Séminaire de Statistique
Organisateurs:


Lundi / Monday 14h  15h15 – SALLE 3001 ENSAE 
2019 
Yury Poliansky MIT 
Smoothed Empirical Measures and Entropy Estimation Abstract: In this talk we discuss behavior of
the empirical measure P_n corresponding to iid samples from a distribution P on a ddimensional
space. Let Q_n and Q denote the result of
convolving P_n and P, As an application, we show that differential
entropy of Q_n converges to that of Q at parametric
rate 1/sqrt(n) regardless of dimension. An estimator of differential
entropy of Q, in turn, allows us to estimate the inputoutput mutual
information in noisy neural networks. Joint work with Ziv Goldfeld, Kristjan Greenewald
and Jonathan Weed. 
Sept 23 2019 
Matthieu Lerasle ENSAE 
Pair Matching as a tricky bandit problem Abstract:
The pairmatching problem appears in many
applications where one wants to discover good matches between pairs of
individuals. The set of individuals is represented by the nodes of a
graph where the edges, unobserved at first, represents the good matches. A
pair matching algorithm queries sequentially pairs of nodes and observes the
presence/absence of edges. Its goal is to discover as many edges as
possible with a fixed budget of queries. Pairmatching is a particular instance of
multiarmed bandit problem in which the arms are pairs of individuals and the
rewards are edges linking these pairs. This bandit problem is non
standard since each arm can only be played once. Given this last constraint, sublinear regret
can be expected only if the graph presents some underlying structure. In
the talk, I will show that sublinear regret is achievable in the case where
the graph is generated according to a stochastic block model with two
communities. Optimal regret bounds are computed for this pairmatching
problem. They exhibit a phase transition related to the KestenStigund threshold for community detection in the
stochastic block model. To limit the concentration of queried pairs,
the pairmatching problem is also considered in the case where each node is
constrained to be sampled less than a given amount of times. I will show how
this constraint deteriorates optimal regret rates. This
talk is based on the submitted paper arXiv:1905.07342. 
Sept 30 2019 
Alexandra
Carpentier University of Magdeburg 

2019 
Vianney Perchet ENSAE 

Oct 14 2019 
Séminaire IHP 

Oct 21 2019 
Pas de séminaire 

Oct 28 2019 
Pas de séminaire 

2019 
Richard Samworth University of Cambridge 
Highdimensional principal
component analysis with heterogeneous missingness Abstract: We
study the problem of highdimensional Principal Component Analysis (PCA) with
missing observations. In simple, homogeneous missingness
settings with a noise level of constant order, we show that an existing
inverseprobability weighted (IPW) estimator of the leading principal
components can (nearly) attain the minimax optimal rate of convergence.
However, deeper investigation reveals both that, particularly in more realistic
settings where the missingness mechanism is
heterogeneous, the empirical performance of the IPW estimator can be
unsatisfactory, and moreover that, in the noiseless case, it fails to provide
exact recovery of the principal components. We therefore introduce a new
method for highdimensional PCA, called `primePCA', that is
designed to cope with situations where observations may be missing in a
heterogeneous manner. Starting from the IPW estimator, primePCA
iteratively projects the observed entries of the data matrix onto the column
space of our current estimate to impute the missing entries, and then updates
our estimate by computing the leading right singular space of the imputed
data matrix. It turns out that the interaction between the heterogeneity of missingness and the lowdimensional structure is crucial
in determining the feasibility of the problem. This leads us to impose an
incoherence condition on the principal components and we prove that in the
noiseless case, the error of primePCA converges to
zero at a geometric rate when the signal strength is not too small. An
important feature of our theoretical guarantees is that they depend on
average, as opposed to worstcase, properties of the missingness
mechanism.

Nov 11 2019 
Férié 

Nov 18 2019 


Nov 25 2019 
Séminaire IHP 

2019 
Henry
Reeve University of Birmingham 

Dec 9 2019 
Gilles
Blanchard 

Dec 16 2019 
Pas de séminaire 

2020 


Jan 13 2020 


Jan 20 2020 
Séminaire IHP 

Jan 27 2020 


2020 


Feb 10 2020 


Feb 17 2020 
Séminaire IHP 

Feb 24 2020 


2020 
Richard Nickl University of Cambridge 

March 9 2020 


March 16 2020 
Séminaire IHP 

March 23 2020 


March 30 2020 


2020 


April 13 2020 


April 20 2020 


April 27 2020 
Séminaire IHP 

2020 


2020 
Séminaire IHP 

Lundi / Monday 14h  15h15 – SALLE 3001 ENSAE 
Alexander
Meister University of Rostock 
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
SchmidtHieber 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
SchmidtHieber Leiden University 
Cours
OFPR 2/4 Theoretical results for deep neural
networks 
Jan 21 2019 14h –
16h30 Salle
2016 
Johannes
SchmidtHieber Leiden University 
Cours
OFPR 3/4 Theoretical results for deep neural
networks 
Jan 24 2019 14h –
16h30 Salle
2016 
Johannes
SchmidtHieber 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: Efficient multivariate functional Abstract: Many statistical procedures, including goodnessoffit tests
and methods for independent component analysis, rely critically on the estimation
of the entropy of a distribution. In this talk I will first describe new
entropy estimators that are efficient and achieve the local asymptotic
minimax lower bound with respect to squared error loss. These estimators are
constructed as weighted averages of the estimators originally proposed by Kozachenko and Leonenko (1987),
based on the knearest neighbour distances of a
sample of n independent and identically distributed
random vectors taking values in R^d . A careful
choice of weights enables us to obtain an efficient estimator for arbitrary
d, given sufficient smoothness, while the original unweighted estimator is
typically only efficient for d ≤ 3. I will also
discuss newer results on the estimation of more general functionals,
in settings where we have samples from two different distributions. The next
part of the talk will be to use our entropy estimators to propose a test of
independence of two multivariate random vectors, given a sample from the
underlying population. Our approach, which we call MINT, is based on the
estimation of mutual information, which we may decompose into joint and
marginal entropies. The proposed critical values, which may be obtained from
simulation in the case where an approximation to one marginal is available or
resampling otherwise, facilitate size guarantees, and we provide local power
analyses, uniformly over classes of densities whose mutual information
satisfies a lower bound. Our ideas may be extended to provide a new
goodnessoffit tests of normal linear models based on assessing the
independence of our vector of covariates and an appropriatelydefined notion
of an error vector. 
Feb 11 2019 
CANCELLED 

Feb 18 2019 
Séminaire Parisien de Statistique IHP 

Feb 25 2019 
Pas de séminaire 

2019 
Pas de séminaire 

March 11 2019 
Ismael Castillo Sorbonne
Université 
Title: On frequentist false discovery rate of
Bayesian multiple testing procedure Abstract : In many high dimensional statistical settings, a central task is to identify active variables
among a large number of candidates. For the practitioner, a key concern
is not to make too many `false positives’, which correspond to declaring
as active an inactive variable. Given a multiple testing procedure, a
typical aim is then to control its false discovery rate (FDR), that is the average number of

March 18 2019 
Séminaire Parisien de Statistique IHP 

March 25 2019 
Tengyuan
Liang University of Chicago Booth School of Business 
New Thoughts
on Adaptivity, Generalization and Interpolation
Motivated from Neural Networks Abstract: Consider
the problem: given data pair (x, y) drawn from a population with f_*(x) = E[yx], specify a neural network
and run gradient flow on the weights over time until reaching any
stationarity. How does f_t, the function computed
by the neural network at time t, relate to f_*, in terms of approximation and
representation? What are the provable benefits of the adaptive representation
by neural networks compared to the prespecified fixed basis representation
in the classical nonparametric literature? We answer the above questions via
a dynamic reproducing kernel Hilbert space (RKHS) approach indexed by the
training process of neural networks. We show that when reaching any local
stationarity, gradient flow learns an adaptive RKHS representation, and
performs the global least squares projection onto the adaptive RKHS,
simultaneously. In addition, we prove that as the RKHS is dataadaptive and
taskspecific, the residual for f˚ lies in a subspace that is smaller
than the orthogonal complement of the RKHS, formalizing the representation
and approximation benefits of neural networks. Then we will move to discuss generalization
for interpolating methods in RKHS. In the absence of explicit regularization,
Kernel “Ridgeless” Regression with nonlinear kernels
has the potential to fit the training data perfectly. It has been observed
empirically, however, that such interpolated solutions can still generalize
well on test data. We isolate a phenomenon of implicit regularization for
minimumnorm interpolated solutions which is due to a combination of high
dimensionality of the input data, curvature of the kernel function, and
favorable geometric properties of the data such as an
eigenvalue decay of the empirical covariance and kernel matrices. In addition
to deriving a datadependent upper bound on the outofsample error, we
present experimental evidence suggesting that the phenomenon occurs in the
MNIST dataset. 
2019 
Botond Szabo Leiden
University 
On the fundamental understanding of distributed computation Abstract: In
recent years, the amount of available information has become so vast in
certain fields of applications that it is infeasible or undesirable to carry
out the computations on a single server. This has motivated the design and
study of distributed statistical or learning methods. In distributed methods,
the data is split amongst different administrative units and computations are
carried out locally, in parallel to each other. The outcome of the local
computations are then aggregated into a final result on a central machine. We consider the limitations and guarantees of
distributed methods under communication constraints (i.e. only limited, fixed
amount of bits are allowed to be transmitted between the local and the
central machines) in context of the random design regression model. We derive
minimax lower bounds (which depending on the communication budget can be
substantially higher than the standard nondistributed minimax rates),
matching upper bounds and provide adaptive estimators reaching these limits.
We also consider the case where the number of transmitted bits is taken to be
datadriven and investigate whether one can achieve the minimax
nondistributed estimation rate and at the same time transmit in some sense
the optimal amount of information between the machines. This is a joint work with Harry van Zanten. 
April 8 2019 
Asaf Weinstein Carnegie
Mellon University 
A power analysis for knockoffs using Lasso and thresholdedLasso
statistics Practitioners using
the Lasso are well aware of its limitations as a variable selector. That good
prediction usually leads to many falsely selected variables implies that to
capture most of the signal, one necessarily pays with a high number of
false positives. It is also well known that this situation can be mitigated
by thresholding the Lasso estimates, i.e., by discarding small estimates one
can reduce considerably the number of false selections. Recent works
have studied both these phenomena from a theoretical perspective in the
approximate messagepassing (AMP) framework, providing exact asymptotic
predictions for Type I and Type II error rates. These existing works are
important because they allow to answer both quantitative and qualitative
questions (for example, where to stop on the Lasso path to ensure FDR\leq \alpha, or at which value of \lambda should the thresholded Lasso estimates be computed for optimal
power?) and compare Lasso to Thresholded Lasso.
However, many of these answers depend on the distribution of the underlying
signal. In this talk I’ll focus on our experience with using Knockoffs to
mimic these oracle procedures in the absence of knowledge about the signal.
It will be demonstrated that the sensitivity of power to the fraction of fake
variables added, is very different for Lasso and for Thresholded
Lasso. 
April 15 2019 
Séminaire Parisien de Statistique IHP 

April 22 2019 
Férié 

April 29 2019 
Pas de séminaire 

2019 
Pas de séminaire 

May 13 2019 
Alexey Naumov Higher School of Economics, Moscow 
Gaussian approximation for
maxima of large number of quadratic forms of highdimensional
random vectors Let (X_i)_{i=1, ... , n} be independent
identically distributed random observations taking values in a high dimensional
space and (Q_j)_{j=1, ..., p} be symmetric
positive definite
matrices. We consider joint distribution function of quadratic forms (Q_j S_n, S_n), where S_n is the
normalized sum of observations, and prove the rate of Gaussian
approximation with explicit dependence on n, p and dimension. We also
compare this result with results of Bentkus (2003)
and Chernozhukov, Chetverikov,
Kato (2016). Statistical applications will be discussed as well. The
talk is based on the joint project with Friedrich Goetze,
Vladimir Spokoiny and Alexander Tikhomirov. 
May 20 2019 
Journée de l’Ecole doctorale 9h00 – 11h00 

May 20 2019 – 2 p.m. 
Yohann De Castro Ecole
Ponts ParisTech 
Exact False Negative Control using Stopping Times on the LAR's Path In this talk we introduce a new exact testing
procedure in high dimensional linear regression framework using the outcomes
of the standard Least Angle Regression (LAR) algorithm. Under the Gaussian
noise assumption, we give the exact law of the sequence of knots conditional
on the sequence of variables entering the model (i.e., the ‘‘postselection''
law of the knots of the LAR). Based on this result, we introduce a new exact
testing procedure on the existence of false negatives. This testing procedure
can be deployed after any support selection procedure that will
produce an estimation of the support (i.e., the indexes of nonzero
coefficients). The type I error of the test can be exactly controlled as long
as the selection procedure follows some elementary hypotheses, referred to as
‘‘admissible selection procedures''. These support selection procedures are
such that the estimation of the support is given by the k first variables
entering the model where the random variable k is a stopping time. 
May 27 2019 
Geoffrey Chinot CREST, ENSAE 
ERM and RERM are tractable
and optimal estimators in the εcontamination model We study the ERM and RERM with Lipschitz and
convex loss functions under a subgaussian
assumption on the design. We consider a setting where O outliers may
contaminate the labels. In that case, we show that the error rate is bounded
by r(N) + O/N, where N is the total number of
observations and r(N) is the optimal error rate in the noncontaminated
setting. The main result can be used for both nonregularized
and regularized procedures. For instance we present results for the Huber's
Mestimators without penalization or regularized by the l1norm. For these
two applications we get minimaxoptimal rates in the εcontamination model. 
2019 
Ilias Diakonikolas University of Southern California 
Algorithmic Questions in Robust HighDimensional Statistics Fitting a model to a
collection of observations is one of the quintessential questions in
statistics. The standard assumption is that the data was generated by a model
of a given type (e.g., a mixture model). This simplifying assumption is at
best only approximately valid, as real datasets are typically exposed to some
source of contamination. Hence, any estimator designed for a particular model
must also be robust in the presence of corrupted data. This is the
prototypical goal in robust statistics, a field that took shape in the 1960s
with the pioneering works of Tukey and Huber. Until recently, even for the
basic problem of robustly estimating the mean of a highdimensional dataset,
all known robust estimators were hard to compute. Moreover, the quality of
the common heuristics degrades badly as the dimension increases. In this talk, we will survey
the recent progress in algorithmic highdimensional robust statistics. We
will describe the first computationally efficient algorithms for robust mean
and covariance estimation and the main insights behind them. We will also
present practical applications of these estimators to exploratory data
analysis and adversarial machine learning. Finally, we will discuss new
directions and opportunities for future work. The talk will be based on a
number of joint works with (various subsets of) G. Kamath, D. Kane, J. Li, A.
Moitra, and A. Stewart. 
June 10 2019 
Férié 

June 17 2019 
Pas de séminaire 

June 24 2019 10h30 
Tracy Ke Harvard University 
Optimal Adaptivity of SignedPolygon
Statistics for Network Testing Given a symmetric social
network, we are interested in testing whether it has only one community or
multiple communities. The desired tests should (a) accommodate severe degree
heterogeneity, (b) accommodate mixedmemberships, (c) have a tractable null
distribution, and (d) adapt automatically to different levels of sparsity,
and achieve the optimal phase diagram. How to find such a test is a
challenging problem. We propose the Signed Polygon
as a class of new tests. Fixing m ≥ 3, for each mgon
in the network, define a score using the centered adjacency matrix. The sum
of such scores is then the mth order Signed
Polygon statistic. The Signed Triangle (SgnT) and
the Signed Quadrilateral (SgnQ) are special
examples of the Signed Polygon. We show that both the SgnT
and SgnQ tests satisfy (a)(d), and especially,
they work well for both very sparse and less sparse networks. Our proposed
tests compare favorably with the existing tests. For example, the EZ and GC
tests behave unsatisfactorily in the less sparse case and do not achieve the
optimal phase diagram. Also, many existing tests do not allow for severe
heterogeneity or mixedmemberships, and they behave unsatisfactorily in our
settings. The analysis of the SgnT and SgnQ tests is delicate
and tedious, and the main reason is that we need a unified proof that covers
a wide range of sparsity levels and a wide range of degree heterogeneity. For
lower bound theory, we use a phase transition framework, which includes the
standard minimax argument, but is more informative. The proof uses classical
theorems on matrix scaling. (Joint work with Jiashun
Jin and Shengming
Luo. arXiv preprint: https://arxiv.org/abs/1904.09532) 
June 24 2019 14h00 
Jonas
Peters University of Copenhagen 
The Impossibility of Conditional Independence
Testing and Causality in Dynamical Systems In this talk, we (1) discuss in which sense conditional independence
testing for continuous random variables is an unsolvable statistical problem.
(2) We also introduce CausalKinetiX, a framework
that aims at learning the underlying structure in dynamical systems by
trading off invariance and predictability. The talk contains joint work with Rajen Shah, Niklas Pfister, and Stefan Bauer. No prior knowledge about causality is required. 
July 8 2019 14h00 
Vladimir
Ulyanov Moscow University 
Asymptotic expansions for the distributions of statistics with random sample size In
practice, we often encounter situations where a sample size is not de_ned in advance and can be random itself. In Gnedenko (1989) it is demonstrated that the asymptotic
properties of the statistics can be radically changed when the nonrandom
sample size is replaced by a random value. In the talk, the second order Chebyshev_Edgeworth and Cornish_Fisher
type expansions (see Ulyanov, Aoshima, Fujikoshi,
2016) based on Student's t and Laplace distributions and their quantiles
are derived for sample mean and sample median with random sample size of a
special kind. We use general transfer theorem (see Bening,
Galieva, Korolev, 2013)
which enables us to construct the asymptotic expansions for the distributions
of the randomly normalized statistics applying the asymptotic expansions for
the distributions of the considered nonrandomly normalized statistics and
for the distributions of the random size of the underlying sample. 
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 