arXiv subjects

Emmanuel Müller

Publications and source records attributed to Emmanuel Müller.

35 records · Page 2Linked to original sources

arXiv2023

On the Consistency and Robustness of Saliency Explanations for Time Series Classification

Interpretable machine learning and explainable artificial intelligence have become essential in many applications. The trade-off between interpretability and model performance is the traitor to developing intrinsic and model-agnostic interpretation methods. Although model explanation approaches have achieved significant success in vision and natural language domains, explaining time series remains challenging. The complex pattern in the feature domain, coupled with the additional temporal dimension, hinders efficient interpretation. Saliency maps have been applied to interpret time series windows as images. However, they are not naturally designed for sequential data, thus suffering various issues. This paper extensively analyzes the consistency and robustness of saliency maps for time series features and temporal attribution. Specifically, we examine saliency explanations from both perturbation-based and gradient-based explanation models in a time series classification task. Our experimental results on five real-world datasets show that they all lack consistent and robust performances to some extent. By drawing attention to the flawed saliency explanation models, we motivate to develop consistent and robust explanations for time series classification.

cs.LG↗

arXiv2023

Redundancy-aware unsupervised rankings for collections of gene sets

The biological roles of gene sets are used to group them into collections. These collections are often characterized by being high-dimensional, overlapping, and redundant families of sets, thus precluding a straightforward interpretation and study of their content. Bioinformatics looked for solutions to reduce their dimension or increase their intepretability. One possibility lies in aggregating overlapping gene sets to create larger pathways, but the modified biological pathways are hardly biologically justifiable. We propose to use importance scores to rank the pathways in the collections studying the context from a set covering perspective. The proposed Shapley values-based scores consider the distribution of the singletons and the size of the sets in the families; Furthermore, a trick allows us to circumvent the usual exponential complexity of Shapley values' computation. Finally, we address the challenge of including a redundancy awareness in the obtained rankings where, in our case, sets are redundant if they show prominent intersections. The rankings can be used to reduce the dimension of collections of gene sets, such that they show lower redundancy and still a high coverage of the genes. We further investigate the impact of our selection on Gene Sets Enrichment Analysis. The proposed method shows a practical utility in bioinformatics to increase the interpretability of the collections of gene sets and a step forward to include redundancy into Shapley values computations.

q-bio.QM↗

arXiv2023

Prototypes as Explanation for Time Series Anomaly Detection

Detecting abnormal patterns that deviate from a certain regular repeating pattern in time series is essential in many big data applications. However, the lack of labels, the dynamic nature of time series data, and unforeseeable abnormal behaviors make the detection process challenging. Despite the success of recent deep anomaly detection approaches, the mystical mechanisms in such black-box models have become a new challenge in safety-critical applications. The lack of model transparency and prediction reliability hinders further breakthroughs in such domains. This paper proposes ProtoAD, using prototypes as the example-based explanation for the state of regular patterns during anomaly detection. Without significant impact on the detection performance, prototypes shed light on the deep black-box models and provide intuitive understanding for domain experts and stakeholders. We extend the widely used prototype learning in classification problems into anomaly detection. By visualizing both the latent space and input space prototypes, we intuitively demonstrate how regular data are modeled and why specific patterns are considered abnormal.

cs.LG↗

arXiv2023

Graph Clustering with Graph Neural Networks

Graph Neural Networks (GNNs) have achieved state-of-the-art results on many graph analysis tasks such as node classification and link prediction. However, important unsupervised problems on graphs, such as graph clustering, have proved more resistant to advances in GNNs. Graph clustering has the same overall goal as node pooling in GNNs - does this mean that GNN pooling methods do a good job at clustering graphs? Surprisingly, the answer is no - current GNN pooling methods often fail to recover the cluster structure in cases where simple baselines, such as k-means applied on learned representations, work well. We investigate further by carefully designing a set of experiments to study different signal-to-noise scenarios both in graph structure and attribute data. To address these methods' poor performance in clustering, we introduce Deep Modularity Networks (DMoN), an unsupervised pooling method inspired by the modularity measure of clustering quality, and show how it tackles recovery of the challenging clustering structure of real-world graphs. Similarly, on real-world data, we show that DMoN produces high quality clusters which correlate strongly with ground truth labels, achieving state-of-the-art results with over 40% improvement over other pooling methods across different metrics.

cs.LG↗

arXiv2023

RODD: Robust Outlier Detection in Data Cubes

Data cubes are multidimensional databases, often built from several separate databases, that serve as flexible basis for data analysis. Surprisingly, outlier detection on data cubes has not yet been treated extensively. In this work, we provide the first framework to evaluate robust outlier detection methods in data cubes (RODD). We introduce a novel random forest-based outlier detection approach (RODD-RF) and compare it with more traditional methods based on robust location estimators. We propose a general type of test data and examine all methods in a simulation study. Moreover, we apply ROOD-RF to real world data. The results show that RODD-RF can lead to improved outlier detection.

cs.DB↗

arXiv2023

FREDE: Anytime Graph Embeddings

Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require the computation of a quadratic similarity matrix, inducing a tradeoff between space complexity and embedding quality. To date, no graph embedding work combines (i) linear space complexity, (ii) a nonlinear transform as its basis, and (iii) nontrivial quality guarantees. In this paper we introduce FREDE (FREquent Directions Embedding), a graph embedding based on matrix sketching that combines those three desiderata. Starting out from the observation that embedding methods aim to preserve the covariance among the rows of a similarity matrix}, FREDE iteratively improves on quality while individually processing rows of a nonlinearly transformed PPR similarity matrix derived from a state-of-the-art graph embedding method} and provides, at any iteration, column-covariance approximation guarantees in due course almost indistinguishable from those of the optimal approximation by SVD. Our experimental evaluation on variably sized networks shows that FREDE performs almost as well as SVD and competitively against state-of-the-art embedding methods in diverse data science tasks, even when it is based on as little as 10% of node similarities.

cs.LG↗

arXiv2022

Spectral Graph Complexity

We introduce a spectral notion of graph complexity derived from the Weyl's law. We experimentally demonstrate its correlation to how well the graph can be embedded in a low-dimensional Euclidean space.

cs.SI↗

arXiv2022

Unsupervised Features Ranking via Coalitional Game Theory for Categorical Data

Not all real-world data are labeled, and when labels are not available, it is often costly to obtain them. Moreover, as many algorithms suffer from the curse of dimensionality, reducing the features in the data to a smaller set is often of great utility. Unsupervised feature selection aims to reduce the number of features, often using feature importance scores to quantify the relevancy of single features to the task at hand. These scores can be based only on the distribution of variables and the quantification of their interactions. The previous literature, mainly investigating anomaly detection and clusters, fails to address the redundancy-elimination issue. We propose an evaluation of correlations among features to compute feature importance scores representing the contribution of single features in explaining the dataset's structure. Based on Coalitional Game Theory, our feature importance scores include a notion of redundancy awareness making them a tool to achieve redundancy-free feature selection. We show that the deriving features' selection outperforms competing methods in lowering the redundancy rate while maximizing the information contained in the data. We also introduce an approximated version of the algorithm to reduce the complexity of Shapley values' computations.

cs.LG↗

arXiv2021

Differentiable Segmentation of Sequences

Segmented models are widely used to describe non-stationary sequential data with discrete change points. Their estimation usually requires solving a mixed discrete-continuous optimization problem, where the segmentation is the discrete part and all other model parameters are continuous. A number of estimation algorithms have been developed that are highly specialized for their specific model assumptions. The dependence on non-standard algorithms makes it hard to integrate segmented models in state-of-the-art deep learning architectures that critically depend on gradient-based optimization techniques. In this work, we formulate a relaxed variant of segmented models that enables joint estimation of all model parameters, including the segmentation, with gradient descent. We build on recent advances in learning continuous warping functions and propose a novel family of warping functions based on the two-sided power (TSP) distribution. TSP-based warping functions are differentiable, have simple closed-form expressions, and can represent segmentation functions exactly. Our formulation includes the important class of segmented generalized linear models as a special case, which makes it highly versatile. We use our approach to model the spread of COVID-19 with Poisson regression, apply it on a change point detection task, and learn classification models with concept drift. The experiments show that our approach effectively learns all these tasks with standard algorithms for gradient descent.

cs.LG↗

arXiv2020

Statistical Evaluation of Anomaly Detectors for Sequences

Although precision and recall are standard performance measures for anomaly detection, their statistical properties in sequential detection settings are poorly understood. In this work, we formalize a notion of precision and recall with temporal tolerance for point-based anomaly detection in sequential data. These measures are based on time-tolerant confusion matrices that may be used to compute time-tolerant variants of many other standard measures. However, care has to be taken to preserve interpretability. We perform a statistical simulation study to demonstrate that precision and recall may overestimate the performance of a detector, when computed with temporal tolerance. To alleviate this problem, we show how to obtain null distributions for the two measures to assess the statistical significance of reported results.

cs.LG↗

arXiv2020

Does Terrorism Trigger Online Hate Speech? On the Association of Events and Time Series

Hate speech is ubiquitous on the Web. Recently, the offline causes that contribute to online hate speech have received increasing attention. A recurring question is whether the occurrence of extreme events offline systematically triggers bursts of hate speech online, indicated by peaks in the volume of hateful social media posts. Formally, this question translates into measuring the association between a sparse event series and a time series. We propose a novel statistical methodology to measure, test and visualize the systematic association between rare events and peaks in a time series. In contrast to previous methods for causal inference or independence tests on time series, our approach focuses only on the timing of events and peaks, and no other distributional characteristics. We follow the framework of event coincidence analysis (ECA) that was originally developed to correlate point processes. We formulate a discrete-time variant of ECA and derive all required distributions to enable analyses of peaks in time series, with a special focus on serial dependencies and peaks over multiple thresholds. The analysis gives rise to a novel visualization of the association via quantile-trigger rate plots. We demonstrate the utility of our approach by analyzing whether Islamist terrorist attacks in Western Europe and North America systematically trigger bursts of hate speech and counter-hate speech on Twitter.

stat.AP↗

arXiv2020

The Shape of Data: Intrinsic Distance for Data Distributions

The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data distributions focus on global data properties such as mean and covariance; in that sense, they are extrinsic and uni-scale. We develop a first-of-its-kind intrinsic and multi-scale method for characterizing and comparing data manifolds, using a lower-bound of the spectral variant of the Gromov-Wasserstein inter-manifold distance, which compares all data moments. In a thorough experimental study, we demonstrate that our method effectively discerns the structure of data manifolds even on unaligned data of different dimensionalities; moreover, we showcase its efficacy in evaluating the quality of generative models.

stat.ML↗

arXiv2020

Deep Semi-Supervised Anomaly Detection

Deep approaches to anomaly detection have recently shown promising results over shallow methods on large and complex datasets. Typically anomaly detection is treated as an unsupervised learning problem. In practice however, one may have---in addition to a large set of unlabeled samples---access to a small pool of labeled samples, e.g. a subset verified by some domain expert as being normal or anomalous. Semi-supervised approaches to anomaly detection aim to utilize such labeled samples, but most proposed methods are limited to merely including labeled normal samples. Only a few methods take advantage of labeled anomalies, with existing deep approaches being domain-specific. In this work we present Deep SAD, an end-to-end deep methodology for general semi-supervised anomaly detection. We further introduce an information-theoretic framework for deep anomaly detection based on the idea that the entropy of the latent distribution for normal data should be lower than the entropy of the anomalous distribution, which can serve as a theoretical interpretation for our method. In extensive experiments on MNIST, Fashion-MNIST, and CIFAR-10, along with other anomaly detection benchmark datasets, we demonstrate that our method is on par or outperforms shallow, hybrid, and deep competitors, yielding appreciable performance improvements even when provided with only little labeled data.

cs.LG↗

arXiv2020

Two-Sample Testing for Event Impacts in Time Series

In many application domains, time series are monitored to detect extreme events like technical faults, natural disasters, or disease outbreaks. Unfortunately, it is often non-trivial to select both a time series that is informative about events and a powerful detection algorithm: detection may fail because the detection algorithm is not suitable, or because there is no shared information between the time series and the events of interest. In this work, we thus propose a non-parametric statistical test for shared information between a time series and a series of observed events. Our test allows identifying time series that carry information on event occurrences without committing to a specific event detection methodology. In a nutshell, we test for divergences of the value distributions of the time series at increasing lags after event occurrences with a multiple two-sample testing approach. In contrast to related tests, our approach is applicable for time series over arbitrary domains, including multivariate numeric, strings or graphs. We perform a large-scale simulation study to show that it outperforms or is on par with related tests on our task for univariate time series. We also demonstrate the real-world applicability of our approach on datasets from social media and smart home environments.

stat.ME↗

arXiv2018

SGR: Self-Supervised Spectral Graph Representation Learning

Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately, a "one-size-fits-all" solution is unattainable, as different analytical tasks may require different attention to global or local graph features. We develop SGR, the first, to our knowledge, method for learning graph representations in a self-supervised manner. Grounded on spectral graph analysis, SGR seamlessly combines all aforementioned desirable properties. In extensive experiments, we show how our approach works on large graph collections, facilitates self-supervised representation learning across a variety of application domains, and performs competitively to state-of-the-art methods without re-training.

cs.SI↗

arXiv2018

NetLSD: Hearing the Shape of a Graph

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable. Unfortunately, these properties have not been addressed together. Graph comparisons still rely on direct approaches, graph kernels, or representation-based methods, which are all inefficient and impractical for large graph collections. In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation method that allows for straightforward comparisons of large graphs. NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it hears the shape of a graph. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency.

cs.SI↗

arXiv2018

VERSE: Versatile Graph Embeddings from Similarity Measures

Embedding a web-scale information network into a low-dimensional vector space facilitates tasks such as link prediction, classification, and visualization. Past research has addressed the problem of extracting such embeddings by adopting methods from words to graphs, without defining a clearly comprehensible graph-related objective. Yet, as we show, the objectives used in past works implicitly utilize similarity measures among graph nodes. In this paper, we carry the similarity orientation of previous works to its logical conclusion; we propose VERtex Similarity Embeddings (VERSE), a simple, versatile, and memory-efficient method that derives graph embeddings explicitly calibrated to preserve the distributions of a selected vertex-to-vertex similarity measure. VERSE learns such embeddings by training a single-layer neural network. While its default, scalable version does so via sampling similarity information, we also develop a variant using the full information per vertex. Our experimental study on standard benchmarks and real-world datasets demonstrates that VERSE, instantiated with diverse similarity measures, outperforms state-of-the-art methods in terms of precision and recall in major data mining tasks and supersedes them in time and space efficiency, while the scalable sampling-based variant achieves equally good results as the non-scalable full variant.

cs.SI↗