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Modal Seminar (2018-2019)

Usual day: Tuesday at 11.00.

Place: Inria Lille - Nord Europe.

How to get there: en français, in english.

Organizers: Pascal Germain and Benjamin Guedj.

Calendar feed: iCalendar (hosted by the seminars platform of University of Lille)

Most slides (and even some videos!) are available: check past sessions and archives.

Archives: 2017-2018, 2016-2017, 2015-2016, 2014-2015, 2013-2014.


Michelle Carey

  • Date: June 18, 2019 at 11.00 (Plenary Room)
  • Affiliation: University College Dublin
  • Webpage: Link.
  • Title: Data2LD and Data2PDE: Dynamic model calibration and parameter estimation
  • Abstract: The arrival of mass amounts of data from imaging, sensors, business transactions and social media has brought with it significant challenges for data science. Traditional parametric models are not flexible enough to capture the complexity of these datasets, and non-parametric approaches are prone to overfitting them. Methods that produce flexible parsimonious models from partially observed noisy data are both rare and desirable. We propose two smoothing methods called Data2LD and Data2PDE, for developing and estimating linear dynamical systems from data. These build on the collocation inference approach of Ramsay et al. (2007), by taking advantage of the linearity of the system and developing a new iterative scheme to achieve fast and stable computation. Data2LD and Data2PDE are used to attain dynamical systems that adequately represent real data from medicine, climatology and biomechanics.

Past Seminars

Adrien Saumard

  • Date: May 28, 2019 at 11.00 (Plenary Room)
  • Affiliation: ENSAI, Bruz, France
  • Webpage: Link.
  • Title: Over-cross-validation
  • Abstract: Cross-validation, possibly V -folded (in this case denoted for short VFCV in the following), is a versatile tool for hyper-parameter tuning in statistical inference. In particular, it is very popular in the machine learning community. Reasons for this success combine a relatively low computational cost with good efficiency and wide applicability. The rationale behind cross-validation indeed barely only relies on the assumption that the sample is made of (nearly) independent and identically distributed random variables. Cross-validation of the risks of a collection of M-estimators for model selection can be seen through the prism of penalization. It is then quite transparent that, at least for a fixed value of the number of folds V , VFCV is asymptotically sub-optimal. It is also legitimate to think that it should be improvable in the non-asymptotic regime. More precisely, the main drawback of VFCV is that it provides a biased estimate of the ideal penalty. But, very interestingly, debiasing this estimate does not give substantially better performances in practice (actually, it tends to deteriorate the results). This is due to a genuine second-order effect that gives benefit to a slight over-estimation of the ideal penalty. This phenomenon is sometimes called the over-penalization problem in a model selection literature, lacking so far of theoretical understanding. In this talk, we will first give a precise mathematical description of the over-penalization problem, through a formalism involving multiple (pseudo-)testing. Then we will propose a possible modification of VFCV and compare its theoretical guarantees with those of the classical VFCV on a non-parametric regression problem, with random design and heteroscedastic noise. We will conclude by discussing encouraging experimental results and stating some open problems. This talk is based on joint works with Amandine Dubois and Fabien Navarro.

Vlad Stefan Barbu

  • Date: March 12, 2019 at 11.00 (Plenary Room)
  • Affiliation: Laboratoire de Mathématiques Raphaël Salem, Université de Rouen Normandie
  • Title: Statistical topics of semi-Markov processes and new stochastic frameworks of (semi-)Markov type
  • Abstract: This presentation concerns statistical topics of semi-Markov processes, as well as new types of processes of Markov or semi-Markov type, capable of capturing some features that are important for applications. After introducing the semi-Markov framework and discussing some statistical techniques, we first present the so called drifting (semi-)Markov models. These are non-homogeneous Markov models for which the Markov transition matrix is a linear (polynomial) function/mixture of two (several) (semi-)Markov kernels. This is a “smooth” alternative to the hypothesis of homogeneity with respect to time that is used in many mathematical models. Applications in reliability/survival analysis will also be considered. Second, we will introduce and investigate step semi-Markov processes ; these are semi-Markov processes for which an additional insight is brought : the sojourn time in a state before making a transition represents the addition of two or several times that correspond to different physical causes.
  • This talk is mainly based on:
    1. V. S. Barbu, N. Vergne, Reliability and survival analysis for drifting Markov models: modelling and estimation, Methodology and Computing in Applied Probability, 1-23, 2018
    2. V. S. Barbu, G. D'Amico, R. Manca, F. Petroni, Step semi-Markov models and application to manpower management, ESAIM: Probability and Statistics, 20, 555-571, 2016

Martin Wahl

  • Date: February 5, 2019 at 11.00 (room A11)
  • Affiliation: Institut für Mathematik, Humboldt University of Berlin
  • Title: On the reconstruction error of PCA
  • Abstract: We analyze the reconstruction error of principal component analysis (PCA) and prove non-asymptotic upper bounds for the corresponding excess risk. These bounds unify and improve existing upper bounds from the literature. In particular, they give oracle inequalities under mild eigenvalue conditions. The bounds reveal that the excess risk differs considerably from usually considered subspace distances based on canonical angles. As an application, we analyze the prediction error of principal component regression (PCR). This talk is based on joint work with Markus Reiß.

Vera Shalaeva

  • Date: September 18, 2018 at 11.00 (Plenary Room)
  • Affiliation: Laboratoire d'Informatique de Grenoble
  • Title: Multi-operator Temporal Decision Tree
  • Abstract: Rising interest in mining and analyzing time series data in many domains motivates designing machine learning (ML) algorithms that are capable of tackling such complex data. Except of the need in modification, improvement, and creation of novel ML algorithms that initially works with static data, criteria of its interpretability, accuracy and computational efficiency have to be fulfilled. For a domain expert it becomes crucial to extract knowledge from data, and appealing when a yielded model is transparent and interpretable. So that, no preliminary knowledge of ML is required to read and understand results. Indeed, an emphasized by many recent works, it is more and more needed for a domain experts to get a transparent and interpretable model from the learning tool, thus allowing them to use it, even if they have few knowledge about ML's theories. Decision Tree is an algorithm that focuses on providing interpretable and quite accurate classification model. More precisely, in this talk we address the problem of interpretable time series classification by Decision Tree (DT) method. Firstly, we present Temporal Decision Tree, which is the modification of classical DT algorithm. The gist of this change is the definition of a node's split. Secondly, we propose an extension, called Multi-operator Temporal Decision Tree (MTDT), of the modified algorithm for temporal data that is able to capture different geometrical classes structures. The resulting algorithm improves model readability, while preserving the classification accuracy. Furthermore, we explore two complementary issues: computational efficiency of extended algorithm and its classification accuracy. We suggest that decreasing of the former is reachable using a Local Search approach to built nodes. And preserving of the latter can be handled by discovering and weighting discriminative time stamps of time series.
  • Slides: Link

Robert M. Gower

  • Date: September 4, 2018 at 11.00 (Room A00)
  • Affiliation: Signal, Statistics and Machine Learning group, Telecom-ParisTech
  • Title: Stochastic Quasi-Gradient Methods: Variance Reduction via Jacobian Sketching
  • Abstract: We develop a new family of variance reduced stochastic gradient descent methods for minimizing the average of a very large number of smooth functions. Our method –JacSketch– is motivated by novel developments in randomized numerical linear algebra, and operates by maintaining a stochastic estimate of a Jacobian matrix composed of the gradients of individual functions. In each iteration, JacSketch efficiently updates the Jacobian matrix by first obtaining a random linear measurement of the true Jacobian through (cheap) sketching, and then projecting the previous estimate onto the solution space of a linear matrix equation whose solutions are consistent with the measurement. The Jacobian estimate is then used to compute a variance-reduced unbiased estimator of the gradient. Our strategy is analogous to the way quasi-Newton methods maintain an estimate of the Hessian, and hence our method can be seen as a stochastic quasi-gradient method. We prove that for smooth and strongly convex functions, JacSketch converges linearly with a meaningful rate dictated by a single convergence theorem which applies to general sketches. We also provide a refined convergence theorem which applies to a smaller class of sketches. This enables us to obtain sharper complexity results for variants of JacSketch with importance sampling. By specializing our general approach to specific sketching strategies, JacSketch reduces to the stochastic average gradient (SAGA) method, and several of its existing and many new minibatch, reduced memory, and importance sampling variants. Our rate for SAGA with importance sampling is the current best-known rate for this method, resolving a conjecture by Schmidt et al (2015). The rates we obtain for minibatch SAGA are also superior to existing rates.
  • Slides: Link

Archives: 2017-2018, 2016-2017, 2015-2016, 2014-2015, 2013-2014.

Other Seminars

seminars.txt · Last modified: 2019/06/05 09:21 by germain