## Mohamad Dia## Biography
## Research Interests
My research interests lie at the interface between statistical inference, machine learning, coding theory, and statistical physics of spin glasses.
I was involved in developing new data science tools and applying deep learning techniques for the “Euclid” space mission project in order to
investigate dark matter. My PhD research at EPFL's Information Processing Group (IPG) was principally focused on inference and learning over graphical models,
which includes problems from error-correcting codes, compressed sensing, and community detection.
My work spans both the practical and theoretical aspects of such problems. This covers the design and analysis of optimal low-complexity message-passing algorithms,
the application of statistical physics methods, the derivation of information theoretic limits, and the development of rigorous proof techniques.
## Astronomical Data Processing - Euclid Space MissionThe stunning discovery of the accelerated expansion rate of the universe in the late 1990s, as opposed to the former prevailing belief on the decelerated expansion, has changed the modern perception of the cosmos and presented several challenges in astrophysics. Such acceleration can be attributed to the presence of a mysterious invisible “dark energy” inducing a repulsive gravitational force; so that Einstein's general relativity continues to hold on the cosmological scale. “Euclid” is the first satellite, scheduled for launch by the ESA (European Space Agency), to map the geometry of dark energy and dark matter. It will provide images of 2 billion galaxies with unprecedented quality. The Euclid consortium includes 1400 scientists across Europe and the USA. My work in the astroinformatics group covers the crucial pre-launch period (2017-2020) with a focus on software and algorithmic development for the scientific ground-segment activities. My research within Euclid revolves around solving inverse problems in order to investigate dark matter using high-spatial resolution imagery. This includes the development of new data science tools and the application of deep learning techniques to find patterns in cosmic structure. ## Statistical Physics - Phase Transitions and Rigorous PredictionsOver the last century, statistical physics techniques have developed with the aim to describe the behaviour of systems with a large number of degrees of freedom and to give predictions which would be very difficult to guess. One of these techniques is the Replica method, which was conjectured to predict the asymptotic mutual information of a random graphical model and to detect the algorithmic and optimal phase transitions (see figure below). We prove that the Replica formula is exact in many problems that have been studied in the context of error correcting codes, compressed sensing and machine learning (mainly the random linear estimation and low-rank matrix factorization problems). Hence, we are able to come up with rigorous information-theoretical limits for many open problems. Moreover, we prove that, for a large set of parameters, an efficient iterative algorithm called Approximate Message-Passing (AMP) is optimal in the Bayesian setting. Our proof technique has an interest of its own as it is transposable to various inference problems and it exploits three essential ingredients: the Guerra-interpolation method introduced in statistical physics, the analysis of the AMP algorithm through State Evolution (SE) and the theory of spatial coupling and threshold saturation in coding. ## Spatial Coupling - Algorithmic Tools and Proof TechniquesSpatial coupling is a powerful graphical representation used to improve the algorithmic message-passing performance. It is the underlying principle behind the threshold saturation phenomenon (where the algoritmic threshold achieves the optimal one). Such representation was successfully applied to multiple graphical models ranging from LDPC codes to compressed sensing. Spatial coupling can be represented via a graphical model starting from the original factor graph. Assume that we have a factor graph of size \(N\). We take several instances of this factor graph and we place them next to each other on a chain of length \(Γ\). We then locally couple the underlying factor graphs with a coupling window \(w\) to obtain a bigger factor graph of size \(Γ × N\) (see figure below). In the resulting factor graph, each variable node is connected to the corresponding check nodes of the same underlying factor graph and to the check nodes of the neighboring factor graphs. This construction creates a spatial dimension, along the positions of the chain, that will help the algorithm. The second step in constructing efficient spatially coupled graphs is to introduce a seed at a certain position of the chain. This seed can be introduced as a side information which helps the algorithm at the boundaries and initiates a “wave” that propagates inwards and boosts the performance. Interestingly, spatial coupling can be used both as a “construction technique” to boost the algorithmic performance and as a “proof technique” to compute some information theoretic quantities. Therefore, even if the problem at hand does not provide the freedom of constructing a spatially coupled model in practice, one can still use spatial coupling for an auxiliary model. Intuitively speaking, since the low-complexity algorithm on the auxiliary model is optimal by the threshold saturation phenomenon, it is easier to compute the information theoretic quantities on that model and then apply them to the underlying model. ## Selected Publications## PhD ThesisHigh-Dimensional Inference on Dense Graphs with Applications to Coding Theory and Machine Learning , Mohamad Dia, EPFL, 2018. (The official EPFL Infoscience copy is available here.)
## ConferencesGalaxy Image Simulation Using Progressive GANs, Mohamad Dia, Elodie Savary, Martin Melchior, Frederic Courbin, in the Astronomical Data Analysis Software & Systems Conference (ADASS), October 2019. A Compressed Sensing Approach for Distribution Matching, Mohamad Dia, Vahid Aref, Laurent Schmalen, in Information Theory Proceedings (ISIT), 2018 IEEE International Symposium on, June 2018. Generalized Approximate Message-Passing Decoder for Universal Sparse Superposition Codes, Erdem Bıyık, Jean Barbier, Mohamad Dia, in Information Theory Proceedings (ISIT), 2017 IEEE International Symposium on, June 2017. Mutual Information for Symmetric Rank-One Matrix Estimation: A Proof of the Replica Formula, Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, Lenka Zdeborova, Advances in Neural Information Processing Systems 29 (NIPS 2016), December 2016. The Mutual Information in Random Linear Estimation, Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, in the 54th Annual Allerton Conference on Communication, Control, and Computing, September 2016. Threshold Saturation of Spatially Coupled Sparse Superposition Codes for All Memoryless Channels, Jean Barbier, Mohamad Dia, Nicolas Macris, in Information Theory Workshop (ITW), 2016 IEEE, September 2016. Proof of Threshold Saturation for Spatially Coupled Sparse Superposition Codes, Jean Barbier, Mohamad Dia, Nicolas Macris, in Information Theory Proceedings (ISIT), 2016 IEEE International Symposium on, July 2016. On the Design of Energy-Aware 3G/WiFi Heterogeneous Networks under Realistic Conditions, Sireen Taleb, Mohamad Dia, Jamal Farhat, Zaher Dawy, Hazem Hajj, Advanced Information Networking and Applications Workshops (WAINA), 2013 27th International Conference on, March 2013.
## JournalsRank-One Matrix Estimation: Analysis of Algorithmic and Information Theoretic Limits by the Spatial Coupling Method , Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Lenka Zdeborova, Submitted to Journal of Machine Learning Research, 2019. Universal Sparse Superposition Codes with Spatial Coupling and GAMP Decoding , Jean Barbier, Mohamad Dia, Nicolas Macris, IEEE Transactions on Information Theory, 2018. Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation, Jean Barbier, Nicolas Macris, Mohamad Dia, Florent Krzakala, IEEE Transactions on Information Theory, 2018.
Note: Authors are listed in alphabetical and/or affiliation order. |