A Survey on Embedding Dynamic Graphs

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks present dynamic behavior, including topological evolution, feature evolution, and diffusion. Therefore, several methods for embedding dynamic graphs have been proposed to learn network representations over time, facing novel challenges, such as time-domain modeling, temporal features to be captured, and the temporal granularity to be embedded. In this survey, we overview dynamic graph embedding, discussing its fundamentals and the recent advances developed so far. We introduce the formal definition of dynamic graph embedding, focusing on the problem setting and introducing a novel taxonomy for dynamic graph embedding input and output. We further explore different dynamic behaviors that may be encompassed by embeddings, classifying by topological evolution, feature evolution, and processes on networks. Afterward, we describe existing techniques and propose a taxonomy for dynamic graph embedding techniques based on algorithmic approaches, from matrix and tensor factorization to deep learning, random walks, and temporal point processes. We also elucidate main applications, including dynamic link prediction, anomaly detection, and diffusion prediction, and we further state some promising research directions in the area.

Interactive Deep Learning for Shelf Life Prediction of Muskmelons Based on an Active Learning Approach

A pivotal topic in agriculture and food monitoring is the assessment of the quality and ripeness of agricultural products by using non-destructive testing techniques. Acoustic testing offers a rapid in situ analysis of the state of the agricultural good, obtaining global information of its interior. While deep learning (DL) methods have outperformed state-of-the-art benchmarks in various applications, the reason for lacking adaptation of DL algorithms such as convolutional neural networks (CNNs) can be traced back to its high data inefficiency and the absence of annotated data. Active learning is a framework that has been heavily used in machine learning when the labelled instances are scarce or cumbersome to obtain. This is specifically of interest when the DL algorithm is highly uncertain about the label of an instance. By allowing the human-in-the-loop for guidance, a continuous improvement of the DL algorithm based on a sample efficient manner can be obtained. This paper seeks to study the applicability of active learning when grading ‘Galia’ muskmelons based on its shelf life. We propose k-Determinantal Point Processes (k-DPP), which is a purely diversity-based method that allows to take influence on the exploration within the feature space based on the chosen subset k. While getting coequal results to uncertainty-based approaches when k is large, we simultaneously obtain a better exploration of the data distribution. While the implementation based on eigendecomposition takes up a runtime of O(n3), this can further be reduced to O(n·poly(k)) based on rejection sampling. We suggest the use of diversity-based acquisition when only a few labelled samples are available, allowing for better exploration while counteracting the disadvantage of missing the training objective in uncertainty-based methods following a greedy fashion.

Marked point processes and intensity ratios for limit order book modeling

This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline intensity, a state-dependent component specific to each process, and a state-dependent component specific to each mark within each process. We show that for specific mark distributions, this model is a combination of the ratio models defined in Muni Toke and Yoshida (2020). We prove convergence results for the quasi-maximum and quasi-Bayesian likelihood estimators of this model and provide numerical illustrations of the asymptotic variances. We use these ratio processes to model transactions occurring in a limit order book. Model flexibility allows us to investigate both state-dependency (emphasizing the role of imbalance and spread as significant signals) and clustering. Calibration, model selection and prediction results are reported for high-frequency trading data on multiple stocks traded on Euronext Paris. We show that the marked ratio model outperforms other intensity-based methods (such as “pure” Hawkes-based methods) in predicting the sign and aggressiveness of market orders on financial markets.

Point process simulation of generalised inverse Gaussian processes and estimation of the Jaeger integral

In this paper novel simulation methods are provided for the generalised inverse Gaussian (GIG) Lévy process. Such processes are intractable for simulation except in certain special edge cases, since the Lévy density associated with the GIG process is expressed as an integral involving certain Bessel functions, known as the Jaeger integral in diffusive transport applications. We here show for the first time how to solve the problem indirectly, using generalised shot-noise methods to simulate the underlying point processes and constructing an auxiliary variables approach that avoids any direct calculation of the integrals involved. The resulting augmented bivariate process is still intractable and so we propose a novel thinning method based on upper bounds on the intractable integrand. Moreover, our approach leads to lower and upper bounds on the Jaeger integral itself, which may be compared with other approximation methods. The shot noise method involves a truncated infinite series of decreasing random variables, and as such is approximate, although the series are found to be rapidly convergent in most cases. We note that the GIG process is the required Brownian motion subordinator for the generalised hyperbolic (GH) Lévy process and so our simulation approach will straightforwardly extend also to the simulation of these intractable processes. Our new methods will find application in forward simulation of processes of GIG and GH type, in financial and engineering data, for example, as well as inference for states and parameters of stochastic processes driven by GIG and GH Lévy processes.

A Neural Approach for Modeling Continuous Time Sequences with Intermittent Observations

A large fraction of data generated via human activities such as online purchases, health records, spatial mobility etc. can be represented as continuous-time event sequences (CTES) i.e. sequences of discrete events over a continuous time. Learning neural models over CTES is a non-trivial task as it involves modeling the ever-increasing event timestamps, inter-event time gaps, event types, and the influences between different events within and across different sequences. Moreover, existing sequence modeling techniques consider a complete observation scenario i.e. the event sequence being modeled is completely observed with no missing events – an ideal setting that is rarely applicable in real-world applications. In this paper, we highlight our approach[8] for modeling CTES with intermittent observations. Buoyed by the recent success of neural marked temporal point processes (MTPP) for modeling the generative distribution of CTES, we provide a novel unsupervised model and inference method for learning MTPP in presence of event sequences with missing events. Specifically, we first model the generative processes of observed events and missing events using two MTPP, where the missing events are represented as latent random variables. Then, we devise an unsupervised training method that jointly learns both the MTPP using variational inference. Experiments across real-world datasets show that our modeling framework outperforms state-of-the-art techniques for future event prediction and imputation. This work appeared in AISTATS 2021.

A study on stochastic modelling of the repairable system

All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible.When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.