For non-UCI datasets, the test and train set sizes are shown in brackets, e.g.

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over the depth of neural networks. Di erent depths correspond to subnetworks which share weights and whose predictions are combined via marginalisation, yielding model uncertainty. By exploiting the sequential structure of feed-forward networks, we are able to both evaluate our training objective and make predictions with a single forward pass.

We propose a novel inventory reserving algorithm which draws new insights into Bandits with Knapsacks (Bwk) problems in piecewise-stationary environments.

In this paper, we introduce Era3D, a novel multiview diffusion method that generates high-resolution multiview images from a single-view image. Despite significant advancements in multiview generation, existing methods still suffer from camera prior mismatch, inefficacy, and low resolution, resulting in poor-quality multiview images. Specifically, these methods assume that the input images should comply with a predefined camera type, e.g. a perspective camera with a fixed focal length, leading to distorted shapes when the assumption fails. Moreover, the fullimage or dense multiview attention they employ leads to a dramatic explosion of computational complexity as image resolution increases, resulting in prohibitively expensive training costs. To bridge the gap between assumption and reality, Era3D first proposes a diffusion-based camera prediction module to estimate the focal length and elevation of the input image, which allows our method to generate images without shape distortions. Furthermore, a simple but efficient attention layer, named row-wise attention, is used to enforce epipolar priors in the multiview diffusion, facilitating efficient cross-view information fusion. Consequently, compared with state-of-the-art methods, Era3D generates high-quality multiview images with up to a 512 512 resolution while reducing computation complexity of multiview attention by 12x times. Comprehensive experiments demonstrate the superior generation power of Era3D-it can reconstruct high-quality and detailed 3D meshes from diverse single-view input images, significantly outperforming baseline multiview diffusion methods.

The field of Multimodal Sentiment Analysis (MSA) has recently witnessed an emerging direction seeking to tackle the issue of data incompleteness. Recognizing that the language modality typically contains dense sentiment information, we consider it as the dominant modality and present an innovative Languagedominated Noise-resistant Learning Network (LNLN) to achieve robust MSA. The proposed LNLN features a dominant modality correction (DMC) module and dominant modality based multimodal learning (DMML) module, which enhances the model's robustness across various noise scenarios by ensuring the quality of dominant modality representations. Aside from the methodical design, we perform comprehensive experiments under random data missing scenarios, utilizing diverse and meaningful settings on several popular datasets (e.g., MOSI, MOSEI, and SIMS), providing additional uniformity, transparency, and fairness compared to existing evaluations in the literature. Empirically, LNLN consistently outperforms existing baselines, demonstrating superior performance across these challenging and extensive evaluation metrics.

Causal discovery is essential for understanding relationships among variables of interest in many scientific domains. In this paper, we focus on permutation-based methods for learning causal graphs in Linear Gaussian Acyclic Models (LiGAMs), where the permutation encodes a causal ordering of the variables. Existing methods in this setting do not scale due to their high computational complexity.

Networks are a natural representation of complex systems across the sciences, and higher-order dependencies are central to the understanding and modeling of these systems. However, in many practical applications such as online social networks, networks are massive, dynamic, and naturally streaming, where pairwise interactions among vertices become available one at a time in some arbitrary order. The massive size and streaming nature of these networks allow only partial observation, since it is infeasible to analyze the entire network. Under such scenarios, it is challenging to study the higher-order structural and connectivity patterns of streaming networks. In this work, we consider the fundamental problem of estimating the higher-order dependencies using adaptive sampling.

We study online classification when the learner has access to predictions about future examples. We design an online learner whose expected regret is never worse than the worst-case regret, gracefully improves with the quality of the predictions, and can be significantly better than the worst-case regret when the predictions of future examples are accurate. As a corollary, we show that if the learner is always guaranteed to observe data where future examples are easily predictable, then online learning can be as easy as transductive online learning. Our results complement recent work in online algorithms with predictions and smoothed online classification, which go beyond a worse-case analysis by using machine-learned predictions and distributional assumptions respectively.

The distributionally robust tree structured prediction problem based on moment divergence in Eq. (1) can be rewritten as min E The objective function is convex in P and concave in Q because it is affine in both. The simplex constraints are omitted. Theorem 2. Given m samples, a non-negative loss l(,) such that |l(,)| K, a feature function ϕ(,) such that ϕ(,) B, a positive ambiguity level ε > 0, then, for any ρ (0, 1], with a probability at least 1 ρ, the following excess true worst-case risk bound holds: () ln(4/ρ) max As per the assumption, ϕ(,) B. This further implies that f(θ K ε i = 1, 2. ε We then follow the proof of Theorem 3 in Farnia and Tse [2016]. Our formulation differs from Nowak-Vila et al. [2020] in the fact that we allow probabilistic prediction to be ground truth. Proposition 4. Let G be a multi-graph.

Structured prediction of tree-shaped objects is heavily studied under the name of syntactic dependency parsing. Current practice based on maximum likelihood or margin is either agnostic to or inconsistent with the evaluation loss. Risk minimization alleviates the discrepancy between training and test objectives but typically induces a non-convex problem. These approaches adopt explicit regularization to combat overfitting without probabilistic interpretation. We propose a momentbased distributionally robust optimization approach for tree structured prediction, where the worst-case expected loss over a set of distributions within bounded moment divergence from the empirical distribution is minimized. We develop efficient algorithms for arborescences and other variants of trees. We derive Fisher consistency, convergence rates and generalization bounds for our proposed method. We evaluate its empirical effectiveness on dependency parsing benchmarks.