In a wide range of spatio-temporal datasets, from sociology to seismology, self-exciting dynamics are often observed, characterized by event triggering and clustering across both space and time. Space-time Hawkes processes provide a powerful framework to model such phenomena. This paper introduces a flexible parametric inference method to estimate the underlying kernel parameters involved in the intensity function of a space-time Hawkes process based on such data. Our approach combines three core components: 1) kernels with finite support, 2) discretization of the space-time domain, and 3) efficient (possibly approximate) precomputations. The inference method we propose then relies on a gradient-based solver that offers both computational efficiency and strong statistical performance. Alongside a detailed presentation of the algorithmic framework, we present numerical experiments on synthetic and real spatio-temporal data, offering solid empirical evidence of the validity and applicability of the proposed methodology.

Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point of view of machine learning have been concerned with precise per-individual predictions instead of population studies, driven by the rise of individualized medicine. We introduce here a conditional normalizing flow based estimate of the time-to-event density as a way to model highly flexible and individualized conditional survival distributions. We use a novel hierarchical formulation of normalizing flows to enable efficient fitting of flexible conditional distributions without overfitting and show how the normalizing flow formulation can be efficiently adapted to the censored setting. We experimentally validate the proposed approach on a synthetic dataset as well as four open medical datasets and an example of a common financial problem.

The technological advances in the transportation and automotive industry led to the use of new types of sensing systems more cost-effective and adapted to large-scale dense deployment. Those sensing techniques allow continuously gathering traffic measurements times series in different geospatial locations. The accuracy of the obtained raw measurements is often hindered by different factors related to the sensing environment and the sensing process itself and thus fail to capture the short-term traffic variations crucial for real-time traffic monitoring. In this paper, we propose the DGC-LSTM model for area-wide traffic estimation from error-prone measurements time series. The backbone of the DGC-LSTM model is a graph convolutional Long Short Term Memory model with a dynamic adjacency matrix. The adjacency matrix is learned and optimized during the model training. The adjacency matrix values are estimated from the set of contextual features that impact the dynamicity of the dependencies in both the spatial and temporal dimensions. Experiments on a realistic synthetic labelled Bluetooth counts dataset is used for model evaluation. Lastly, we highlight the importance of transfer learning methods to improve the model applicability by ensuring model adaptation to the new deployment site while avoiding the extensive data-labelling effort.

The technological advances in the transportation and automotive industry led to the use of new types of sensing systems more cost-effective and adapted to large-scale dense deployment. Those sensing techniques allow continuously gathering traffic measurements times series in different geospatial locations. The accuracy of the obtained raw measurements is often hindered by different factors related to the sensing environment and the sensing process itself and thus fail to capture the short-term traffic variations crucial for real-time traffic monitoring. In this paper, we propose the DGC-LSTM model for area-wide traffic estimation from error-prone measurements time series. The backbone of the DGC-LSTM model is a graph convolutional Long Short Term Memory model with a dynamic adjacency matrix. The adjacency matrix is learned and optimized during the model training. The adjacency matrix values are estimated from the set of contextual features that impact the dynamicity of the dependencies in both the spatial and temporal dimensions. Experiments on a realistic synthetic labelled Bluetooth counts dataset is used for model evaluation. Lastly, we highlight the importance of transfer learning methods to improve the model applicability by ensuring model adaptation to the new deployment site while avoiding the extensive data-labelling effort.

The ability to detect an unusual concentration of extreme observations in a connected region of a graph is fundamental in a number of use cases, ranging from traffic accident detection in road networks to intrusion detection in computer networks. This task is usually performed using scan statistics-based methods, which require explicitly finding the most anomalous subgraph and thus are computationally intensive. We propose a more scalable method in the case where the observations are assigned to the edges of a large-scale network. The rationale behind our work is that if an anomalous cluster exists in the graph, then the subgraph induced by the most individually anomalous edges should contain an unexpectedly large connected component. We therefore reformulate our problem as the detection of anomalous sample paths of a percolation process on the graph, and our contribution can be seen as a generalization of previous work on percolation-based cluster detection. We evaluate our method through extensive simulations.

In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full sample is hardly feasible, if not unfeasible. A natural approach in this context consists in using survey schemes and substituting the “full data” statistics with their counterparts based on the resulting random samples, of manageable size. It is the purpose of this paper to investigate the impact of survey sampling with unequal inclusion probabilities on (stochastic) gradient descent-based M-estimation methods in large-scale statistical-learning problems. We prove that, in presence of some a priori information, one may significantly reduce the number of terms that must be averaged to estimate the gradient at each step with overwhelming probability, while preserving the asymptotic accuracy. These striking results are described here by limit theorems.

Data representing preferences of users are at the core of many Big Data modern applications, such as recommender systems or search engines. While most of the introduced machine learning approaches are designed to handle preference data under the form of cardinal scores, such as ratings given by the users to the items, many situations require to deal with ordinal preferences, coming from implicit feedback data for instance. Methods relying on the analysis of ranking data are best suited for these situations, but they face a great computational challenge insofar as the number of ways to express ordinal preferences on a catalog of n items explodes with n. It is the main purpose of this paper to promote a new representation of preference data when they come under the form of incomplete rankings, that is to say ordinal preferences on small subsets of items. The representation exploits the “multiscale” structure of incomplete rankings and though it relies on recent results in algebraic topology, it is used and interpreted similar to classic wavelet multiresolution analysis on a Euclidean space. We apply it to the problem of incomplete rankings prediction and show at the same time that it is statistically consistent and that it can be computed at a reasonable cost given the complexity of the original data. It is illustrated by very encouraging empirical work based on real datasets.

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the matrix of interest are observed gradually. Precisely, we place ourselves in the situation where the predictive rule should be refined incrementally, rather than recomputed from scratch each time the sample of observed entries increases. The extension of existing matrix completion methods to the sequential prediction context is indeed a major issue in the Big Data era, and yet little addressed in the literature. The algorithm promoted in this article builds upon the SOFT IMPUTE approach introduced in [1]. The major novelty essentially arises from the use of a randomised technique for both computing and updating the Singular Value Decomposition (SVD) involved in the algorithm. Though of disarming simplicity, the method proposed turns out to be very efficient, while requiring reduced computations. Several numerical experiments based on real datasets illustrating its performance are displayed, together with preliminary results giving it a theoretical basis.

This paper is devoted to investigate binary classification in a distributed and on-line setting. In the Big Data era, datasets can be so large that it may be impossible to process them using a single processor. The framework considered accounts for situations where both the training and test phases have to be performed by taking advantage of a network architecture by the means of local computations and exchange of limited information between neighbor nodes. An online learning gossip algorithm (OLGA) is introduced, together with a variant which implements a node selection procedure. Beyond a discussion of the practical advantages of the algorithm we promote, the paper proposes an asymptotic analysis of the accuracy of the rules it produces, together with preliminary experimental results.

It is the goal of this paper to extend the Empirical Risk Minimization (ERM) paradigm, from a practical perspective, to the situation where a natural estimate of the risk is of the form of a K-sample U-statistics, as it is the case in the K-partite ranking problem for instance. Indeed, the numerical computation of the empirical risk is hardly feasible if not infeasible, even for moderate samples sizes. Precisely, it involves averaging O(nd1+…+dK) terms, when considering a U-statistic of degrees (d1, …, dK) based on samples of sizes proportional to n. We propose here to consider a drastically simpler Monte-Carlo version of the empirical risk based on O(n) terms solely, which can be viewed as an incomplete generalized U-statistic, and prove that, remarkably, the approximation stage does not damage the ERM procedure and yields a learning rate of order Oℙ(1/√n). Beyond a theoretical analysis guaranteeing the validity of this approach, numerical experiments are displayed for illustrative purpose.

In percolation theory, vertices within a graph have a binary state: either active or inactive. Furthermore, a percolation process decides how activation spreads within the graph. Firstly, we propose and analyse a simple data-driven percolation process in which percolations are preliminarily learnt from a graph with observed percolations. Secondly, we study a problem related to the one solved by Kempe et al. in [1]: given a percolation process, which k vertices should one choose in order to maximise the number of active vertices at the end of process? This question is important in many areas, ranging from viral marketing to the study of epidemic spread. We generalise the problem by considering activations in [0, 1], measuring the “quality” of percolation, and percolation decays along edges in the percolation graph. For a varying cost of activating each vertex, we maximise the total activation whilst keeping within a budget L. The problem can be solved with a greedy algorithm with a guaranteed approximation quality, and furthermore we show its connection to the maximal coverage problem. The resulting algorithm is analysed empirically over predicted percolation graphs on a synthetic dataset and on a real dataset modelling information diffusion within a social network.