# Pierre C. Bellec

Assistant Professor (tenure-track), Department of Statistics, Rutgers University.

I am broadly interested in the properties of machine learning algorithms that extract structured information from noisy/corrupted data, with a focus on providing provable, certifiable guarantees on the output of these algorithms, e.g. with confidence intervals or other forms of uncertainty quantification.

### Education

2016: PhD,
ENSAE ParisTech, France, advised by Alexandre Tsybakov.

2012: Part III (MASt), University of Cambridge,
UK.

2011: Diplôme d'Ingénieur, Ecole Polytechnique, France.

### Selected works

- [1]
- Out-of-sample error estimate for
robust M-estimators with convex penalty.
Pierre C Bellec.

arXiv:2008.11840, 2020. - [2]
- Second
order Poincare inequalities and de-biasing arbitrary convex regularizers when
p/n → γ.
Pierre C Bellec and Cun-Hui Zhang.

arXiv:1912.11943, 2019. - [3]
- Second order
Stein: SURE for SURE and other applications in high-dimensional
inference.
Pierre C Bellec and Cun-Hui Zhang.

Ann. Statist., to appear. - [4]
- The noise barrier and the large
signal bias of the Lasso and other convex estimators.
Pierre C Bellec.

arXiv:1804.01230, 2018. - [5]
- De-biasing
the Lasso with degrees-of-freedom adjustment.
Pierre C Bellec and Cun-Hui Zhang.

arXiv:1902.08885, 2019. - [6]
- Optimal bounds for aggregation of
affine estimators.
Pierre C. Bellec.

Ann. Statist., 46(1):30–59, 02 2018. - [7]
- Slope meets Lasso: Improved
oracle bounds and optimality.
Pierre C. Bellec, Guillaume Lecué, and
Alexandre B. Tsybakov.

Ann. Statist., 46(6B):3603–3642, 2018. - [8]
- Sharp oracle inequalities for
Least Squares estimators in shape restricted regression.
Pierre C. Bellec.

Ann. Statist., 46(2):745–780, 2018.

### Awards and Grants

- NSF award DMS 1945428
(Principal Investigator):
*CAREER: Post-Differentiation Inference*, 2020-2024. - NSF award DMS 1811976 (Principal Investigator):
*Uncertainty Quantification in High-Dimensional Structured Regression Problems*, 2018-2021. - Blaise Pascal PhD Award, 2017 edition.

### All publications

#### Preprints and submitted articles

- [1]
- Out-of-sample error estimate for
robust M-estimators with convex penalty.
Pierre C Bellec.

arXiv:2008.11840, 2020. - [2]
- Second
order Poincare inequalities and de-biasing arbitrary convex regularizers when
p/n → γ.
Pierre C Bellec and Cun-Hui Zhang.

arXiv:1912.11943, 2019. - [3]
- De-biasing
the Lasso with degrees-of-freedom adjustment.
Pierre C Bellec and Cun-Hui Zhang.

arXiv:1902.08885, 2019. - [4]
- The noise barrier and the large
signal bias of the Lasso and other convex estimators.
Pierre C Bellec.

arXiv:1804.01230, 2018. - [5]
- Optimistic lower bounds for
convex regularized least-squares.
Pierre C Bellec.

arXiv:1703.01332, 2017. - [6]
- Concentration of quadratic forms
under a Bernstein moment assumption.
Pierre C. Bellec.

Technical report. Arxiv:1901.08726, 2014.

#### Journal articles

- [1]
- Second order
Stein: SURE for SURE and other applications in high-dimensional
inference.
Pierre C Bellec and Cun-Hui Zhang.

Ann. Statist., to appear. - [2]
- Optimal bounds for aggregation of
affine estimators.
Pierre C. Bellec.

Ann. Statist., 46(1):30–59, 02 2018. - [3]
- Sharp oracle inequalities for
Least Squares estimators in shape restricted regression.
Pierre C. Bellec.

Ann. Statist., 46(2):745–780, 2018. - [4]
- On the prediction loss of the
lasso in the partially labeled setting.
Pierre C. Bellec, Arnak S. Dalalyan,
Edwin Grappin, and Quentin Paris.

Electron. J. Statist., 12(2):3443–3472, 2018. - [5]
- Slope meets Lasso: Improved
oracle bounds and optimality.
Pierre C. Bellec, Guillaume Lecué, and
Alexandre B. Tsybakov.

Ann. Statist., 46(6B):3603–3642, 2018. - [6]
- Localized Gaussian width of
M-convex hulls with applications to Lasso and convex aggregation.
Pierre C Bellec.

Bernoulli, to appear, 2017. - [7]
- Optimal exponential bounds for
aggregation of density estimators.
Pierre C. Bellec.

Bernoulli, 23(1):219–248, 2017. - [8]
- Bounds on the prediction error of
penalized least squares estimators with convex penalty.
Pierre C Bellec and Alexandre B Tsybakov.
In

Modern Problems of Stochastic Analysis and Statistics, Selected Contributions In Honor of Valentin Konakov. Springer, 2017. - [9]
- Towards the study of least
squares estimators with convex penalty.
Pierre C Bellec, Guillaume Lecué, and
Alexandre B Tsybakov.
In

Seminaire et Congres, to appear, number 39. Societe mathematique de France, 2017. - [10]
- A sharp oracle inequality for
Graph-Slope.
Pierre C. Bellec, Joseph Salmon, and
Samuel Vaiter.

Electron. J. Statist., 11(2):4851–4870, 2017. - [11]
- Adaptive confidence sets in shape
restricted regression.
Pierre C. Bellec.

Bernoulli, to appear, 2016. - [12]
- Sharp Oracle Bounds for
Monotone and Convex Regression Through Aggregation.
Pierre C. Bellec and Alexandre B. Tsybakov.

Journal of Machine Learning Research, 16:1879–1892, 2015.

#### Conference proceedings

- [1]
- The cost-free nature of optimally
tuning Tikhonov regularizers and other ordered smoothers.
Pierre C Bellec and Dana Yang.

Accepted at International Conference on Machine Learning (ICML) 2020. arXiv:1905.12517, 2019. - [2]
- First
order expansion of convex regularized estimators.
Pierre Bellec and Arun Kuchibhotla.
In

Advances in Neural Information Processing Systems, pages 3457–3468, 2019. - [3]
- Aggregation of supports along
the Lasso path.
Pierre C. Bellec.

Accepted at Conference On Learning Theory (COLT) 2016, 2016.

### Student supervision

- Yiwei Shen (PhD student, 2018-present), co-advised with Cun-Hui Zhang.
- Gabriel Romon (MSc, Spring 2020), now PhD at ENSAE.

### Courses and teaching material

Some of my teaching material is released under Creative Commons and available at https://github.com/bellecp/CC-BY-SA-teaching-material/ .

- 654 Stochastic Processes (Spring 2018, 2019).
Some teaching material:
- A take-home assignment on perfect sampling via coupling from the past,
- a homework on the Doob-h transform and Markov Chains conditioned on avoiding obstacles,
- a sample midterm exam and another midterm exam.

- 680 High dimensional probability (Fall 2018).
- 382, 582: Intro to probability theory (Spring 2017, Fall 2018).
- 588 Data-mining (Fall 2016).

### Past and upcoming talks

- International Conference on Machine Learning (ICML) 2020 (Virtual)
- Mathematical Methods of Modern Statistics 2, CIRM Luminy, France, June 15-19, 2020. (Conference happening virtually due to COVID-19).
- Otto-von-Guericke-Universität Magdeburg. Fakultät für Mathematik, Germany, January 9, 2020.
- Meeting in Mathematics Statistics, CIRM Luminy, France, December 16, 2019.
- CMStatistics conference, London, UK, December 14, 2019.
- Indiana University, Bloomington, November 18, 2019.
- University of South California, Probability Seminar, Los Angeles, November 2, 2019.
- Statistics Seminar, Columbia University, New York, April 15, 2019.
- Department of Statistics Seminar, University of Michigan, Ann Arbor, October 2018.
- Workshop on Higher-Order Asymptotics and Post-Selection Inference (WHOA-PSI), Washington University in St-Louis, September 2018.
- Joint Statistical Meeting (JSM), Vancouver, August 2018.
- Conference on Statistical Learning and Data Science (SLDS), Columbia University, June 2018.
- Oberwolfach, "Statistical Inference for Structured High-dimensional Models", March 2018.
- 'Structural Inference in Statistics' spring school, March 8, 2017. Lubbenau, Spreewald, Germany.
- Meeting in Mathematical Statistics (MMS), Luminy, Dec 2017.
- Baruch College, CUNY, November 2017.
- ICSA, June 2017, Chicago.
- UConn, April 2017. The 31st New England Statistics Symposium.
- NJIT, Department of Mathematical Sciences, April 2017.
- NYU Stern, March 2017.
- MIT, Feb 2017. MIT Stochastics and Statistics seminar series.
- Meeting in Mathematical Statistics (MMS), Dec 2016.
- George Mason University, Nov 18, 2016.
- Conference On Learning Theory (COLT), June 2016. Columbia University,
- Columbia University, Feb 3, 2016. Statistics student seminar.
- Rutgers University, Feb 2, 2016. Statistics seminar.
- Yale University, Jan 29, 2016. YPNG seminar.
- Stanford University, Jan 26, 2016. Statistics seminar.
- Orsay, Laboratoire de Mathematiques, Jan 21, 2016.
- Institut Mathematiques de Toulouse, Jan 12, 2016.
- Meeting in Mathematical Statistics (MMS), Dec 2015.
- Heidelberg University, July 2014. Workshop "Nonparametric and high-dimensional statistics".
- Meeting in Mathematical Statistics (MMS), Dec 2014. CIRM, Luminy.
- Yale University, April 2014. YPNG seminar.

### Professional Service

- Reviewer for Conference on Learning Theory (COLT) 2016, 2017, 2018, 2019.
- Reviewer for Conference on Neural Information Processing Systems (NeurIPS) 2016, 2017.
- Reviewer for Journal of the Royal Statistical Society, Statistical Methodology, Series B. 2018
- Reviewer for the Annals of Statistics. 2015-2019
- Reviewer for Bernoulli Journal. 2014-2018
- Reviewer for the Journal of Multivariate Analysis. 2018
- Reviewer for ESAIM (European Series in Applied and Industrial Mathematics) Probability and Statistics. 2018
- Reviewer for IEEE Transactions on Information Theory. 2017-2018
- Reviewer for Electronic Journal of Statistics. 2016-2018
- Reviewer for Scandinavian Journal of Statistics. 2016.

### Software

Fast-p (https://github.com/bellecp/fast-p), a fast command-line tool to browse hundreds or thousands of academic PDFs.

### Reach me

Department of Statistics

Rutgers University

501 Hill Center, Busch Campus

110 Frelinghuysen Road

Piscataway, NJ 08854