Usual day: Tuesday at 11.00.
Place: Inria Lille – Nord Europe.
How to get there: en français, in english.
Organizer: Hemant Tyagi
Calendar feed: iCalendar (hosted by the seminars platform of University of Lille)
Most slides are available: check past sessions and archives.
Archives: 2021-22, 2020-2021, 2019-2020, 2018-2019, 2017-2018, 2016-2017, 2015-2016, 2014-2015, 2013-2014
Upcoming
Date: April 11, 2023 (Tuesday) at 11.00 (Room A11)
Affiliation: University of Manchester, UK
Title: Multi-Means Gaussian Processes: A novel probabilistic framework for multi-correlated longitudinal data
Abstract: Modelling and forecasting time series, even with a probabilistic flavour, is a common and well-handled problem nowadays. However, suppose now that one is collecting data from hundreds of individuals, each of them gathering thousands of gene-related measurements, all evolving continuously over time. Such a context, frequently arising in biological or medical studies, quickly leads to highly correlated datasets where dependencies come from different sources (temporal trend, gene or individual similarities, for instance). Explicit modelling of overly large covariance matrices accounting for these underlying correlations is generally unreachable due to theoretical and computational limitations. Therefore, practitioners often need to restrict their analysis by working on subsets of data or making arguable assumptions (fixing time, studying genes or individuals independently, …). To tackle these issues, we recently proposed a new framework for multi-task Gaussian processes, tailored to handle multiple time series simultaneously. By sharing information between tasks through a mean process instead of an explicit covariance structure, this method leads to a learning and forecasting procedure with linear complexity in the number of tasks. The resulting predictions remain Gaussian distributions and thus offer an elegant probabilistic approach to deal with correlated time series. Finally, we will present the current development of an extended framework in which as many sources of correlation as desired can be considered (multiple individuals and genes could be handled jointly, for example). Intuitively, the approach relies on the definition of multiple latent mean processes, each being estimated with an adequate subset of data, and leads to an adaptive prediction associated with a mean process specific to the considered correlation.
Past talks
Carlos Brunet Martins-Filho
Date: March 21, 2023 (Tuesday) at 11.00 (Plenary room)
Affiliation: University of Colorado at Boulder, USA
Title: Optimal nonparametric estimation of distribution functions, convergence rates for Fourier inversion theorems and applications
Abstract: We obtain two sets of results in this paper. First, we consider broad classes of kernel based nonparametric estimators of an unrestricted distribution function $F$. We develop improved lower and upper bounds for the bias of the estimators at points of continuity of $F$ as well as for jumps of $F$. Second, we provide new Fourier inversion theorems with rates of convergence and use them to obtain new convergence results for deconvolution estimators for distribution functions under measurement error.
Date: March 17, 2023 (Friday) at 11.00 (Plenary room)
Affiliation: Instituto de Estadística, Chile
Title: Diagnostic tests for stocks with time-varying zero returns probability
Abstract: The first and second order serial correlations of illiquid stock’s price changes are studied, allowing for unconditional heteroscedasticity and time-varying zero returns probability. Depending on the set up, we investigate how the usual autocorrelations can be accommodated, to deliver an accurate representation of the price changes serial correlations. We shed some light on the properties of the different tools, by means of Monte Carlo experiments. The theoretical arguments are illustrated considering shares from the Chilean stock market.and Facebook 1-minute returns.
Issam Ali Moindjie
Date: February 14, 2023 (Tuesday) at 11.00 (Plenary room)
Affiliation: Inria Lille
Webpage:
Title: Classification of multivariate functional data on different domains with Partial Least Squares approaches
Abstract: Classification (supervised learning) of multivariate functional data is considered when the elements of the underlying random functional vector are defined on different domains. In this setting, PLS classification and tree PLS-based methods for multivariate functional data are presented. From a computational point of view, we show that the PLS components of the regression with multivariate functional data can be obtained using only the PLS methodology with univariate functional data. This offers an alternative way to present the PLS algorithm for multivariate functional data.
Reference:
Issam-Ali Moindjié, Cristian Preda, Sophie Dabo-Niang. Classification of multivariate functional data on different domains with Partial Least Squares approaches. 2022. ⟨hal-03908634⟩
Génia Babykina
Date: January 10, 2023 (Tuesday) at 11.00 (Plenary room)
Affiliation: Université de Lille
Title: Clustering of recurrent event data
Abstract: Nowadays data are often timestamped, thus, when analysing the events which may occur several times (recurrent events), it is desirable to model the whole dynamics of the counting process rather than to focus on a total number of events. Such kind of data can be encountered in hospital re-admissions, disease recurrences or repeated failures of industrial systems. Recurrent events can be analysed in the counting process framework, as in the Andersen-Gill model, assuming that the baseline intensity depends on time and on covariates, as in the Cox model. However, observed covariates are often insufficient to explain the observed heterogeneity in the data.
In this take, a mixture model for recurrent events is proposed, allowing to account for the unobserved heterogeneity and to perform clustering of individuals. Within each cluster, the recurrent event process intensity is specified parametrically and is adjusted for covariates. Model parameters are estimated by maximum likelihood using the EM algorithm; the BIC criterion is adopted to choose an optimal number of clusters. The model feasibility is checked on simulated data. A real data on hospital readmissions of elderly people, which motivated the development of the proposed clustering model, are analysed. The obtained results allow a fine understanding of the recurrent event process in each cluster.
Date: November 29, 2022 (Tuesday) at 11.00 (online seminar)
Affiliation: IIT Delhi, India
Title: Graph Dimensionality Reduction with Guarantees and its
Applications
Abstract: Graph coarsening is a dimensionality reduction technique that
aims to learn a smaller-tractable graph while preserving the properties
of the original input graph. However, many real-world graphs also have
features or contexts associated with each node. The existing graph
coarsening methods do not consider the node features and rely solely on
a graph matrix, (eg., adjacency and Laplacian) to coarsen graphs. In this
talk, we introduce a novel optimization-based framework for graph
coarsening that takes both the graph matrix and the node features as the
input and learns the coarsened graph matrix and the coarsened feature
matrix jointly while ensuring desired properties. We also provide a
guarantee that the learned coarsened graph is $\epsilon \in (0, 1)$
similar to the original graph. Extensive experiments with both real and
synthetic benchmark datasets elucidate the efficacy and the
applicability of the proposed framework for numerous graph-based
applications including graph clustering, stochastic block model
identification, and graph summarization.This talk is based on the following work.
A Unified Framework for Optimization-Based Graph Coarsening
–
https://arxiv.org/pdf/2210.00437.pdf
Serguei Dachian
Date: November 8, 2022 (Tuesday) at 11.00 (Plenary room)
Affiliation: University of Lille
Title: On Smooth Change-Point Location Estimation for Poisson Processes and Skorokhod Topologies
Abstract: We consider the problem of estimation of the location of what we call “smooth change-point” from $n$ independent observations of an inhomogeneous Poisson process. The “smooth change-point” is a transition of the intensity function of the process from one level to another which happens smoothly, but over such a small interval, that its length $\delta_n$ is considered to be decreasing to 0 as $n$ goes to infinity.
We study the maximum likelihood estimator (MLE) and the Bayesian estimators (BEs), and show that there is a “phase transition” in the asymptotic behavior of the estimators depending on the rate at which $\delta_n$ goes to 0 ; more precisely, on if it is slower (slow case) or quicker (fast case) than $1/n$.
It should be noted that all these results were obtained using the likelihood ratio analysis method developed by Ibragimov and Khasminskii, which equally yields the convergence of polynomial moments of the considered estimators. On the other hand, for the study of the MLE, this method needs the convergence of the normalized likelihood ratio in some functional space, and up to the best of our knowledge, until now it was only applied using either the space of continuous functions equipped with the topology induced by the supremum norm, or the space of càdlàg functions equipped with the usual Skorokhod topology (called “J_1” by Skorokhod himself). However, we will see that in the fast case of our problem this convergence can not take place in neither of these topologies. So, in order to be able to apply the Ibragimov-Khasminskii method in this case, we extend it to use a weaker topology “M_1” (also introduced by Skorokhod).
Date: October 25, 2022 (Tuesday) at 11.00 (Plenary room)
Affiliation: University of Lille
Title: One dimensional scan statistics associated to some dependent models
Abstract: The one dimensional scan statistics is presented in the context of block-factor dependent models. The longest success run statistic is related to the scan statistics in this framework. An application to the movingaverage process is also presented.
The presentation is based on the papers :
1) Amarioarei, A.; Preda, C. One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems. Mathematics 2020, 8, 576. https://doi.org/10.3390/math8040576 (open access)
2) G. Haiman, C. Preda (2013), One dimensional scan statistics generated by some dependent stationary sequences, Statistics and Probability Letters, Volume 83, Issue 5, 1457- 1463.
Date: September 9, 2022 (Friday) at 11.00 (Room A11)
Affiliation: Imperial College, London
Title: Digital Acquisition via Modulo Folding: Revisiting the Legacy of Shannon-Nyquist
Abstract: Digital data capture is the backbone of all modern day systems and “Digital Revolution” has been aptly termed as the Third Industrial Revolution. Underpinning the digital representation is the Shannon-Nyquist sampling theorem and more recent developments such as compressive sensing approaches. The fact that there is a physical limit to which sensors can measure amplitudes poses a fundamental bottleneck when it comes to leveraging the performance guaranteed by recovery algorithms. In practice, whenever a physical signal exceeds the maximum recordable range, the sensor saturates, resulting in permanent information loss. Examples include (a) dosimeter saturation during the Chernobyl reactor accident, reporting radiation levels far lower than the true value, and (b) loss of visual cues in self-driving cars coming out of a tunnel (due to sudden exposure to light).To reconcile this gap between theory and practice, we introduce a computational sensing approach—the Unlimited Sensing framework (USF)—that is based on a co-design of hardware and algorithms. On the hardware front, our work is based on a radically different analog-to-digital converter (ADC) design, which allows for the ADCs to produce modulo or folded samples. On the algorithms front, we develop new, mathematically guaranteed recovery strategies.
In the first part of this talk, we prove a sampling theorem akin to the Shannon-Nyquist criterion. Despite the non-linearity in the sensing pipeline, the sampling rate only depends on the signal’s bandwidth. Our theory is complemented with a stable recovery algorithm. Beyond the theoretical results, we also present a hardware demo that shows the modulo ADC in action.
Building on the basic sampling theory result, we consider certain variations on the theme that arise from practical implementation of the USF. This leads to a new Fourier-domain recovery algorithm that is empirically robust to noise and allows for recovery of signals upto 25 times modulo threshold, when working with modulo ADC hardware.
Moving further, we reinterpret the USF as a generalized linear model that motivates a new class of inverse problems. We conclude this talk by presenting a research overview in the context of sparse super-resolution, single-shot high-dynamic-range (HDR) imaging and sensor array processing.
