A geometric perspective on functional outlier detection

• URL: http://arxiv.org/abs/2109.06849v1
• Date: Tue, 14 Sep 2021 17:42:57 GMT
• Title: A geometric perspective on functional outlier detection
• Authors: Moritz Herrmann and Fabian Scheipl
• Abstract summary: We develop a conceptualization of functional outlier detection that is more widely applicable and realistic than previously proposed. We show that simple manifold learning methods can be used to reliably infer and visualize the geometric structure of functional data sets. Our experiments on synthetic and real data sets demonstrate that this approach leads to outlier detection performances at least on par with existing functional data-specific methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We consider functional outlier detection from a geometric perspective, specifically: for functional data sets drawn from a functional manifold which is defined by the data's modes of variation in amplitude and phase. Based on this manifold, we develop a conceptualization of functional outlier detection that is more widely applicable and realistic than previously proposed. Our theoretical and experimental analyses demonstrate several important advantages of this perspective: It considerably improves theoretical understanding and allows to describe and analyse complex functional outlier scenarios consistently and in full generality, by differentiating between structurally anomalous outlier data that are off-manifold and distributionally outlying data that are on-manifold but at its margins. This improves practical feasibility of functional outlier detection: We show that simple manifold learning methods can be used to reliably infer and visualize the geometric structure of functional data sets. We also show that standard outlier detection methods requiring tabular data inputs can be applied to functional data very successfully by simply using their vector-valued representations learned from manifold learning methods as input features. Our experiments on synthetic and real data sets demonstrate that this approach leads to outlier detection performances at least on par with existing functional data-specific methods in a large variety of settings, without the highly specialized, complex methodology and narrow domain of application these methods often entail.

Related papers

• Prospector Heads: Generalized Feature Attribution for Large Models & Data [82.02696069543454]
  We introduce prospector heads, an efficient and interpretable alternative to explanation-based attribution methods. We demonstrate how prospector heads enable improved interpretation and discovery of class-specific patterns in input data.
  arXiv  Detail & Related papers  (2024-02-18T23:01:28Z)
• Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data [15.26007975367927]
  We introduce a functional linear structural equation model for causal structure learning. To enhance interpretability, our model involves a low-dimensional causal embedded space. We prove that the proposed model is causally identifiable under standard assumptions.
  arXiv  Detail & Related papers  (2023-10-31T15:19:24Z)
• On the Joint Interaction of Models, Data, and Features [82.60073661644435]
  We introduce a new tool, the interaction tensor, for empirically analyzing the interaction between data and model through features. Based on these observations, we propose a conceptual framework for feature learning. Under this framework, the expected accuracy for a single hypothesis and agreement for a pair of hypotheses can both be derived in closed-form.
  arXiv  Detail & Related papers  (2023-06-07T21:35:26Z)
• Offline Reinforcement Learning with Differentiable Function Approximation is Provably Efficient [65.08966446962845]
  offline reinforcement learning, which aims at optimizing decision-making strategies with historical data, has been extensively applied in real-life applications. We take a step by considering offline reinforcement learning with differentiable function class approximation (DFA) Most importantly, we show offline differentiable function approximation is provably efficient by analyzing the pessimistic fitted Q-learning algorithm.
  arXiv  Detail & Related papers  (2022-10-03T07:59:42Z)
• A geometric framework for outlier detection in high-dimensional data [0.0]
  Outlier or anomaly detection is an important task in data analysis. We provide a framework that exploits the metric structure of a data set. We show that exploiting this structure significantly improves the detection of outlying observations in high-dimensional data.
  arXiv  Detail & Related papers  (2022-07-01T12:07:51Z)
• Functional Nonlinear Learning [0.0]
  We propose a functional nonlinear learning (FunNoL) method to represent multivariate functional data in a lower-dimensional feature space. We show that FunNoL provides satisfactory curve classification and reconstruction regardless of data sparsity.
  arXiv  Detail & Related papers  (2022-06-22T23:47:45Z)
• A Functional Information Perspective on Model Interpretation [30.101107406343665]
  This work suggests a theoretical framework for model interpretability. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information. We show that our method surpasses existing interpretability sampling-based methods on various data signals.
  arXiv  Detail & Related papers  (2022-06-12T09:24:45Z)
• Amortized Inference for Causal Structure Learning [72.84105256353801]
  Learning causal structure poses a search problem that typically involves evaluating structures using a score or independence test. We train a variational inference model to predict the causal structure from observational/interventional data. Our models exhibit robust generalization capabilities under substantial distribution shift.
  arXiv  Detail & Related papers  (2022-05-25T17:37:08Z)
• Measuring dissimilarity with diffeomorphism invariance [94.02751799024684]
  We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces. We prove that DID enjoys properties which make it relevant for theoretical study and practical use.
  arXiv  Detail & Related papers  (2022-02-11T13:51:30Z)
• Efficient Multidimensional Functional Data Analysis Using Marginal Product Basis Systems [2.4554686192257424]
  We propose a framework for learning continuous representations from a sample of multidimensional functional data. We show that the resulting estimation problem can be solved efficiently by the tensor decomposition. We conclude with a real data application in neuroimaging.
  arXiv  Detail & Related papers  (2021-07-30T16:02:15Z)
• Invariant Feature Coding using Tensor Product Representation [75.62232699377877]
  We prove that the group-invariant feature vector contains sufficient discriminative information when learning a linear classifier. A novel feature model that explicitly consider group action is proposed for principal component analysis and k-means clustering.
  arXiv  Detail & Related papers  (2019-06-05T07:15:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.