Séminaire de Statistique
Organisateurs:


Lundi / Monday 14h  15h15 – SALLE 3001 ENSAE 
Alexander Meister 
Title: Nonparametric density estimation for intentionally corrupted
functional data Abstract: We consider statistical models where functional data are artificially contaminated by
independent Wiener processes in order to satisfy privacy constraints. We
show that the corrupted observations have a Wiener density which
determines the distribution of the original functional random variables
uniquely, and we construct a nonparametric estimator of that density. We
derive an upper bound for its mean integrated squared error which This talk is based on a joint work with
Aurore Delaigle (University of Melbourne,
Australia). 

Sept 17 2018 
Christophe
Giraud University Paris Sud 
Title: Partial recovery bounds
for clustering with (corrected) relaxed Kmeans
(1/2)

Sept 24 2018 
Séminaire Parisien de Statistique IHP 

Christophe
Giraud University Paris Sud 
Title: Partial recovery bounds
for clustering with (corrected) relaxed Kmeans
(2/2) 

Oct 8 2018 
Stefan Wager Stanford University 
Title: Machine Learning for Causal Inference Abstract : Flexible
estimation of heterogeneous treatment effects lies at the heart of many
statistical challenges, such as personalized medicine and optimal resource
allocation. In this talk, I will discuss general principles for estimating
heterogeneous treatment effects in observational studies via loss
minimization, and then present a random forest algorithm that builds on these
principles. As established both formally and empirically, the proposed
approach is an order of magnitude more robust to confounding that direct regressionbased
baselines. 
Oct 15 2018 
Mathias Drtn Université de Copenhague 
Title : Causal discovery in linear nonGaussian
models Abstract:
We consider the problem of
inferring the causal graph underlying a structural equation model from an i.i.d. sample. It is well known that this graph is
identifiable only under special assumptions. We consider
one such set of assumptions, namely, linear structural equations with
nonGaussian errors, and discuss inference of the causal graph in
highdimensional settings as well as in the presence of latent confounders. Joint work
with Y. Samuel Wang. 
Oct 18 et 19, 2018 14 – 16 :30 Salle 2043 
Anatoly Judtsky Université
GrenobleAlpes Cours OFPR –1 et 2 
Title:
Statistical Estimation via Convex Optimization Abstract: When speaking
about links between Statistics and Optimization, what comes to mind first is
the indispensable role played by optimization algorithms in the “numerical
toolbox” of Statistics. The goal of this course is to present another type of
links between Optimization and Statistics. We are speaking of situations
where Optimization theory (theory, not algorithms!) is of methodological
value in Statistics, acting as the source of statistical inferences. We focus
on utilizing Convex Programming theory, mainly due to its power, but also due
to the desire to end up with inference routines reducing to solving convex
optimization problems and thus implementable in a computationally efficient fashion. The topics we consider
are: ·
As a starter, we consider estimation of a
linear functional of unknown “signal” (a signal in the “usual sense,” a
distribution, or an intensity of a Poisson process, etc).
We also discuss the problem of estimating quadratic functional by “lifting”
linear functional estimates. As an application, we consider a signal recovery
procedure – “polyhedral estimate” – which relies upon efficient estimation of
linear functionals. ·
Next, we turn to general problem of linear
estimation of signals from noisy observations of their linear images. Here
application of Convex Optimization allows to propose provably optimal (or
nearly so) estimation procedures. The exposition does not
require prior knowledge of Statistics and Optimization; as far as these
disciplines are concerned, all necessary for us facts and concepts are
introduced before being used. The actual prerequisites are elementary
Calculus, Probability, Linear Algebra and (last but by far not least) general
mathematical culture. 
Oct 22 2018 
Vacances 

Oct 29 2018 
Séminaire Parisien de Statistique IHP 

Pas de séminaire 


Nov 7 et 9 2018 14 – 16 :30 Salle 2043 
Anatoly Judtsky Université
GrenobleAlpes Cours OFPR –3 et 4 
Title:
Statistical Estimation via Convex Optimization 
Nov 12 2018 
Karim Lounici Ecole Polytechnique 
Title:
Online PCA: nonasymptotics statistical guarantees
for the Krasulina scheme Principal Component
Analysis is a popular method used to analyse the
covariance structure $\Sigma$ of a random vector. Recent results on the
statistical properties of standard PCA have highlighted the importance of the
effective rank as a measure of the intrinsic statistical complexity in the
PCA problem. In particular, optimal rates of estimation of the spectral
projectors have been established in the offline setting where all the
observations are available at once and a batch estimation method is
implemented. In the online setting, observations arrive in a stream and our
estimate of eigenvalues and spectral projectors are updated every time a new
observation is available. This problem has attracted a lot a
attention recently but little is known on the statistical properties of the
existing methods. In this work, we consider the Krasulina
scheme (stochastic gradient ascent scheme) and establish nonasymptotic
estimation bounds in probability for the spectral projectors. For this
method, the effective rank also plays a central role in the performance of
the method, however the obtained rate is slower than that obtained in the
offline setting. 
Nov 19 2018 
Séminaire Parisien de Statistique IHP 

Nov 20 2018 Mardi/Tuesday 
Guenther Walther Stanford University 
Title : Constructing an optimal confidence set for a distribution function
with applications to visualizing data Abstract: We show how to construct a confidence set of
distribution functions that have the same optimal estimation performance as
the empirical distribution function, but which may be much simpler, that is
the distribution functions may have many fewer jumps. We show how an accelerated dynamic program can
be applied to a relaxed optimization problem in order to find the
distribution function in the confidence set that has the fewest jumps. We propose to use this distribution function
for summarizing and visualizing the data via a histogram, as this
distribution function is the simplest function that optimally addresses the
two main tasks of the histogram: estimating probabilities and detecting
features such as increases and (anti)modes in the distribution. We will
illustrate our methodology with examples. This is joint work with Housen
Li, Axel Munk, and Hannes Sieling. 
Nov 26 2018 
Stanislas
Minsker University of Southern California 
Medianofmeans estimator and its generalizations New results are presented for the class of estimators obtained via the generalization of the medianofmeans (MOM) technique. These results stem from connections between performance of MOMtype estimators and the rates of convergence in normal approximation. We provide tight nonasymptotic deviations guarantees in the form of exponential concentration inequalities, as well as asymptotic results in the form of limit theorems. Finally, we will discuss multivariate extensions. 
Dec 3 2018 
Nabil
Mustafa ESIEE Paris 
Title : Sampling in Geometric
Configurations In this talk I will present recent progress on
the problem of sampling in geometric configurations. A typical problem: given
a set P of n points in ddimensions, and a parameter eps>0, is it possible
to pick a set Q of O(1/eps) points of P such that
any halfspace containing at least eps*n points of P must contain some point
of Q. Based on joint works with Imre Barany, and Arijit Ghosh and Kunal Dutta. 
Dec 10 2018 
Quentin Berthet University
of Cambridge 
Title: Estimation of smooth densities in
Wasserstein distance We describe the
optimal rates of density estimation in Wasserstein distance, for different
notions of smoothness. This is motivated by the growing use of these
distances in various applications, and we also analyze the algorithmic
aspects of this problem. joint work with J. Weed, MIT. 
Dec 17 2018 
Pas
de séminaire 

Jan 7 2019 
Séminaire Parisien de Statistique IHP 

Jan 14 2019 14h –
16h30 Salle
2016 
Johannes SchimdtHieber Leiden University 
Cours
OFPR 1/4 Theoretical results for deep neural
networks Large databases and increasing
computational power have recently resulted in astonishing performances of deep
neural networks for a broad range of extremely complex tasks, including image
and text classification, speech recognition and game playing. These deep
learning methods are build by imitating the action
of the brain and there are few theoretical results as of yet. To formulate a
sound mathematical framework explaining these successes is a major challenge
for current research. The course aims to give an overview
about existing theory for deep neural networks with a strong emphasis on recent
developments. Core topics are approximation theory and complexity bounds for
the function spaces generated by deep networks. Beyond that we also discuss
modelling aspects, theoretical results on the energy landscape and
statistical risk bounds. Literature: Anthony, M., and Bartlett, P. L. Neural
network learning: theoretical foundations. Cambridge University Press, 1999. Bach, F. Breaking the curse of
dimensionality with convex neural networks. JMLR. 2017 Barron, A. Universal approximation
bounds for superpositions of a sigmoidal function. IEEE . 1993. Barron, A. Approximation and estimation
bounds for artificial neural networks. Machine Learning. 1994. Choromanska,
A., Henaff, M., Mathieu, M., Arous,
G. B., LeCun, Y. The loss surface of multilayer
networks. Aistats. 2015. Goodfellow, Bengio, Courville. Deep
Learning. MIT Press, 2016. Pinkus, A.
Approximation theory of the MLP model in neural networks. Acta
Numerica, 143195, 1999. SchmidtHieber,
J. Nonparametric regression using deep neural networks with ReLU activation function. ArXiv
2017. Telgarsky, M.
Benefits of depth in neural networks. ArXiv. 2016. Yarotsky, D.
Error bounds for approximations with deep ReLU
networks. Neural Networks. 2017. 
Jan 17 2019 14h –
16h30 Salle
2016 
Johannes SchimdtHieber Leiden University 
Cours
OFPR 2/4 Theoretical results for deep neural
networks 
Jan 21 2019 14h –
16h30 Salle
2016 
Johannes SchimdtHieber Leiden University 
Cours
OFPR 3/4 Theoretical results for deep neural
networks 
Jan 24 2019 14h –
16h30 Salle
2016 
Johannes SchimdtHieber Leiden University 
Cours
OFPR 4/4 Theoretical results for deep neural
networks 
Jan 28 2019 
Mohamed Ndaoud ENSAE 
Title: Interplay of minimax estimation and minimax
support recovery under sparsity We introduce the notion of
scaled minimaxity for sparse estimation in
highdimensional linear regression model. Fixing the scale of the
signaltonoise ratio, we prove that the estimation error can be much smaller
than the global minimax error. Taking advantage of the interplay between
estimation and support recovery we achieve optimal performance for both
problems simultaneously under orthogonal designs. We also
construct a new optimal estimator for scaled minimax sparse
estimation. Sharp results for the classical minimax risk are recovered
as a consequence of our study. For general designs, we introduce a new
framework based on algorithmic regularization where previous sharp results
hold. Our analysis bridges the gap between optimization and statistical accuracy.
The procedure we present achieves optimal statistical error faster than, for
instance, classical algorithms for the Lasso. As a consequence, we present a new iterative algorithm for
highdimensional linear regression that is scaled minimax optimal, fast
and adaptive. 
2019 
Tom Berrett University of Cambridge 
Title: Abstract: 
Feb 11 2019 


Feb 18 2019 
Séminaire Parisien de Statistique IHP 

Feb 25 2019 
Pas de séminaire 

2019 


March 11 2019 


March 18 2019 
Séminaire Parisien de Statistique IHP 

March 25 2019 
Tengyuan
Liang University of Chicago Booth School of Business 

2019 
Botond Szabo Leiden
University 

April 8 2019 
Asaf Weinstein Carnegie
Melon University 

April 15 2019 
Séminaire Parisien de Statistique IHP 

April 22 2019 
Férié 

April 29 2019 


2019 


May 13 2019 


May 20 2019 


May 27 2019 


2019 


June 10 2019 
Férié 

Arnak Dalalyan ENSAE 
Title : Userfriendly bounds for sampling from a
logconcave density using Langevin Monte Carlo Abstract : We will present new bounds on the sampling error in the case
where the target distribution has a smooth and logconcave density. These
bounds are established for the Langevin Monte Carlo
and its discretized versions involving the Hessian matrix of the logdensity.
We will also discuss the case where accurate evaluation of the gradient is
impossible. 

Sept 18 2017 
Séminaire Parisien de
Statistique  IHP 

Sept 25 2017 
Mathias Trabs Université de Hamburg 
Title :
Volatility estimation for stochastic PDE’s using highfrequency observations Abstract : We study the parameter estimation for parabolic,
linear, second order, stochastic partial differential equations (SPDEs)
observing a mild solution on a discrete grid in time and space. A
highfrequency regime is considered where the mesh of the grid in the time
variable goes to zero. Focusing on volatility estimation, we provide an
explicit and easy to implement method of moments estimator based on the
squared increments of the process. The estimator is consistent and admits a
central limit theorem. Starting from a representation of the solution as an
infinite factor model, the theory considerably differs from the
statistics for semimartingales literature. The performance of the
method is illustrated in a simulation study.




Oct 2 2017 
Nicolas Marie Modal’X (Paris 10)/ ESME Sudria 
Title : Estimation nonparamétrique dans les équations
différentielles dirigées par le mouvement brownien fractionnaire. Abstract : Après avoir introduit quelques notions de calcul stochastique trajectoriel, l’exposé présentera un estimateur type NadarayaWatson de la fonction de drift d’une équation
différentielle dirigée par un bruit multiplicatif fractionnaire. Afin
d’établir la consistance de l’estimateur, les résultats d’ergodicité
de Hairer et Ohashi
(2007) seront énoncés et expliqués. Une fois sa consistence
établie, la question de la vitesse de convergence de l’estimateur sera
abordée. Il s’agit d’un travail en collaboration avec F. Comte. 
Zoltan Szabo Ecole Polytechnique 
Title : Characteristic Tensor Kernels Abstract : Maximum mean discrepancy (MMD) and HilbertSchmidt
independence criterion (HSIC) are popular techniques in data science to
measure the difference and the independence of random variables,
respectively. Thanks to their kernelbased foundations, MMD and HSIC are applicable
on a variety of domains including documents, images, trees, graphs,
time series, mixture models, dynamical systems, sets, distributions, permutations.
Despite their tremendous practical success, quite little is known about
when HSIC characterizes independence and MMD with tensor kernel can
discriminate probability distributions, in terms of the Preprint: https://arxiv.org/abs/1708.08157] 

Oct 16 2017 
Séminaire Parisien de
Statistique  IHP 

Oct 23 2017 
Philip Thompson ENSAE 
Cancelled 
Oct 30 2017 
Vacances 




Nov 6 2017 
Martin Kroll ENSAE 
Title : On
minimax optimal and adaptive estimation of linear functionals
in inverse Gaussian sequence space models Abstract : We consider an inverse
problem in a Gaussian sequence space model where the multiplication
operator is not known but only available via noisy observations. Our aim
is not to reconstruct the solution itself but the value of a linear
functional of the solution. In our setup the optimal rate depends on two
different noise levels, the noise level concerning the observation of the
transformed solution and the noise level concerning the noisy observation of
the operator. We consider this problem from a minimax point of
view and obtain upper and lower bounds under smoothness assumptions on the
multiplication operator and the unknown solution. Finally, we
sketch an approach to the adaptive estimation in the given model using a
method combining both model selection and the GoldenshlugerLepski
method.

Séminaire Parisien de
Statistique  IHP 


Nov 20 2017 
Olivier Collier Université
Paris Nanterre 
Title : Estimation robuste
de la moyenne en temps polynômial Abstract : Il
s'agit de résultats obtenus en collaboration avec Arnak
Dalalyan. Quand les observations sont polluées par
la présence d'outliers, il n'est plus souhaitable
d'estimer l'espérance par la moyenne empirique. Des méthodes optimales ont
été trouvées, comme la profondeur de Tuckey dans le
modèle dit de contamination. Cependant, ce dernier estimateur n'est pas
calculable en temps polynômial. Dans un modèle gaussien, nous remarquerons
que l'estimation de la moyenne revient à l'estimation d'une
fonctionnelle linéaire sous contrainte de sparsité
de groupe. Il est alors naturel d'utiliser grouplasso. Nous pourrons alors
noter plusieurs phénomènes intéressants : dans ce contexte, la sparsité par groupe permet un gain polynômial par rapport
à la seule sparsité, alors que les études
précédentes montraient au mieux un gain logarithmique, et il semble que
l'estimation en temps polynômial ne puisse pas atteindre la performance
optimale des méthodes en temps exponentiel. 
Nov 27 2017 
Elisabeth Gassiat Université
ParisSud 
Title : Estimation of the proportion of explained
variation in high dimensions. Abstract : Estimation of heritability of a phenotypic trait
based on genetic data may be set as estimation of the proportion of explained
variation in high dimensional linear models. I will be interested in
understanding the impact of: — not knowing
the sparsity of the regression parameter, — not knowing the
variance matrix of the covariates on minimax estimation of
heritability. In the
situation where the variance of the design is known, I will present an
estimation procedure that adapts to unknown sparsity. when the variance of the design
is unknown and no prior estimator of it is available, I will show that
consistent estimation of heritability is impossible. (Joint work
with N. Verzelen, and PHD thesis of A. Bonnet). 



Dec 4 2017 
Philip Thomson ENSAE 
Title : Stochastic approximation
with heavier tails Abstract : We consider the solution of convex optimization and variational
inequality problems via the stochastic approximation methodology where the
gradient or operator can only be accessed through an unbiased stochastic
oracle. First, we show that (nonasymptotic) convergence is possible with
unbounded constraints and a "multiplicative noise" model: the
oracle is Lipschitz continuous with a finite pointwise variance which may not
be uniformly bounded (as classically assumed). In this setting, our bounds
depend on local variances at solutions and the method uses noise reduction in
an efficient manner: given a precision, it respects a nearoptimal sample and
averaging complexities of PolyakRuppert's method
but attains the order of the (faster) deterministic iteration complexity.
Second, we discuss a more "robust" version where the Lipschitz
constant L is unknown but, in terms of error precision, nearoptimal
complexities are maintained. A price to pay when L is unknown is that a large
sample regime is assumed (still respecting the complexity of the SAA
estimator) and "nonmartingalelike" dependencies are introduced.
These dependencies are coped with an "iterative localization"
argument based on empirical process theory and selfnormalization. Joint work with A. Iusem (IMPA), A. Jofré
(CMMChile) and R.I. Oliveira (IMPA). 
Jamal Najim CNRS
UPEM 
Title : Grandes
matrices de covariance empiriques Abstract : Les modèles de grandes matrices de covariance
empirique ont été énormément étudiés depuis l’article fondateur de Marchenko et Pastur en 1967,
qui ont décrit le comportement du spectre de telles matrices quand les deux
dimensions (dimension des observations et taille de l’échantillon) croissent
vers l’infini au même rythme. L’objectif
de cet exposé sera dans un premier temps de présenter les résultats standards
(et moins standards!) liés à ces modèles et les outils mathématiques
d’analyse (principalement la transformée de Stieltjes).
On insistera ensuite sur le cas particulier des « spiked
models », modèles de grandes matrices de
covariance dans lesquels quelques valeurs propres sont éloignées de la masse
des valeurs propres de la matrice considérée. Ces « spiked
models » sont très populaires en
finance, économétrie, traitement du signal, etc. Enfin,
on s’intéressera à des grandes matrices de covariance dont les observations
sont issues d’un processus à mémoire longue. Pour de telles observations, on
décria le comportement asymptotique et des fluctuations de la plus grande
valeur propre. Ce travail est issu d’une collaboration avec F. Merlevède et P. Tian. 

Dec 18 2017 
Pas de séminaire 




Eric Moulines Ecole
Polytechnique 
Title : Algorithmes de simulation de Langevin Abstract : Les algorithmes de Langevin
ont connu récemment un vif regain d’intérêt dans la communauté de
l’apprentissage statistique, suite aux travaux de M. Welling
et Y.W. Teh (‘Bayesian learning
via Stochastic gradient Langevin dynamics’, ICML, 2011). Cette méthode couplant
approximation stochastique et méthode de simulation permet d’envisager la
mise en œuvre de méthodes de simulation en grande dimension et pour des
grands ensembles de données. Les applications sont très nombreuses à la fois
dans les domaines «classiques » des statistiques bayésiennes (inférence
bayésienne, choix de modèles) mais aussi en optimisation bayésienne. Dans cet exposé, nous présenterons quelques travaux récents sur l’analyse
de convergence de cet algorithme. Nous montrerons comment obtenir des bornes
explicites de convergence en distance de Wasserstein
et en variation totale dans différents cadres (fortement convexe, convexe
différentiable, superexponentiel, etc.). Nous nous intéresserons tout
particulièrement à la dépendance de ces bornes dans la dimension du
paramètre. Nous montrerons aussi comment étendre ces méthodes pour des
fonctions convexes mais non différentiables en nous inspirant des méthodes de
gradient proximaux. 

Jan 15 2018 
Séminaire Parisien de Statistique
– IHP 

Jan 22 2018 

Data Science 
Jan 29 2018 
Anatoli Juditsky Université de GrenobleAlpes 
Titre : Aggrégation
des estimateurs à partir d’observations indirectes Nous considérons le problème d’agrégation
d'estimation adaptative dans le cas où des observations indirectes du signal
sont disponibles. Nous proposons une approche au problème d’agrégation par
tests quasioptimaux d'hypothèses convexes basée sur la réduction du problème
statistique d’agrégation à des problèmes d'optimisation convexe admettant une
analyse et une mise en œuvre efficace. On montre que cette approche conduit aux algorithmes
quasioptimaux dans le problème classique de l’agrégation  L_2 pour
différents schémas d'observation (par exemple, observations gaussiennes
indirectes, modèle d'observations de Poisson et échantillonnage à partir
d’une loi discrète). Nous discutons également le lien avec le problème lié
d’estimation adaptative. 



2018 
Frédéric Chazal INRIA 
Title: An
introduction to persistent homology in Topological Data Analysis and the
density of expected persistence diagrams. Abstract:
Persistence diagrams play a fundamental role in Topological Data Analysis
(TDA) where they are used as topological descriptors of data represented as
point cloud. They consist in discrete multisets of points in the plane $\R^2$
that can equivalently be seen as discrete measures in $\R^2$. In a first part
of the talk, we will introduce the notions of persistent homology and
persistence diagrams and show how they are built from point cloud data (so no
knowledge in TDA is required to follow the talk). In the second part of the
talk we will show a few properties of persistence diagrams when the data come
as a random point cloud. In this case, persistence diagrams become random
discrete measures and we will show that, in many cases, their expectation has
a density with respect to Lebesgue measure in the plane and we will discuss
its estimation. This is a joint
work with Vincent Divol (ENS Paris / Inria DataShape team) 
Feb 12 2018 
Séminaire Parisien de
Statistique  IHP 

Feb 19 2018 
Laëtitia Comminges Université
ParisDauphine 
Some
effects in adaptive robust estimation under sparsity Abstract: Adaptive estimation
in the sparse mean model and in sparse regression exhibits some interesting
effects. This paper
considers estimation of a sparse target vector, of its $\ell_2$norm and of
the noise variance in the sparse linear model. We establish the optimal rates
of adaptive estimation when adaptation is considered
with respect to the triplet "noise level  noise distribution 
sparsity". These rates turn out to be different from the minimax
nonadaptive rates when the triplet is known. A crucial issue is the
ignorance of the noise level. Moreover, knowing or not knowing the noise
distribution can also influence the rate. For example, the rates of
estimation of the noise level can differ depending on whether the noise is
Gaussian or subGaussian without a precise knowledge of the
distribution. Estimation of noise level in our setting can be viewed as
an adaptive variant of robust estimation of scale in the contamination
model, where instead of fixing the "nominal" distribution in advance
we assume that it belongs to some class of distributions. We also show that
in the problem of estimation of a sparse vector under the $\ell_2$risk when
the variance of the noise in unknown, the optimal rate depends dramatically
on the design. In particular, for noise distributions with polynomial tails,
the rate can range from subGaussian to polynomial depending on the
properties of the design. 
Feb 26 2018 
Vacances 




2018 
Rajarshi Mukherjee Berkeley 
Global Testing
Against Sparse Alternatives under Ising Models Abstract:
We study the effect of dependence on detecting sparse signals. In particular,
we focus on global testing against sparse alternatives for the magnetizations
of an Ising model and establish how the interplay
between the strength and sparsity of a signal determines its detectability
under various notions of dependence (i.e. the coupling constant of the Ising model). The impact of dependence is best
illustrated under the CurieWeiss model where we observe the effect of a
"thermodynamic" phase transition. In particular, the critical state
exhibits a subtle "blessing of dependence" phenomenon in that one
can detect much weaker signals at criticality than otherwise. Furthermore, we
develop a testing procedure that is broadly applicable to account for dependence
and show that it is asymptotically minimax optimal under fairly general
regularity conditions. This talk is based on joint work with Sumit Mukherjee and Ming Yuan. 
Mars 12 2018 
Pas
de séminaire 

Mars 19 2018 
Yihong Wu 10h3012h30 Yale 
Polynomial
method in statistical estimation : from large domain to mixture models –
1 
Mars 22 2018 
Yihong Wu 14h17h Yale 
2 
Mars 26 2018 
Yihong Wu 10h3012h30 Yale 14h00
– 17h00 
3 Ecole doctorale – exposés des
doctorants 
Mars 29 2018 
Yihong Wu 14h17h Yale 
4 



Avril 2 2018 
Férié 

April 5 2018 
Angelika
Rohde 14h15h15 Freiburg Universität 
Geometrizing rates
of convergence under privacy constraints Abstract : We study estimation of a functional $\theta(\Pr)$
of an unknown probability distribution $\Pr \in\P$
in which the original iid sample $X_1,\dots, X_n$ is kept private even from the statistician via an
$\alpha$local differential privacy constraint. Let $\omega_1$ denote the
modulus of continuity of the functional $\theta$ over $\P$, with respect to
total variation distance. For a large class of loss functions $l$, we prove
that the privatized minimax risk is equivalent to $l(\omega_1((n\alpha^2)^{1/2}))$
to within constants, under regularity conditions that are satisfied, in
particular, if $\theta$ is linear and $\P$ is convex. Our results extend the
theory developed by Donoho and Liu (1991) to the
nowadays highly relevant case of privatized data. Somewhat surprisingly, the
difficulty of the estimation problem in the private case is characterized by
$\omega_1$, whereas, it is characterized by the Hellinger modulus of
continuity if the original data $X_1,\dots, X_n$ are available. We also provide a general recipe for
constructing rate optimal privatization mechanisms and illustrate the general
theory in numerous examples. Our theory allows to quantify the price to be
paid for local differential privacy in a large class of estimation problems. 
April 6 2018 
Cheng
Mao – 14h15h15 MIT 
Breaking the n^{1/2} barrier for
permutationbased ranking models Abstract : The task of ranking from
pairwise comparison data arises frequently in various applications, such as
recommender systems, sports tournaments and social choice theory. There has been
a recent surge of interest in studying permutationbased models, such as the
noisy sorting model and the strong stochastic transitivity model, for ranking
from pairwise comparisons. Although permutationbased ranking models are
richer than traditional parametric models, a wide gap exists between the
statistically optimal rate n^{1} and the rate
n^{1/2} achieved by the stateoftheart computationally efficient
algorithms. In this talk, I will discuss new algorithms that achieve rates n^{1} and n^{3/4} for the noisy sorting model and the
more general strong stochastic transitivity model respectively. The talk is based on joint works with Jonathan Weed, Philippe Rigollet, Ashwin Pananjady
and Martin J. Wainwright. 
Avril 9 2018 
Séminaire Parisien de Statistique
 IHP 

Avril 13 2018 
Eric Kolaczyk –
14h15h15 Boston University 
Title:
Dynamic Networks with Multiscale Temporal Structure Abstract: We
describe a novel method for modeling nonstationary multivariate time series,
with timevarying conditional dependencies represented through dynamic
networks. Our proposed approach combines traditional multiscale modeling and
network based neighborhood selection, aiming at capturing temporally local
structure in the data while maintaining sparsity of the potential
interactions. Our multiscale framework is based on recursive dyadic
partitioning, which recursively partitions the temporal axis into finer
intervals and allows us to detect local network structural changes at varying
temporal resolutions. The dynamic neighborhood selection is achieved through
penalized likelihood estimation, where the penalty seeks to limit the number
of neighbors used to model the data. We present theoretical and numerical
results describing the performance of our method, which is motivated and
illustrated using taskbased magnetoencephalography (MEG) data in
neuroscience. This is joint work with Xinyu Kang and Apratim Ganguly. 
Avril 23 2017 
Vacances 

Avril 30 2018 
Pas de
séminaire 




May 7 2018 
Pas
de séminaire 

May 14 2018 


May 21 2018 
Jour férié 

May 22 2018 
Mikhail Belkin 10h13h Ohia State University 
The
Differential Geometry of Data  1 
May 23 2018 
Mikhail Belkin 16h18h Ohia State University 
2 
May 28 2018 
Sivaraman Balakrishnan Carnegie Melon 

May 29 2018 
Mikhail Belkin 10h13h salle2003 Ohia State University 
3 
May
30 2018 
Mikhail Belkin 16h18h sale2040 Ohia State University 
4 



June 4 
Séminaire Parisien de Statistique  IHP 

June
11 2018 
Jeremy Heng Harvard
University 
Title: Controlled sequential Monte Carlo Sequential Monte Carlo methods, also known as particle methods, are a
popular set of techniques to approximate highdimensional probability distributions
and their normalizing constants. They have found numerous applications in
statistics and related fields as they can be applied to perform state
estimation for nonlinear nonGaussian state space models and Bayesian
inference for complex static models. Like many Monte Carlo sampling schemes,
they rely on proposal distributions which have a crucial impact on their
performance. We introduce here a class of controlled sequential Monte Carlo
algorithms, where the proposal distributions are determined by approximating
the solution to an associated optimal control problem using an iterative
scheme. We provide theoretical analysis of our proposed methodology and
demonstrate significant gains over stateoftheart methods at a fixed
computational complexity on a variety of applications. 
June
18 2018 
Mihai Cucuringu Oxford
University 
Title:
Laplacianbased methods for ranking and constrained clustering We consider
the classic problem of establishing a statistical ranking of a set of n items
given a set of inconsistent and incomplete pairwise comparisons between such
items. Instantiations of this problem occur in numerous applications in data
analysis (e.g., ranking teams in sports data), computer vision, and machine
learning. We formulate the above problem of ranking with incomplete noisy
information as an instance of the group synchronization problem over the
group SO(2) of planar rotations, whose usefulness
has been demonstrated in numerous applications in recent years. Its least
squares solution can be approximated by either a spectral or a semidefinite
programming relaxation, followed by a rounding procedure. We perform
extensive numerical simulations on both synthetic and realworld data sets,
showing that our proposed method compares favorably to other algorithms from
the recent literature. We also briefly discuss ongoing work on extensions and
applications of the group synchronization framework to kway synchronization,
list synchronization, synchronization with heterogeneous information and
partial rankings, and phase unwrapping. We also
present a simple spectral approach to the wellstudied constrained clustering
problem. It captures constrained clustering as a generalized eigenvalue problem
with graph Laplacians. The algorithm works in nearlylinear time and provides
concrete guarantees for the quality of the clusters, at least for the case of
2way partitioning, via a generalized Cheeger
inequality. In practice this translates to a very fast implementation that
consistently outperforms existing spectral approaches both in speed and
quality. 
June
27 2018 Wednesday
14h 
Emtiyaz Khan Riken, Tokyo 
Title: Fast yet Simple
NaturalGradient Variational Inference in Complex
Models Approximate
Bayesian inference is promising in improving generalization and reliability
of deep learning, but is computationally challenging. Modern variationalinference (VI) methods circumvent the
challenge by formulating Bayesian inference as an optimization problem and
then solving it using gradientbased methods. In this talk, I will argue in
favor of naturalgradient approaches which can improve convergence of VI by
exploiting the information geometry of the solutions. I will discuss a fast
yet simple naturalgradient method obtained by using a duality associated
with exponentialfamily distributions. I will summarize some of our recent
results on Bayesian deep learning, where naturalgradient methods lead to an
approach which gives simpler updates than existing VI methods while
performing comparably to them. Joint
work with Wu Lin (UBC), Didrik Nielsen (RIKEN), Voot Tangkaratt (RIKEN), Yarin Gal (UOxford), Akash Srivastva (UEdinburgh), Zuozhu Liu (SUTD). Based
on: https://arxiv.org/abs/1806.04854 https://arxiv.org/abs/1703.04265 