For PCA-based methods, the dimensionality reduction is performed via singular value decomposition (SVD) of the input one-hot encoding matrix X. As mentioned above, we utilize grid search for tuning the hyper-parameters. In particular, for the learning-based methods, including GraphSAGE and KS-GNN, the learning rates are selected from {0.1, 0.01, 0.001, 0.0001}. GraphSAGE, SAT, Conv-PCA, KS-PCA, KS-GNN), we swept the number of hidden layers in the set {1, 2, 3, 4, 5}. For the other hyper-parameters used in KS-GNN, such as λ1, λ2 and λ3, we tune them from 0.1 to 1 with a step of 0.1.

Keyword search is a fundamental task to retrieve information that is the most relevant to the query keywords. Keyword search over graphs aims to find subtrees or subgraphs containing all query keywords ranked according to some criteria. Existing studies all assume that the graphs have complete information. However, real-world graphs may contain some missing information (such as edges or keywords), thus making the problem much more challenging. To solve the problem of keyword search over incomplete graphs, we propose a novel model named KS-GNN based on the graph neural network and the auto-encoder. By considering the latent relationships and the frequency of different keywords, the proposed KS-GNN aims to alleviate the effect of missing information and is able to learn low-dimensional representative node embeddings that preserve both graph structure and keyword features. Our model can effectively answer keyword search queries with linear time complexity over incomplete graphs. The experiments on four real-world datasets show that our model consistently achieves better performance than state-of-the-art baseline methods in graphs having missing information.

Laplace approximation (LA) and its linearized variant (LLA) enable effortless adaptation of pretrained deep neural networks to Bayesian neural networks. The generalized Gauss-Newton (GGN) approximation is typically introduced to improve their tractability. However, LA and LLA are still confronted with non-trivial inefficiency issues and should rely on Kronecker-factored, diagonal, or even lastlayer approximate GGN matrices in practical use. These approximations are likely to harm the fidelity of learning outcomes. To tackle this issue, inspired by the connections between LLA and neural tangent kernels (NTKs), we develop a Nyström approximation to NTKs to accelerate LLA.

A.1 Connection to online learning In Section 2 we motivated the update (2) as a way to adjust the size of our prediction sets in response to the realized historical miscoverage frequency. Alternatively, one could also derive (2) as an online gradient descent algorithm with respect to the pinball loss. To be more precise let t:= sup{: Yt 2 Cˆt()}, where we remark that Cˆt( t) can be thought of as the smallest prediction set containing Yt. Because the pinball loss is convex, this gradient descent update falls within a well understood class of algorithms that have been extensively studied in the online learning literature (see e.g. Unfortunately, this notion of regret fails to capture our intuition that t is adaptively tracking the moving target .

We present a novel method for reconstructing 3D objects from a single RGB image. Our method leverages the latest image generation models to infer the hidden 3D structure while remaining faithful to the input image. While existing methods[1, 2] obtain impressive results in generating 3D models from text prompts, they do not provide an easy approach for conditioning on input RGB data. Naïve extensions of these methods often lead to improper alignment in appearance between the input image and the 3D reconstructions. We address these challenges by introducing Image Constrained Radiance Fields (ConRad), a novel variant of neural radiance fields. ConRad is an efficient 3D representation that explicitly captures the appearance of an input image in one viewpoint. We propose a training algorithm that leverages the single RGB image in conjunction with pretrained Diffusion Models to optimize the parameters of a ConRad representation. Extensive experiments show that ConRad representations can simplify preservation of image details while producing a realistic 3D reconstruction. Compared to existing state-of-the-art baselines, we show that our 3D reconstructions remain more faithful to the input and produce more consistent 3D models while demonstrating significantly improved quantitative performance on a ShapeNet object benchmark.