NeurIPS 2024 Papers

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.

Algorithms that utilize bandit feedback to optimize top-k recommendations are vital for online marketplaces, search engines, and content platforms. However, the combinatorial nature of this problem poses a significant challenge, as the possible number of ordered top-k recommendations from $n$ items grows exponentially with $k$. As a result, previous work often relies on restrictive assumptions about the reward or bandit feedback models, such as assuming that the feedback discloses rewards for each recommended item rather than a single scalar feedback for the entire set of top-k recommendations. We introduce a novel contextual bandit algorithm for top-k recommendations, leveraging a Gaussian process with a Kendall kernel to model the reward function. Our algorithm requires only scalar feedback from the top-k recommendations and does not impose restrictive assumptions on the reward structure. Theoretical analysis confirms that the proposed algorithm achieves sub-linear regret in relation to the number of rounds and arms. Additionally, empirical results using a bandit simulator demonstrate that the proposed algorithm outperforms other baselines across various scenarios.

Data assimilation is a vital component in modern global medium-range weather forecasting systems to obtain the best estimation of the atmospheric state by combining the short-term forecast and observations. Recently, AI-based data assimilation approaches have attracted increasing attention for their significant advantages over traditional techniques in terms of computational consumption. However, existing AI-based data assimilation methods can only handle observations with a specific resolution, lacking the compatibility and generalization ability to assimilate observations with other resolutions. Considering that complex real-world observations often have different resolutions, we propose the Fourier Neural Processes (FNP) for arbitrary-resolution data assimilation in this paper. Leveraging the efficiency of the designed modules and flexible structure of neural processes, FNP achieves state-of-the-art results in assimilating observations with varying resolutions, and also exhibits increasing advantages over the counterparts as the resolution and the amount of observations increase. Moreover, our FNP trained on a fixed resolution can directly handle the assimilation of observations with out-of-distribution resolutions and the observational information reconstruction task without additional fine-tuning, demonstrating its excellent generalization ability across data resolutions as well as across tasks. Code is available at https://github.com/OpenEarthLab/FNP.

In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one of several unknown subgroups, each with an unknown input distribution and input-output relationship. We consider one of this setup's most fundamental and important manifestations where the output is a noisy linear combination of the inputs, and there are $k$ subgroups, each with its own regression vector. Prior work [KSS$^+$20] showed that with abundant small-batches, the regression vectors can be learned with only few, $\tilde\Omega( k^{3/2})$, batches of medium-size with $\tilde\Omega(\sqrt k)$ samples each. However, the paper requires that the input distribution for all $k$ subgroups be isotropic Gaussian, and states that removing this assumption is an ``interesting and challenging problem". We propose a novel gradient-based algorithm that improves on the existing results in several ways. It extends the applicability of the algorithm by: (1) allowing the subgroups' underlying input distributions to be different, unknown, and heavy-tailed; (2) recovering all subgroups followed by a significant proportion of batches even for infinite $k$; (3) removing the separation requirement between the regression vectors; (4) reducing the number of batches and allowing smaller batch sizes.

3D Gaussian Splatting (3DGS) has already become the emerging research focus in the fields of 3D scene reconstruction and novel view synthesis. Given that training a 3DGS requires a significant amount of time and computational cost, it is crucial to protect the copyright, integrity, and privacy of such 3D assets. Steganography, as a crucial technique for encrypted transmission and copyright protection, has been extensively studied. However, it still lacks profound exploration targeted at 3DGS. Unlike its predecessor NeRF, 3DGS possesses two distinct features: 1) explicit 3D representation; and 2) real-time rendering speeds. These characteristics result in the 3DGS point cloud files being public and transparent, with each Gaussian point having a clear physical significance. Therefore, ensuring the security and fidelity of the original 3D scene while embedding information into the 3DGS point cloud files is an extremely challenging task. To solve the above-mentioned issue, we first propose a steganography framework for 3DGS, dubbed GS-Hider, which can embed 3D scenes and images into original GS point clouds in an invisible manner and accurately extract the hidden messages. Specifically, we design a coupled secured feature attribute to replace the original 3DGS's spherical harmonics coefficients and then use a scene decoder and a message decoder to disentangle the original RGB scene and the hidden message. Extensive experiments demonstrated that the proposed GS-Hider can effectively conceal multimodal messages without compromising rendering quality and possesses exceptional security, robustness, capacity, and flexibility. Our project is available at: https://xuanyuzhang21.github.io/project/gshider.

Nuanced expressiveness, especially through detailed hand and facial expressions, is pivotal for enhancing the realism and vitality of digital human representations. In this work, we aim to learn expressive human avatars from a monocular RGB video; a setting that introduces new challenges in capturing and animating fine-grained details. To this end, we introduce EVA, a drivable human model that can recover fine details based on 3D Gaussians and an expressive parametric human model, SMPL-X. Focused on enhancing expressiveness, our work makes three key contributions. First, we highlight the importance of aligning the SMPL-X model with the video frames for effective avatar learning. Recognizing the limitations of current methods for estimating SMPL-X parameters from in-the-wild videos, we introduce a reconstruction module that significantly improves the image-model alignment. Second, we propose a context-aware adaptive density control strategy, which is adaptively adjusting the gradient thresholds to accommodate the varied granularity across body parts. Third, we develop a feedback mechanism that predicts per-pixel confidence to better guide the optimization of 3D Gaussians. Extensive experiments on two benchmarks demonstrate the superiority of our approach both quantitatively and qualitatively, especially on the fine-grained hand and facial details. We make our code available at the project website: https://evahuman.github.io.

3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis performance. While conventional methods require per-scene optimization, more recently several feed-forward methods have been proposed to generate pixel-aligned Gaussian representations with a learnable network, which are generalizable to different scenes. However, these methods simply combine pixel-aligned Gaussians from multiple views as scene representations, thereby leading to artifacts and extra memory cost without fully capturing the relations of Gaussians from different images. In this paper, we propose Gaussian Graph Network (GGN) to generate efficient and generalizable Gaussian representations. Specifically, we construct Gaussian Graphs to model the relations of Gaussian groups from different views. To support message passing at Gaussian level, we reformulate the basic graph operations over Gaussian representations, enabling each Gaussian to benefit from its connected Gaussian groups with Gaussian feature fusion. Furthermore, we design a Gaussian pooling layer to aggregate various Gaussian groups for efficient representations. We conduct experiments on the large-scale RealEstate10K and ACID datasets to demonstrate the efficiency and generalization of our method. Compared to the state-of-the-art methods, our model uses fewer Gaussians and achieves better image quality with higher rendering speed.

In *expand-and-sparsify* (EaS) representation, a data point in $\mathcal{S}^{d-1}$ is first randomly mapped to higher dimension $\mathbb{R}^m$, where $m>d$, followed by a sparsification operation where the informative $k \ll m$ of the $m$ coordinates are set to one and the rest are set to zero. We propose two algorithms for non-parametric classification using such EaS representation. For our first algorithm, we use *winners-take-all* operation for the sparsification step and show that the proposed classifier admits the form of a locally weighted average classifier and establish its consistency via Stone's Theorem. Further, assuming that the conditional probability function $P(y=1|x)=\eta(x)$ is H\"{o}lder continuous and for optimal choice of $m$, we show that the convergence rate of this classifier is minimax-optimal. For our second algorithm, we use *empirical $k$-thresholding* operation for the sparsification step, and under the assumption that data lie on a low dimensional manifold of dimension $d_0\ll d$, we show that the convergence rate of this classifier depends only on $d_0$ and is again minimax-optimal. Empirical evaluations performed on real-world datasets corroborate our theoretical results.

We study the problem of PAC learning halfspaces in the reliable agnostic model of Kalai et al. (2012). The reliable PAC model captures learning scenarios where one type of error is costlier than the others. Our main positive result is a new algorithm for reliable learning of Gaussian halfspaces on $\mathbb{R}^d$ with sample and computational complexity $d^{O(\log (\min\{1/\alpha, 1/\epsilon\}))}\min (2^{\log(1/\epsilon)^{O(\log (1/\alpha))}},2^{\mathrm{poly}(1/\epsilon)})$, where $\epsilon$ is the excess error and $\alpha$ is the bias of the optimal halfspace. We complement our upper bound with a Statistical Query lower bound suggesting that the $d^{\Omega(\log (1/\alpha))}$ dependence is best possible. Conceptually, our results imply a strong computational separation between reliable agnostic learning and standard agnostic learning of halfspaces in the Gaussian setting.

We study the constant regret guarantees in reinforcement learning (RL). Our objective is to design an algorithm that incurs only finite regret over infinite episodes with high probability. We introduce an algorithm, Cert-LSVI-UCB, for misspecified linear Markov decision processes (MDPs) where both the transition kernel and the reward function can be approximated by some linear function up to misspecification level $\zeta$. At the core of Cert-LSVI-UCB is an innovative certified estimator, which facilitates a fine-grained concentration analysis for multi-phase value-targeted regression, enabling us to establish an instance-dependent regret bound that is constant w.r.t. the number of episodes. Specifically, we demonstrate that for a linear MDP characterized by a minimal suboptimality gap $\Delta$, Cert-LSVI-UCB has a cumulative regret of $\tilde{\mathcal{O}}(d^3H^5/\Delta)$ with high probability, provided that the misspecification level $\zeta$ is below $\tilde{\mathcal{O}}(\Delta / (\sqrt{d}H^2))$. Here $d$ is the dimension of the feature space and $H$ is the horizon. Remarkably, this regret bound is independent of the number of episodes $K$. To the best of our knowledge, Cert-LSVI-UCB is the first algorithm to achieve a constant, instance-dependent, high-probability regret bound in RL with linear function approximation without relying on prior distribution assumptions.