Traditional anomaly detection methods aim to identify objects that deviate from most other objects by treating all features equally. In contrast, contextual anomaly detection methods aim to detect objects that deviate from other objects within a context of similar objects by dividing the features into contextual features and behavioral features. In this paper, we develop connections between dependency-based traditional anomaly detection methods and contextual anomaly detection methods. Based on resulting insights, we propose a novel approach to inherently interpretable contextual anomaly detection that uses Quantile Regression Forests to model dependencies between features. Extensive experiments on various synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art anomaly detection methods in identifying contextual anomalies in terms of accuracy and interpretability.
相關內容
在數據挖掘中，異常檢測（英語：anomaly detection）對不符合預期模式或數據集中其他項目的項目、事件或觀測值的識別。通常異常項目會轉變成銀行欺詐、結構缺陷、醫療問題、文本錯誤等類型的問題。異常也被稱為離群值、新奇、噪聲、偏差和例外。
特別是在檢測濫用與網絡入侵時，有趣性對象往往不是罕見對象，但卻是超出預料的突發活動。這種模式不遵循通常統計定義中把異常點看作是罕見對象，于是許多異常檢測方法（特別是無監督的方法）將對此類數據失效，除非進行了合適的聚集。相反，聚類分析算法可能可以檢測出這些模式形成的微聚類。
有三大類異常檢測方法。[1] 在假設數據集中大多數實例都是正常的前提下，無監督異常檢測方法能通過尋找與其他數據最不匹配的實例來檢測出未標記測試數據的異常。監督式異常檢測方法需要一個已經被標記“正常”與“異常”的數據集，并涉及到訓練分類器（與許多其他的統計分類問題的關鍵區別是異常檢測的內在不均衡性）。半監督式異常檢測方法根據一個給定的正常訓練數據集創建一個表示正常行為的模型，然后檢測由學習模型生成的測試實例的可能性。
Existing 3D instance segmentation methods typically assume that all semantic classes to be segmented would be available during training and only seen categories are segmented at inference. We argue that such a closed-world assumption is restrictive and explore for the first time 3D indoor instance segmentation in an open-world setting, where the model is allowed to distinguish a set of known classes as well as identify an unknown object as unknown and then later incrementally learning the semantic category of the unknown when the corresponding category labels are available. To this end, we introduce an open-world 3D indoor instance segmentation method, where an auto-labeling scheme is employed to produce pseudo-labels during training and induce separation to separate known and unknown category labels. We further improve the pseudo-labels quality at inference by adjusting the unknown class probability based on the objectness score distribution. We also introduce carefully curated open-world splits leveraging realistic scenarios based on inherent object distribution, region-based indoor scene exploration and randomness aspect of open-world classes. Extensive experiments reveal the efficacy of the proposed contributions leading to promising open-world 3D instance segmentation performance.
Overlapping community detection is a key problem in graph mining. Some research has considered applying graph convolutional networks (GCN) to tackle the problem. However, it is still challenging to incorporate deep graph convolutional networks in the case of general irregular graphs. In this study, we design a deep dynamic residual graph convolutional network (DynaResGCN) based on our novel dynamic dilated aggregation mechanisms and a unified end-to-end encoder-decoder-based framework to detect overlapping communities in networks. The deep DynaResGCN model is used as the encoder, whereas we incorporate the Bernoulli-Poisson (BP) model as the decoder. Consequently, we apply our overlapping community detection framework in a research topics dataset without having ground truth, a set of networks from Facebook having a reliable (hand-labeled) ground truth, and in a set of very large co-authorship networks having empirical (not hand-labeled) ground truth. Our experimentation on these datasets shows significantly superior performance over many state-of-the-art methods for the detection of overlapping communities in networks.
Principal components computed via PCA (principal component analysis) are traditionally used to reduce dimensionality in genomic data or to correct for population stratification. In this paper, we explore the penalized eigenvalue problem (PEP) which reformulates the computation of the first eigenvector as an optimization problem and adds an L1 penalty constraint. The contribution of our article is threefold. First, we extend PEP by applying Nesterov smoothing to the original LASSO-type L1 penalty. This allows one to compute analytical gradients which enable faster and more efficient minimization of the objective function associated with the optimization problem. Second, we demonstrate how higher order eigenvectors can be calculated with PEP using established results from singular value decomposition (SVD). Third, using data from the 1000 Genome Project dataset, we empirically demonstrate that our proposed smoothed PEP allows one to increase numerical stability and obtain meaningful eigenvectors. We further investigate the utility of the penalized eigenvector approach over traditional PCA.
We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a pre-specified mean square error (MSE). These afore-mentioned methods rely on upon the Euler-Maruyama discretization scheme which is well-known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high-dimensions of the diffusion and seemingly under-appreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of $\mathcal{O}(\epsilon^2)$, for $\epsilon>0$ given, the associated work is $\mathcal{O}(\epsilon^{-2})$. Whilst the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples.
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given architecture. This can lead to high-complexity controls which are impractical in applications. In this paper, we take the opposite, constructive approach: We impose various structural restrictions on system dynamics and consequently characterize the class of functions that can be realized by such a system. The systems are implemented as a cascade interconnection of a neural stochastic differential equation (Neural SDE), a deterministic dynamical system, and a readout map. Both probabilistic and geometric (Lie-theoretic) methods are used to characterize the classes of functions realized by such systems.
Computer simulations have become essential for analyzing complex systems, but high-fidelity simulations often come with significant computational costs. To tackle this challenge, multi-fidelity computer experiments have emerged as a promising approach that leverages both low-fidelity and high-fidelity simulations, enhancing both the accuracy and efficiency of the analysis. In this paper, we introduce a new and flexible statistical model, the Recursive Non-Additive (RNA) emulator, that integrates the data from multi-fidelity computer experiments. Unlike conventional multi-fidelity emulation approaches that rely on an additive auto-regressive structure, the proposed RNA emulator recursively captures the relationships between multi-fidelity data using Gaussian process priors without making the additive assumption, allowing the model to accommodate more complex data patterns. Importantly, we derive the posterior predictive mean and variance of the emulator, which can be efficiently computed in a closed-form manner, leading to significant improvements in computational efficiency. Additionally, based on this emulator, we introduce three active learning strategies that optimize the balance between accuracy and simulation costs to guide the selection of the fidelity level and input locations for the next simulation run. We demonstrate the effectiveness of the proposed approach in a suite of synthetic examples and a real-world problem. An R package for the proposed methodology is provided in an open repository.
Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to solving partial differential equations that involves the use of neural operators. Neural operators are neural network architectures that learn mappings between function spaces and have the capability to solve partial differential equations based on data. This study utilizes a novel neural operator called Hyena, which employs a long convolutional filter that is parameterized by a multilayer perceptron. The Hyena operator is an operation that enjoys sub-quadratic complexity and state space model to parameterize long convolution that enjoys a global receptive field. This mechanism enhances the model's comprehension of the input's context and enables data-dependent weight for different partial differential equations instances. To measure how effective the layers are in solving partial differential equations, we conduct experiments on Diffusion-Reaction equation and Navier Stokes equation. Our findings indicate Hyena Neural operator can serve as an efficient and accurate model for learning partial differential equations solution operator. The data and code used can be found at: //github.com/Saupatil07/Hyena-Neural-Operator
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
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.
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