About me
I am a postdoctoral researcher working at MIT, Mathematics Department, with Prof. Elchanan Mossel and Prof. Nike Sun. as a member of the NSF/Simons program Collaboration on the Theoretical Foundations of Deep Learning.
Research Interests
My research lies broadly in the interface of high dimensional statistics, the theory of machine learning and computation and applied probability. A lot of my work has the goal to build and use mathematical tools to bring insights into the computational and statistical challenges of modern machine learning tasks.
Four directions that I have been recently focusing on are:
 Computationalstatistical tradeoffs in inference (see papers 4, 11, 13, 17, 22, 24, 25 below).
 (Sharp) statistical phase transitions (the "AllorNothing phenomenon") (see papers 10, 12, 14, 18, 22 below).
 The power of latticebased methods in inference (see papers 7, 19, 23 below).
 The cost of (differential) privacy in statistics (see papers 6, 15 below).
Short Bio (prior to current position)
From September 2019 to August 2021 I was a CDS
MooreSloan (postdoctoral) fellow at the
Center for Data Science of
New York University and a member of it's
Math and Data (MaD) group.
I received my PhD on September 2019 from the
Operations Research Center of
Massachussets Institute of Technology (MIT) , where I was very fortunate to be advised by Prof.
David Gamarnik. A copy of my PhD thesis can be found
here.
From June 2017 to August 2017 I was an intern at the
Microsoft Research Lab in New England, mentored by
Jennifer Chayes and
Christian Borgs . Prior joining MIT, I completed a Master of Advanced Studies in Mathematics (Part III of the Mathematical Tripos) at the
University of Cambridge and a BA in Mathematics from the Mathematics Department at the
University of Athens.
Recent recorded talks
Research papers (published or under review)
(Note: the order of the authors is alphabetical, unless denoted by (*))
2022+

The FranzParisi Criterion and Computational Tradeoffs in High Dimensional Statistics
Submitted
Afonso Bandeira, Ahmed El Alaoui, Sam Hopkins, Tselil Schramm, Alex Wein, Ilias Zadik.

AlmostLinear Planted Cliques Elude the Metropolis Process
Submitted
Zongchen Chen, Elchanan Mossel, Ilias Zadik.

LatticeBased Methods Surpass SumofSquares in Clustering
To appear in Conference on Learning Theory (COLT), 2022
Ilias Zadik, Min Jae Song, Alex Wein, Joan Bruna. (*)

Statistical and Computational Phase Transitions in Group Testing
To appear in Conference on Learning Theory (COLT), 2022
Amin CojaOghlan, Oliver Gebhard, Max HahnKlimroth, Alex Wein, Ilias Zadik.

Shapes and recession cones in mixedinteger convex representability
Mathematical Programming (Major Revisions)
Ilias Zadik, Miles Lubin, Juan Pablo Vielma. (*)

Stationary Points of Shallow Neural Networks with Quadratic Activation Function (30mins video by Eren  MIT MLTea)
Submitted
David Gamarnik, Eren C. Kızıldağ, Ilias Zadik.
2021

On the Cryptographic Hardness of Learning Single Periodic Neurons
Advances in Neural Information Processing Systems, (NeurIPS), 2021
Min Jae Song, Ilias Zadik, Joan Bruna. (*)

It was “all” for “nothing”: sharp phase transitions for noiseless discrete channels(18mins video  COLT)
Proceedings of the Conference on Learning Theory (COLT), 2021
Jonathan NilesWeed, Ilias Zadik.

Group testing and local search: is there a computationalstatistical gap? (2hrs video by Fotis  IAS)
Proceedings of the Conference on Learning Theory (COLT), 2021
Fotis Iliopoulos, Ilias Zadik.

SelfRegularity of NonNegative Output Weights for Overparameterized TwoLayer Neural Networks
IEEE Transactions of Signal Processing, 2022+
Conference version in Proceedings of the International Symposium on Information Theory (ISIT), 2021
David Gamarnik, Eren C. Kızıldağ, Ilias Zadik.
2020

Optimal Private Median Estimation under Minimal Distributional Assumptions (10mins video by Manolis  NeurIPS spotlight)
Advances in Neural Information Processing Systems, (NeurIPS), 2020
Selected for a Spotlight Presentation (~5% of submitted papers).
Christos Tzamos, Manolis Vlatakis, Ilias Zadik.

The AllorNothing Phenomenon in Sparse Tensor PCA (Poster, ( 25mins video  BIRS workshop)
Advances in Neural Information Processing Systems, (NeurIPS), 2020
Jonathan NilesWeed, Ilias Zadik.

Free Energy Wells and the Overlap Gap Property in Sparse PCA ( 25mins video  Simons workshop)
Communications on Pure and Applied Mathematics, 2022+
Conference version in Proceedings of the Conference of Learning Theory (COLT), 2020
Gèrard Ben Arous, Alex Wein, Ilias Zadik.
2019

The AllorNothing Phenomenon in Sparse Linear Regression (Slides, Poster)
Mathematics of Statistics and Learning, 2021
Conference version in the Proceedings of the Conference on Learning Theory (COLT), 2019
Galen Reeves, Jiaming Xu, Ilias Zadik.

The Landscape of the Planted Clique Problem: Dense Subgraphs and the Overlap Gap Property ( 1hr video  NYU Probability Seminar)
Annals of Applied Probability (Major Revisions)
David Gamarnik, Ilias Zadik.

AllorNothing Phenomena: From SingleLetter to High Dimensions
Proceedings of the International Workshop on Computational Advances in MultiSensor Adaptive Processing (CAMSAP), 2019
Galen Reeves, Jiaming Xu, Ilias Zadik.

Improved bounds on Gaussian MAC and sparse regression via Gaussian inequalities
Proceedings of the International Symposium on Information Theory (ISIT), 2019
Ilias Zadik, Christos Thrampoulidis, Yury Polyanskiy. (*)

A simple bound on the BER of the MAP decoder for massive MIMO systems
Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2019
Christos Thrampoulidis, Ilias Zadik, Yury Polyanskiy. (*)
2018

Inference in HighDimensional Linear Regression via Lattice Basis Reduction and Integer Relation Detection
IEEE Transactions of Information Theory, 2021
Conference version with David Gamarnik, in Advances in Neural Information Processing Systems, (NeurIPS), 2018
David Gamarnik, Eren C. Kızıldağ, Ilias Zadik.

Revealing Network Structure, Confidentially: Improved Rates for NodePrivate Graphon Estimation (Slides, 1h video by Adam Simons)
Proceedings of the Symposium on Foundations of Computer Science (FOCS), 2018
Christian Borgs, Jennifer Chayes, Adam Smith, Ilias Zadik.

Orthogonal Machine Learning: Power and Limitations (Slides, Poster, Code)
Proceedings of International Conference of Machine Learning (ICML), 2018 (20 minute Presentation)
Lester Mackey, Vasilis Syrgkanis, Ilias Zadik.
2017

Sparse HighDimensional Linear Regression. Estimating Squared Error and a Phase Transition.
Annals of Statistics, 2022
David Gamarnik, Ilias Zadik.
This paper merges:
(a) HighDimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transition (Slides, Poster, 20mins video)
Proceedings of the Conference on Learning Theory (COLT), 2017 (20 minutes Presentation)
(b) Sparse HighDimensional Linear Regression. Algorithmic Barriers and a Local Search Algorithm
arXiv preprint, 2017

Mixed integer convex representability (Slides)
Mathematics of Operations Research, 2021
Conference version in Proceedings of the International Conference of Integer Programming and Combinatorial Optimization (IPCO), 2017
Miles Lubin, Juan Pablo Vielma, Ilias Zadik.
Pre2017 (complex analysis):

Universal Padé approximants and their behaviour on the boundary
Monatshefte für Mathematik, Vol. 182, p.p. 173–193, 2017
Ilias Zadik.

Pade approximants, density of rational functions in A^(infinity)(V) and smoothness of the integration operator
Journal of Mathematical Analysis and Applications; Vol. 423, p.p. 1514–1539, 2015
Vassili Nestoridis, Ilias Zadik.
Thesis/Notes/Survey Articles

Computational and Statistical Challenges in High Dimensional Statistical Models
PhD Thesis, Operations Research Center, Massachussets Institute of Technology, 2019

Private Algorithms Can Always Be Extended
Note on the extension of private algorithms
Christian Borgs, Jennifer Chayes, Adam Smith, Ilias Zadik.

Noise Sensitivity with applications to Percolation and Social Choice Theory
Part III Essay, 2014
Advised by Béla Bollobás

A Note on the Density of Rational Functions in Α^{∞ }(Ω)
A complex analysis note on the density of rational functions
New Trends in Approximation Theory; vol 81, p.p. 2735
Javier Falcó, Vassili Nestoridis, Ilias Zadik
Service
 From Spring 2020 to Spring 2021 I had the pleasure to be among the organizers of the virtual MaD+ seminar, which run during the COVID19 pandemic.
 I have served as a reviewer for Annals of Statistics, Operations Research, Probability Theory and Related Fields, Mathematical Programming, SIAM Journal of Discrete Mathematics, SIAM Journal of Optimization, Combinatorica, IEEE Journal on Selected Areas in Information Theory, and for the conferences COLT, NeurIPS, FOCS, STOC, ITCS, ISIT, ICALP and SODA.
 I served in the Program Committee for COLT 2022 and COLT 2021.
Teaching
Instructor
 Fall 2020, DSGA 1005, NYU: Inference and Representation. (Coinstructor: Joan Bruna)
Codesigned and taught an advanced graduatelevel course on modern theoretical aspects of statistics and machine learning.
 Fall 2019, DSGA 1002 (NYU): Probability and Statistics for Data Science. (Coinstructor: Carlos FernandezGranda )
Introductory graduatelevel course on probability and statistics.
Teaching Assistant
 Spring 2017, 6.265/15.070 (MIT): Modern Discrete Probability. (Instructors: Guy Bresler, Yury Polyanskiy)
Advanced graduatelevel course on discrete probability and modern applications to computer science.
 Fall 2016, 6.436J/15.085J (MIT): Fundamentals of Probability. (Instructor: David Gamarnik )
Introductory graduatelevel course on probability.
Awards

Top 400 Reviewers Award for Neurips, 2019.

Honorable Mention for MIT Operations Research Center Best Student Paper Award, 2017
Paper: HighDimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transition.

Senior Scholarship from Trinity College, Cambridge University, 2014.

The Onassis Foundation Scholarship for Master Studies, 20132014

The Cambridge Home and European Scholarship Scheme (CHESS) award, 20132014.

International Mathematics Competition for University Students (IMC): First Prize, 2011, Second Prize, 2010.

South Eastern European Mathematics Olympiad for University Students (SEEMOUS): Gold Medal (first place), 2011, Silver Medal, 2010.