论文检索

Optimization · Optimization and Learning under Uncertainty

Theodore Brown, Alexandru Cioba, Ilija Bogunovic

Bayesian optimisation (BO) is a powerful framework for global optimisation of costly functions, using predictions from Gaussian process models (GPs). In this work, we apply BO to functions that exhibit invariance to a known group of transformations. We show that vanilla and constrained BO algorithms are inefficient when optimising such invariant objectives, and provide a method for incorporating group invariances into the kernel of the GP to produce invariance-aware algorithms that achieve significant improvements in sample efficiency. We derive a bound on the maximum information gain of these invariant kernels, and provide novel upper and lower bounds on the number of observations required for invariance-aware BO algorithms to achieve $\epsilon$-optimality. We demonstrate our method's improved performance on a range of synthetic invariant and quasi-invariant functions. We also apply our method in the case where only some of the invariance is incorporated into the kernel, and find that these kernels achieve similar gains in sample efficiency at significantly reduced computational cost. Finally, we use invariant BO to design a current drive system for a nuclear fusion reactor, finding a high-performance solution where non-invariant methods failed.

Probabilistic Methods · Gaussian Processes

Syrine Belakaria, Ben Letham, Jana Doppa, Barbara Engelhardt, Stefano Ermon, Eytan Bakshy

We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the impact of the thickness of various components on safety objectives. Since function evaluations are expensive, we use active learning to prioritize experimental resources where they yield the most value. We propose novel active learning acquisition functions that directly target key quantities of derivative-based global sensitivity measures (DGSMs) under Gaussian process surrogate models.We showcase the first application of active learning directly to DGSMs, and develop tractable uncertainty reduction and information gain acquisition functions for these measures. Through comprehensive evaluation on synthetic and real-world problems, our study demonstrates how these active learning acquisition strategies substantially enhance the sample efficiency of DGSM estimation, particularly with limited evaluation budgets. Our work paves the way for more efficient and accurate sensitivity analysis in various scientific and engineering applications.

Probabilistic Methods · Monte Carlo and Sampling Methods

Zihui Wu, Yu Sun, Yifan Chen, Bingliang Zhang, Yisong Yue, Katherine Bouman

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.

Probabilistic Methods · Gaussian Processes

Oliver Hamelijnck, Arno Solin, Theodoros Damoulas

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.

Computational Biology

Peter Mørch Groth, Mads Kerrn, Lars Olsen, Jesper Salomon, Wouter Boomsma

Reliable prediction of protein variant effects is crucial for both protein optimization and for advancing biological understanding. For practical use in protein engineering, it is important that we can also provide reliable uncertainty estimates for our predictions, and while prediction accuracy has seen much progress in recent years, uncertainty metrics are rarely reported. We here provide a Gaussian process regression model, Kermut, with a novel composite kernel for modeling mutation similarity, which obtains state-of-the-art performance for supervised protein variant effect prediction while also offering estimates of uncertainty through its posterior. An analysis of the quality of the uncertainty estimates demonstrates that our model provides meaningful levels of overall calibration, but that instance-specific uncertainty calibration remains more challenging.

Probabilistic Methods · Gaussian Processes

Sebastian Ament, Elizabeth Santorella, David Eriksson, Ben Letham, Maximilian Balandat, Eytan Bakshy

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian noise, while many real-world applications are subject to non-Gaussian corruptions. Variants of GPs that are more robust to alternative noise models have been proposed, and entail significant trade-offs between accuracy and robustness, and between computational requirements and theoretical guarantees. In this work, we propose and study a GP model that achieves robustness against sparse outliers by inferring data-point-specific noise levels with a sequential selection procedure maximizing the log marginal likelihood that we refer to as relevance pursuit. We show, surprisingly, that the model can be parameterized such that the associated log marginal likelihood is strongly concave in the data-point-specific noise variances, a property rarely found in either robust regression objectives or GP marginal likelihoods. This in turn implies the weak submodularity of the corresponding subset selection problem, and thereby proves approximation guarantees for the proposed algorithm. We compare the model’s performance relative to other approaches on diverse regression and Bayesian optimization tasks, including the challenging but common setting of sparse corruptions of the labels within or close to the function range.

Computer Vision · Video Generation

Yuedong Chen, Chuanxia Zheng, Haofei Xu, Bohan Zhuang, Andrea Vedaldi, Tat-Jen Cham, Jianfei Cai

We introduce MVSplat360, a feed-forward approach for 360° novel view synthesis (NVS) of diverse real-world scenes, using only sparse observations. This setting is inherently ill-posed due to minimal overlap among input views and insufficient visual information provided, making it challenging for conventional methods to achieve high-quality results. Our MVSplat360 addresses this by effectively combining geometry-aware 3D reconstruction with temporally consistent video generation. Specifically, it refactors a feed-forward 3D Gaussian Splatting (3DGS) model to render features directly into the latent space of a pre-trained Stable Video Diffusion (SVD) model, where these features then act as pose and visual cues to guide the denoising process and produce photorealistic 3D-consistent views. Our model is end-to-end trainable and supports rendering arbitrary views with as few as 5 sparse input views. To evaluate MVSplat360's performance, we introduce a new benchmark using the challenging DL3DV-10K dataset, where MVSplat360 achieves superior visual quality compared to state-of-the-art methods on wide-sweeping or even 360° NVS tasks. Experiments on the existing benchmark RealEstate10K also confirm the effectiveness of our model. Readers are highly recommended to view the video results at [donydchen.github.io/mvsplat360](https://donydchen.github.io/mvsplat360).

Probabilistic Methods · Bayesian Models and Methods

Rafael Oliveira, Dino Sejdinovic, David Howard, Edwin Bonilla

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current machine learning approaches, however, mostly rely on rerunning simulations over a fixed set of designs available in the observed data, potentially neglecting informative correlations across the design space and requiring a large amount of simulations. Instead, we consider the calibration process from the perspective of Bayesian adaptive experimental design and propose a data-efficient algorithm to run maximally informative simulations within a batch-sequential process. At each round, the algorithm jointly estimates the parameters posterior distribution and optimal designs by maximising a variational lower bound of the expected information gain. The simulator is modelled as a sample from a Gaussian process, which allows us to correlate simulations and real data with the unknown calibration parameters. We show the benefits of our method when compared to related approaches across synthetic and real-data problems.

Probabilistic Methods · Bayesian Models and Methods

Amber Hu, David Zoltowski, Aditya Nair, David Anderson, Lea Duncker, Scott Linderman

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.

Generative Models · Diffusion models

Xunpeng Huang, Difan Zou, Hanze Dong, Zhang, Yian Ma, Tong Zhang

To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the entire denoising diffusion process into several segments, each corresponding to a reverse transition kernel (RTK) sampling subproblem. Specifically, DDPM uses a Gaussian approximation for the RTK, resulting in low per-subproblem complexity but requiring a large number of segments (i.e., subproblems), which is conjectured to be inefficient. To address this, we develop a general RTK framework that enables a more balanced subproblem decomposition, resulting in $\tilde O(1)$ subproblems, each with strongly log-concave targets. We then propose leveraging two fast sampling algorithms, the Metropolis-Adjusted Langevin Algorithm (MALA) and Underdamped Langevin Dynamics (ULD), for solving these strongly log-concave subproblems. This gives rise to the RTK-MALA and RTK-ULD algorithms for diffusion inference. In theory, we further develop the convergence guarantees for RTK-MALA and RTK-ULD in total variation (TV) distance: RTK-ULD can achieve $\epsilon$ target error within $\tilde{\mathcal O}(d^{1/2}\epsilon^{-1})$ under mild conditions, and RTK-MALA enjoys a $\mathcal{O}(d^{2}\log(d/\epsilon))$ convergence rate under slightly stricter conditions. These theoretical results surpass the state-of-the-art convergence rates for diffusion inference and are well supported by numerical experiments.

Probabilistic Methods · Bayesian Models and Methods

Tristan Cinquin, Marvin Pförtner, Vincent Fortuin, Philipp Hennig, Robert Bamler

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While the choice of prior strongly affects the resulting posterior distribution, computational tractability and lack of interpretability of the weight space typically limit the Laplace approximation to isotropic Gaussian priors, which are known to cause pathological behavior as depth increases. As a remedy, we directly place a prior on function space. More precisely, since Lebesgue densities do not exist on infinite-dimensional function spaces, we recast training as finding the so-called weak mode of the posterior measure under a Gaussian process (GP) prior restricted to the space of functions representable by the neural network. Through the GP prior, one can express structured and interpretable inductive biases, such as regularity or periodicity, directly in function space, while still exploiting the implicit inductive biases that allow deep networks to generalize. After model linearization, the training objective induces a negative log-posterior density to which we apply a Laplace approximation, leveraging highly scalable methods from matrix-free linear algebra. Our method provides improved results where prior knowledge is abundant (as is the case in many scientific inference tasks). At the same time, it stays competitive for black-box supervised learning problems, where neural networks typically excel.

Graph Neural Networks

Bastian Epping, Alexandre René, Moritz Helias, Michael T Schaub

Graph neural networks (GNNs) have emerged as powerful tools for processing relational data in applications. However, GNNs suffer from the problem of oversmoothing, the property that features of all nodes exponentially converge to the same vector over layers, prohibiting the design of deep GNNs. In this work we study oversmoothing in graph convolutional networks (GCNs) by using their Gaussian process (GP) equivalence in the limit of infinitely many hidden features. By generalizing methods from conventional deep neural networks (DNNs), we can describe the distribution of features at the output layer of deep GCNs in terms of a GP: as expected, we find that typical parameter choices from the literature lead to oversmoothing. The theory, however, allows us to identify a new, non-oversmoothing phase: if the initial weights of the network have sufficiently large variance, GCNs do not oversmooth, and node features remain informative even at large depth. We demonstrate the validity of this prediction in finite-size GCNs by training a linear classifier on their output. Moreover, using the linearization of the GCN GP, we generalize the concept of propagation depth of information from DNNs to GCNs. This propagation depth diverges at the transition between the oversmoothing and non-oversmoothing phase. We test the predictions of our approach and find good agreement with finite-size GCNs. Initializing GCNs near the transition to the non-oversmoothing phase, we obtain networks which are both deep and expressive.

Computer Vision

Yushan Zhang, Bastian Wandt, Maria Magnusson, Michael Felsberg

Scene flow estimation is an essential ingredient for a variety of real-world applications, especially for autonomous agents, such as self-driving cars and robots. While recent scene flow estimation approaches achieve reasonable accuracy, their applicability to real-world systems additionally benefits from a reliability measure. Aiming at improving accuracy while additionally providing an estimate for uncertainty, we propose DiffSF that combines transformer-based scene flow estimation with denoising diffusion models. In the diffusion process, the ground truth scene flow vector field is gradually perturbed by adding Gaussian noise. In the reverse process, starting from randomly sampled Gaussian noise, the scene flow vector field prediction is recovered by conditioning on a source and a target point cloud. We show that the diffusion process greatly increases the robustness of predictions compared to prior approaches resulting in state-of-the-art performance on standard scene flow estimation benchmarks. Moreover, by sampling multiple times with different initial states, the denoising process predicts multiple hypotheses, which enables measuring the output uncertainty, allowing our approach to detect a majority of the inaccurate predictions. The code is available at https://github.com/ZhangYushan3/DiffSF.

Computer Vision

Chen-Long Duan, Yong Li, Xiu-Shen Wei, Lin Zhao

Pre-training plays a vital role in various vision tasks, such as object recognition and detection. Commonly used pre-training methods, which typically rely on randomized approaches like uniform or Gaussian distributions to initialize model parameters, often fall short when confronted with long-tailed distributions, especially in detection tasks. This is largely due to extreme data imbalance and the issue of simplicity bias. In this paper, we introduce a novel pre-training framework for object detection, called Dynamic Rebalancing Contrastive Learning with Dual Reconstruction (2DRCL). Our method builds on a Holistic-Local Contrastive Learning mechanism, which aligns pre-training with object detection by capturing both global contextual semantics and detailed local patterns. To tackle the imbalance inherent in long-tailed data, we design a dynamic rebalancing strategy that adjusts the sampling of underrepresented instances throughout the pre-training process, ensuring better representation of tail classes. Moreover, Dual Reconstruction addresses simplicity bias by enforcing a reconstruction task aligned with the self-consistency principle, specifically benefiting underrepresented tail classes. Experiments on COCO and LVIS v1.0 datasets demonstrate the effectiveness of our method, particularly in improving the mAP/AP scores for tail classes.

Reinforcement Learning · Deep RL

Yinuo Wang, Likun Wang, Yuxuan Jiang, Wenjun Zou, Tong Liu, Xujie Song, Wenxuan Wang, Liming Xiao, Jiang Wu, Jingliang Duan 等

Reinforcement learning (RL) has proven highly effective in addressing complex decision-making and control tasks. However, in most traditional RL algorithms, the policy is typically parameterized as a diagonal Gaussian distribution with learned mean and variance, which constrains their capability to acquire complex policies. In response to this problem, we propose an online RL algorithm termed diffusion actor-critic with entropy regulator (DACER). This algorithm conceptualizes the reverse process of the diffusion model as a novel policy function and leverages the capability of the diffusion model to fit multimodal distributions, thereby enhancing the representational capacity of the policy. Since the distribution of the diffusion policy lacks an analytical expression, its entropy cannot be determined analytically. To mitigate this, we propose a method to estimate the entropy of the diffusion policy utilizing Gaussian mixture model. Building on the estimated entropy, we can learn a parameter $\alpha$ that modulates the degree of exploration and exploitation. Parameter $\alpha$ will be employed to adaptively regulate the variance of the added noise, which is applied to the action output by the diffusion model. Experimental trials on MuJoCo benchmarks and a multimodal task demonstrate that the DACER algorithm achieves state-of-the-art (SOTA) performance in most MuJoCo control tasks while exhibiting a stronger representational capacity of the diffusion policy.

Computer Vision

Zhaoliang Zhang, Tianchen Song, Yongjae Lee, Li Yang, Cheng Peng, Rama Chellappa, Deliang Fan

Recently, 3D Gaussian Splatting (3DGS) has become one of the mainstream methodologies for novel view synthesis (NVS) due to its high quality and fast rendering speed. However, as a point-based scene representation, 3DGS potentially generates a large number of Gaussians to fit the scene, leading to high memory usage. Improvements that have been proposed require either an empirical pre-set pruning ratio or importance score threshold to prune the point cloud. Such hyperparameters require multiple rounds of training to optimize and achieve the maximum pruning ratio while maintaining the rendering quality for each scene. In this work, we propose learning-to-prune 3DGS (LP-3DGS), where a trainable binary mask is applied to the importance score to automatically find a favorable pruning ratio. Instead of using the traditional straight-through estimator (STE) method to approximate the binary mask gradient, we redesign the masking function to leverage the Gumbel-Sigmoid method, making it differentiable and compatible with the existing training process of 3DGS. Extensive experiments have shown that LP-3DGS consistently achieves a good balance between efficiency and high quality.

Probabilistic Methods · Gaussian Processes

Zicheng Sun, Yixuan Zhang, Zenan Ling, Xuhui Fan, Feng Zhou

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels. This technique relaxes the constraints on kernel types and stationarity, allowing for more flexible modeling while reducing computational complexity to the linear level. Additionally, we introduce a deep kernel variant by hierarchically stacking multiple spectral feature mappings, further enhancing the model's expressiveness to capture complex patterns in data. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach, particularly in scenarios with pronounced data nonstationarity. Additionally, ablation studies are conducted to provide insights into the impact of various hyperparameters on model performance.

Reinforcement Learning · Batch Offline

Ruoqi Zhang, Ziwei Luo, Jens Sjölund, Thomas Schön, Per Mattsson

Diffusion policy has shown a strong ability to express complex action distributions in offline reinforcement learning (RL). However, it suffers from overestimating Q-value functions on out-of-distribution (OOD) data points due to the offline dataset limitation. To address it, this paper proposes a novel entropy-regularized diffusion policy and takes into account the confidence of the Q-value prediction with Q-ensembles. At the core of our diffusion policy is a mean-reverting stochastic differential equation (SDE) that transfers the action distribution into a standard Gaussian form and then samples actions conditioned on the environment state with a corresponding reverse-time process. We show that the entropy of such a policy is tractable and that can be used to increase the exploration of OOD samples in offline RL training. Moreover, we propose using the lower confidence bound of Q-ensembles for pessimistic Q-value function estimation. The proposed approach demonstrates state-of-the-art performance across a range of tasks in the D4RL benchmarks, significantly improving upon existing diffusion-based policies. The code is available at https://github.com/ruoqizzz/entropy-offlineRL.

Generative Models · Diffusion models

Ruofeng Yang, Zhijie Wang, Bo Jiang, Shuai Li

Variance exploding (VE) based diffusion models, an important class of diffusion models, have shown state-of-the-art (SOTA) performance. However, only a few theoretical works analyze VE-based models, and those works suffer from a worse forward convergence rate $1/\text{poly}(T)$ than the $\exp{(-T)}$ of variance preserving (VP) based models, where $T$ is the forward diffusion time and the rate measures the distance between forward marginal distribution $q_T$ and pure Gaussian noise. The slow rate is due to the Brownian Motion without a drift term. In this work, we design a new drifted VESDE forward process, which allows a faster $\exp{(-T)}$ forward convergence rate. With this process, we achieve the first efficient polynomial sample complexity for a series of VE-based models with reverse SDE under the manifold hypothesis. Furthermore, unlike previous works, we allow the diffusion coefficient to be unbounded instead of a constant, which is closer to the SOTA models. Besides the reverse SDE, the other common reverse process is the probability flow ODE (PFODE) process, which is deterministic and enjoys faster sample speed. To deepen the understanding of VE-based models, we consider a more general setting considering reverse SDE and PFODE simultaneously, propose a unified tangent-based analysis framework, and prove the first quantitative convergence guarantee for SOTA VE-based models with reverse PFODE.We also show that the drifted VESDE can balance different error terms and improve generated samples without training through synthetic and real-world experiments.

Probabilistic Methods · Gaussian Processes

Alexander Terenin, David Burt, Artem Artemev, Seth Flaxman, Mark van der Wilk, Carl Edward Rasmussen, Hong Ge

Gaussian processes are frequently deployed as part of larger machine learning and decision-making systems, for instance in geospatial modeling, Bayesian optimization, or in latent Gaussian models. Within a system, the Gaussian process model needs to perform in a stable and reliable manner to ensure it interacts correctly with other parts of the system. In this work, we study the numerical stability of scalable sparse approximations based on inducing points. To do so, we first review numerical stability, and illustrate typical situations in which Gaussian process models can be unstable. Building on stability theory originally developed in the interpolation literature, we derive sufficient and in certain cases necessary conditions on the inducing points for the computations performed to be numerically stable. For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions. This is done via a modification of the cover tree data structure, which is of independent interest. We additionally propose an alternative sparse approximation for regression with a Gaussian likelihood which trades off a small amount of performance to further improve stability. We provide illustrative examples showing the relationship between stability of calculations and predictive performance of inducing point methods on spatial tasks.