61 research outputs found
Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings
Mapping complex input data into suitable lower dimensional manifolds is a
common procedure in machine learning. This step is beneficial mainly for two
reasons: (1) it reduces the data dimensionality and (2) it provides a new data
representation possibly characterised by convenient geometric properties.
Euclidean spaces are by far the most widely used embedding spaces, thanks to
their well-understood structure and large availability of consolidated
inference methods. However, recent research demonstrated that many types of
complex data (e.g., those represented as graphs) are actually better described
by non-Euclidean geometries. Here, we investigate how embedding graphs on
constant-curvature manifolds (hyper-spherical and hyperbolic manifolds) impacts
on the ability to detect changes in sequences of attributed graphs. The
proposed methodology consists in embedding graphs into a geometric space and
perform change detection there by means of conventional methods for numerical
streams. The curvature of the space is a parameter that we learn to reproduce
the geometry of the original application-dependent graph space. Preliminary
experimental results show the potential capability of representing graphs by
means of curved manifold, in particular for change and anomaly detection
problems.Comment: To be published in IEEE IJCNN 201
Change Point Methods on a Sequence of Graphs
Given a finite sequence of graphs, e.g., coming from technological,
biological, and social networks, the paper proposes a methodology to identify
possible changes in stationarity in the stochastic process generating the
graphs. In order to cover a large class of applications, we consider the
general family of attributed graphs where both topology (number of vertexes and
edge configuration) and related attributes are allowed to change also in the
stationary case. Novel Change Point Methods (CPMs) are proposed, that (i) map
graphs into a vector domain; (ii) apply a suitable statistical test in the
vector space; (iii) detect the change --if any-- according to a confidence
level and provide an estimate for its time occurrence. Two specific
multivariate CPMs have been designed: one that detects shifts in the
distribution mean, the other addressing generic changes affecting the
distribution. We ground our proposal with theoretical results showing how to
relate the inference attained in the numerical vector space to the graph
domain, and vice versa. We also show how to extend the methodology for handling
multiple change points in the same sequence. Finally, the proposed CPMs have
been validated on real data sets coming from epileptic-seizure detection
problems and on labeled data sets for graph classification. Results show the
effectiveness of what proposed in relevant application scenarios
Graph Kalman Filters
The well-known Kalman filters model dynamical systems by relying on
state-space representations with the next state updated, and its uncertainty
controlled, by fresh information associated with newly observed system outputs.
This paper generalizes, for the first time in the literature, Kalman and
extended Kalman filters to discrete-time settings where inputs, states, and
outputs are represented as attributed graphs whose topology and attributes can
change with time. The setup allows us to adapt the framework to cases where the
output is a vector or a scalar too (node/graph level tasks). Within the
proposed theoretical framework, the unknown state-transition and the readout
functions are learned end-to-end along with the downstream prediction task.Comment: Added empirical validatio
AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs
We present the first whiteness test for graphs, i.e., a whiteness test for
multivariate time series associated with the nodes of a dynamic graph. The
statistical test aims at finding serial dependencies among close-in-time
observations, as well as spatial dependencies among neighboring observations
given the underlying graph. The proposed test is a spatio-temporal extension of
traditional tests from the system identification literature and finds
applications in similar, yet more general, application scenarios involving
graph signals. The AZ-test is versatile, allowing the underlying graph to be
dynamic, changing in topology and set of nodes, and weighted, thus accounting
for connections of different strength, as is the case in many application
scenarios like transportation networks and sensor grids. The asymptotic
distribution -- as the number of graph edges or temporal observations increases
-- is known, and does not assume identically distributed data. We validate the
practical value of the test on both synthetic and real-world problems, and show
how the test can be employed to assess the quality of spatio-temporal
forecasting models by analyzing the prediction residuals appended to the graphs
stream
Change Detection in Graph Streams by Learning Graph Embeddings on Constant-Curvature Manifolds
The space of graphs is often characterised by a non-trivial geometry, which
complicates learning and inference in practical applications. A common approach
is to use embedding techniques to represent graphs as points in a conventional
Euclidean space, but non-Euclidean spaces have often been shown to be better
suited for embedding graphs. Among these, constant-curvature Riemannian
manifolds (CCMs) offer embedding spaces suitable for studying the statistical
properties of a graph distribution, as they provide ways to easily compute
metric geodesic distances. In this paper, we focus on the problem of detecting
changes in stationarity in a stream of attributed graphs. To this end, we
introduce a novel change detection framework based on neural networks and CCMs,
that takes into account the non-Euclidean nature of graphs. Our contribution in
this work is twofold. First, via a novel approach based on adversarial
learning, we compute graph embeddings by training an autoencoder to represent
graphs on CCMs. Second, we introduce two novel change detection tests operating
on CCMs. We perform experiments on synthetic data, as well as two real-world
application scenarios: the detection of epileptic seizures using functional
connectivity brain networks, and the detection of hostility between two
subjects, using human skeletal graphs. Results show that the proposed methods
are able to detect even small changes in a graph-generating process,
consistently outperforming approaches based on Euclidean embeddings.Comment: 14 pages, 8 figure
Sparse Graph Learning from Spatiotemporal Time Series
Outstanding achievements of graph neural networks for spatiotemporal time
series analysis show that relational constraints introduce an effective
inductive bias into neural forecasting architectures. Often, however, the
relational information characterizing the underlying data-generating process is
unavailable and the practitioner is left with the problem of inferring from
data which relational graph to use in the subsequent processing stages. We
propose novel, principled - yet practical - probabilistic score-based methods
that learn the relational dependencies as distributions over graphs while
maximizing end-to-end the performance at task. The proposed graph learning
framework is based on consolidated variance reduction techniques for Monte
Carlo score-based gradient estimation, is theoretically grounded, and, as we
show, effective in practice. In this paper, we focus on the time series
forecasting problem and show that, by tailoring the gradient estimators to the
graph learning problem, we are able to achieve state-of-the-art performance
while controlling the sparsity of the learned graph and the computational
scalability. We empirically assess the effectiveness of the proposed method on
synthetic and real-world benchmarks, showing that the proposed solution can be
used as a stand-alone graph identification procedure as well as a graph
learning component of an end-to-end forecasting architecture.Comment: updated and extended versio
Taming Local Effects in Graph-based Spatiotemporal Forecasting
Spatiotemporal graph neural networks have shown to be effective in time
series forecasting applications, achieving better performance than standard
univariate predictors in several settings. These architectures take advantage
of a graph structure and relational inductive biases to learn a single (global)
inductive model to predict any number of the input time series, each associated
with a graph node. Despite the gain achieved in computational and data
efficiency w.r.t. fitting a set of local models, relying on a single global
model can be a limitation whenever some of the time series are generated by a
different spatiotemporal stochastic process. The main objective of this paper
is to understand the interplay between globality and locality in graph-based
spatiotemporal forecasting, while contextually proposing a methodological
framework to rationalize the practice of including trainable node embeddings in
such architectures. We ascribe to trainable node embeddings the role of
amortizing the learning of specialized components. Moreover, embeddings allow
for 1) effectively combining the advantages of shared message-passing layers
with node-specific parameters and 2) efficiently transferring the learned model
to new node sets. Supported by strong empirical evidence, we provide insights
and guidelines for specializing graph-based models to the dynamics of each time
series and show how this aspect plays a crucial role in obtaining accurate
predictions.Comment: Accepted at NeurIPS 202
Graph Deep Learning for Time Series Forecasting
Graph-based deep learning methods have become popular tools to process
collections of correlated time series. Differently from traditional
multivariate forecasting methods, neural graph-based predictors take advantage
of pairwise relationships by conditioning forecasts on a (possibly dynamic)
graph spanning the time series collection. The conditioning can take the form
of an architectural inductive bias on the neural forecasting architecture,
resulting in a family of deep learning models called spatiotemporal graph
neural networks. Such relational inductive biases enable the training of global
forecasting models on large time-series collections, while at the same time
localizing predictions w.r.t. each element in the set (i.e., graph nodes) by
accounting for local correlations among them (i.e., graph edges). Indeed,
recent theoretical and practical advances in graph neural networks and deep
learning for time series forecasting make the adoption of such processing
frameworks appealing and timely. However, most of the studies in the literature
focus on proposing variations of existing neural architectures by taking
advantage of modern deep learning practices, while foundational and
methodological aspects have not been subject to systematic investigation. To
fill the gap, this paper aims to introduce a comprehensive methodological
framework that formalizes the forecasting problem and provides design
principles for graph-based predictive models and methods to assess their
performance. At the same time, together with an overview of the field, we
provide design guidelines, recommendations, and best practices, as well as an
in-depth discussion of open challenges and future research directions
A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection
Time series are the primary data type used to record dynamic system
measurements and generated in great volume by both physical sensors and online
processes (virtual sensors). Time series analytics is therefore crucial to
unlocking the wealth of information implicit in available data. With the recent
advancements in graph neural networks (GNNs), there has been a surge in
GNN-based approaches for time series analysis. Approaches can explicitly model
inter-temporal and inter-variable relationships, which traditional and other
deep neural network-based methods struggle to do. In this survey, we provide a
comprehensive review of graph neural networks for time series analysis
(GNN4TS), encompassing four fundamental dimensions: Forecasting,
classification, anomaly detection, and imputation. Our aim is to guide
designers and practitioners to understand, build applications, and advance
research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy
of GNN4TS. Then, we present and discuss representative research works and,
finally, discuss mainstream applications of GNN4TS. A comprehensive discussion
of potential future research directions completes the survey. This survey, for
the first time, brings together a vast array of knowledge on GNN-based time
series research, highlighting both the foundations, practical applications, and
opportunities of graph neural networks for time series analysis.Comment: 27 pages, 6 figures, 5 table
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