGS, which captures both semantic representations and view-consistent instance indices for each Gaussian. We optimize IDSF with a two-step alternating strategy: semantics help to extract coherent instances in 3D space, while the resulting instances regularize the injection of stable semantics from 2D space. Additionally, we adopt a 2D-3D joint contrastive loss to enhance the complementarity between view-consistent 3D geometry and rich semantics during the bootstrapping process, enabling FreeGS to uniformly perform tasks such as novel-view semantic segmentation, object selection, and 3D object detection. Extensive experiments on LERF-Mask, 3D-OVS, and ScanNet datasets demonstrate that FreeGS performs comparably to state-of-the-art methods while avoiding the complex data preprocessing workload.

Zhaojie Zeng, Yuesong Wang, Lili Ju, Tao Guan

By adaptively controlling the density and generating more Gaussians in regions with high-frequency information, 3D Gaussian Splatting (3DGS) can better represent scene details. From the signal processing perspective, representing details usually needs more Gaussians with relatively smaller scales. However, 3DGS currently lacks an explicit constraint linking the density and scale of 3D Gaussians across the domain, leading to 3DGS using improper-scale Gaussians to express frequency information, resulting in the loss of accuracy. In this paper, we propose to establish a direct relation between density and scale through the reparameterization of the scaling parameters and ensure the consistency between them via explicit constraints (i.e., density responds well to changes in frequency). Furthermore, we develop a frequency-aware density control strategy, consisting of densification and deletion, to improve representation quality with fewer Gaussians. A dynamic threshold encourages densification in high-frequency regions, while a scale-based filter deletes Gaussians with improper scale. Experimental results on various datasets demonstrate that our method outperforms existing state-of-the-art methods quantitatively and qualitatively.

Xiaobao Wei, Peng Chen, Ming Lu, Hui Chen, Feng Tian

Rendering photorealistic head avatars from arbitrary viewpoints is crucial for various applications like virtual reality. Although previous methods based on Neural Radiance Fields (NeRF) can achieve impressive results, they lack fidelity and efficiency. Recent methods using 3D Gaussian Splatting (3DGS) have improved rendering quality and real-time performance but still require significant storage overhead. In this paper, we introduce a method called GraphAvatar that utilizes Graph Neural Networks (GNN) to generate 3D Gaussians for the head avatar. Specifically, GraphAvatar trains a geometric GNN and an appearance GNN to generate the attributes of the 3D Gaussians from the tracked mesh. Therefore, our method can store the GNN models instead of the 3D Gaussians, significantly reducing the storage overhead to just 10MB. To reduce the impact of face-tracking errors, we also present a novel graph-guided optimization module to refine face-tracking parameters during training. Finally, we introduce a 3D-aware enhancer for post-processing to enhance the rendering quality. We conduct comprehensive experiments to demonstrate the advantages of GraphAvatar, surpassing existing methods in visual fidelity and storage consumption. The ablation study sheds light on the trade-offs between rendering quality and model size.

Hongsong Wang, Andi Xu, Pinle Ding, Jie Gui

Video Anomaly Detection (VAD) is essential for computer vision and multimedia research. Existing VAD methods utilize either reconstruction-based or prediction-based frameworks. The former excels at detecting irregular patterns or structures, whereas the latter is capable of spotting abnormal deviations or trends. We address pose-based video anomaly detection and introduce a novel framework called Dual Conditioned Motion Diffusion (DCMD), which enjoys the advantages of both approaches. The DCMD integrates conditioned motion and conditioned embedding to comprehensively utilize the pose characteristics and latent semantics of observed movements, respectively. In the reverse diffusion process, a motion transformer is proposed to capture potential correlations from multi-layered characteristics within the spectrum space of human motion. To enhance the discriminability between normal and abnormal instances, we design a novel United Association Discrepancy (UAD) regularization that primarily relies on a Gaussian kernel-based time association and a self-attention-based global association. Finally, a mask completion strategy is introduced during the inference stage of the reverse diffusion process to enhance the utilization of conditioned motion for the prediction branch of anomaly detection. Extensive experiments conducted on four datasets demonstrate that our method dramatically outperforms state-of-the-art methods and exhibits superior generalization performance.

Jiaqi Lin, Zhihao Li, Binxiao Huang, Xiao Tang, Jianzhuang Liu, Shiyong Liu, Xiaofei Wu, Fenglong Song, Wenming Yang

Gaussian Splatting has emerged as a prominent 3D representation in novel view synthesis, but it still suffers from appearance variations, which are caused by various factors, such as modern camera ISPs, different time of day, weather conditions, and local light changes. These variations can lead to floaters and color distortions in the rendered images/videos. Recent appearance modeling approaches in Gaussian Splatting are either tightly coupled with the rendering process, hindering real-time rendering, or they only account for mild global variations, performing poorly in scenes with local light changes. In this paper, we propose DAVIGS, a method that decouples appearance variations in a plug-and-play and efficient manner. By transforming the rendering results at the image level instead of the Gaussian level, our approach can model appearance variations with minimal optimization time and memory overhead. Furthermore, our method gathers appearance-related information in 3D space to transform the rendered images, thus building 3D consistency across views implicitly. We validate our method on several appearance-variant scenes, and demonstrate that it achieves state-of-the-art rendering quality with minimal training time and memory usage, without compromising rendering speeds. Additionally, it provides performance improvements for different Gaussian Splatting baselines in a plug-and-play manner.

Hyunjun Kim, Nam Ik Cho

Recent advancements in self-supervised denoising have made it possible to train models without needing a large amount of noisy-clean image pairs. A significant development in this area is the use of blind-spot networks (BSNs), which use single noisy images as training pairs by masking some input information to prevent noise transmission to the network output. Researchers have shown that BSNs are capable of reconstructing clean pixels from various types of independent pixel-wise degradations, such as synthetic additive white Gaussian noise (AWGN). However, unlike synthetic noise, real noise often contains highly correlated components which can induce noise transmission and reduce the performance of BSNs. To address the spatial correlation of real noise, we propose the Adjacent Pixel Replacer (APR), which decorrelates noise without a downsampling process that is widely adopted in previous research. The dissimilarity in our APR-generated pairs serves as relatively different noise components during training. Hence, it enables the BSN to block noise transmission while utilizing clean information effectively. As a result, BSN can utilize denser information to reconstruct the corresponding center pixel. We also propose Recharged Distillation (RD) to enhance high-frequency textures without additional network modifications. This method selectively refines clean information from recharged noisy pixels during distillation. Extensive experimental results demonstrate that our proposed method outperforms the existing state-of-the-art self-supervised denoising methods in real sRGB space.