The Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and finite-data posteriors it is often too crude an approximation. A recent generalization of the Laplace Approximation transforms the Gaussian approximation according to a chosen Riemannian geometry providing a richer approximation family, while still retaining computational efficiency. However, as shown here, its properties heavily depend on the chosen metric, indeed the metric adopted in previous work results in approximations that are overly narrow as well as being biased even at the limit of infinite data. We correct this shortcoming by developing the approximation family further, deriving two alternative variants that are exact at the limit of infinite data, extending the theoretical analysis of the method, and demonstrating practical improvements in a range of experiments.
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Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i.e. the function spaces over which they define a probability measure on, is lacking. In practice, GPs are not constructed through a probability measure, but instead through a mean function and a covariance kernel. In this paper we provide necessary and sufficient conditions on the covariance kernel for the sample paths of the corresponding GP to attain a given regularity. We use the framework of H\"older regularity as it grants us particularly straightforward conditions, which simplify further in the cases of stationary and isotropic GPs. We then demonstrate that our results allow for novel and unusually tight characterisations of the sample path regularities of the GPs commonly used in machine learning applications, such as the Mat\'ern GPs.
An information-theoretic confidential communication is achievable if the eavesdropper has a degraded channel compared to the legitimate receiver. In wireless channels, beamforming and artificial noise can enable such confidentiality. However, only distribution knowledge of the eavesdropper channels can be assumed. Moreover, the transmission of artificial noise can lead to an increased electromagnetic field (EMF) exposure, which depends on the considered location and can thus also be seen as a random variable. Hence, we optimize the $\varepsilon$-outage secrecy rate under a $\delta$-outage exposure constraint in a setup, where the base station (BS) is communicating to a user equipment (UE), while a single-antenna eavesdropper with Rayleigh distributed channels is present. Therefore, we calculate the secrecy outage probability (SOP) in closed-form. Based on this, we convexify the optimization problem and optimize the $\varepsilon$-outage secrecy rate iteratively. Numerical results show that for a moderate exposure constraint, artificial noise from the BS has a relatively large impact due to beamforming, while for a strict exposure constraint artificial noise from the UE is more important.
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity and tractability. However, these models are typically inappropriate since the implied distributional assumptions cannot be supported by hard evidence. It is natural then to relax these assumptions. This leads to the class of semiparametric models. These models have been studied in a local asymptotic setting, in which the Convolution Theorem yields bounds on the performance of regular estimators. Alternatively, local asymptotics can be based on the Local Asymptotic Minimax Theorem and on the Local Asymptotic Spread Theorem, both valid for any sequence of estimators. This Local Asymptotic Spread Theorem is a straightforward consequence of a Finite Sample Spread Inequality, which has some intrinsic value for estimation theory in general. We will discuss both the Finite Sample and Local Asymptotic Spread Theorem, as well as the Convolution Theorem.
With the emergence of the Quantum Internet, the need for advanced quantum networking techniques has significantly risen. Various models of quantum repeaters have been presented, each delineating a unique strategy to ensure quantum communication over long distances. We focus on repeaters that employ entanglement generation and swapping. This revolves around establishing remote end-to-end entanglement through repeaters, a concept we denote as the "quantum-native" repeaters (also called "first-generation" repeaters in some literature). The challenges in routing with quantum-native repeaters arise from probabilistic entanglement generation and restricted coherence time. Current approaches use synchronized time slots to search for entanglement-swapping paths, resulting in inefficiencies. Here, we propose a new set of asynchronous routing protocols for quantum networks by incorporating the idea of maintaining a dynamic topology in a distributed manner, which has been extensively studied in classical routing for lossy networks, such as using a destination-oriented directed acyclic graph (DODAG) or a spanning tree. The protocols update the entanglement-link topology asynchronously, identify optimal entanglement-swapping paths, and preserve unused direct-link entanglements. Our results indicate that asynchronous protocols achieve a larger upper bound with an appropriate setting and significantly higher entanglement rate than existing synchronous approaches, and the rate increases with coherence time, suggesting that it will have a much more profound impact on quantum networks as technology advances.
In LiDAR-based 3D object detection for autonomous driving, the ratio of the object size to input scene size is significantly smaller compared to 2D detection cases. Overlooking this difference, many 3D detectors directly follow the common practice of 2D detectors, which downsample the feature maps even after quantizing the point clouds. In this paper, we start by rethinking how such multi-stride stereotype affects the LiDAR-based 3D object detectors. Our experiments point out that the downsampling operations bring few advantages, and lead to inevitable information loss. To remedy this issue, we propose Single-stride Sparse Transformer (SST) to maintain the original resolution from the beginning to the end of the network. Armed with transformers, our method addresses the problem of insufficient receptive field in single-stride architectures. It also cooperates well with the sparsity of point clouds and naturally avoids expensive computation. Eventually, our SST achieves state-of-the-art results on the large scale Waymo Open Dataset. It is worth mentioning that our method can achieve exciting performance (83.8 LEVEL 1 AP on validation split) on small object (pedestrian) detection due to the characteristic of single stride. Codes will be released at //github.com/TuSimple/SST
Recently, contrastive learning (CL) has emerged as a successful method for unsupervised graph representation learning. Most graph CL methods first perform stochastic augmentation on the input graph to obtain two graph views and maximize the agreement of representations in the two views. Despite the prosperous development of graph CL methods, the design of graph augmentation schemes -- a crucial component in CL -- remains rarely explored. We argue that the data augmentation schemes should preserve intrinsic structures and attributes of graphs, which will force the model to learn representations that are insensitive to perturbation on unimportant nodes and edges. However, most existing methods adopt uniform data augmentation schemes, like uniformly dropping edges and uniformly shuffling features, leading to suboptimal performance. In this paper, we propose a novel graph contrastive representation learning method with adaptive augmentation that incorporates various priors for topological and semantic aspects of the graph. Specifically, on the topology level, we design augmentation schemes based on node centrality measures to highlight important connective structures. On the node attribute level, we corrupt node features by adding more noise to unimportant node features, to enforce the model to recognize underlying semantic information. We perform extensive experiments of node classification on a variety of real-world datasets. Experimental results demonstrate that our proposed method consistently outperforms existing state-of-the-art baselines and even surpasses some supervised counterparts, which validates the effectiveness of the proposed contrastive framework with adaptive augmentation.
Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.
We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, called the judge, decides whether the fact is true or false. The two agents can be considered as sparse, adversarial feature generators that present interpretable evidence for either the thesis or the antithesis. In contrast to other black-box methods, the arguments allow users to get an understanding of the decision of the judge. Since the focus of this work is to create an explainable method that maintains a competitive predictive accuracy, we benchmark our method on the triple classification and link prediction task. Thereby, we find that our method outperforms several baselines on the benchmark datasets FB15k-237, WN18RR, and Hetionet. We also conduct a survey and find that the extracted arguments are informative for users.
It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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