My principal research interests are in the area of data processing, algorithm development, and machine learning. In choosing research topics, I like to investigate theoretical problems that are motivated by and abstracted from real-world practices, and to work on applied topics that can have a positive and far-reaching impact on society. The overall themes of my research are learning sparse signal representations, convex and nonconvex optimization problems and, statistical inference problems with practical applications, developing tractable learning algorithms for non-convex optimization problems encountered in machine learning and deep learning.

Exact dynamics of learning algorithms for large-scale non-convex optimization problems

We are experiencing a data-driven revolution at the moment with data being collected at an unprecedented rate. In particular, there is an increasing excitement toward autonomous systems with learning capabilities. Several data-driven applications have already shown significant practical benefit revealing the power of having access to more data, e.g., health care systems, self-driving cars, instant machine translation, and recommendation systems. However, large acceptance of such systems heavily depends on their stability, tractability and reproducibility, where current applications fall inadequate in providing such features. The scale and complexity of modern datasets often render classical data processing techniques infeasible, and therefore, several new algorithms are required to address new technical challenges associated with the nature of the data.

This project focuses on developing efficient and tractable solutions for large-scale learning problems encountered in machine learning and signal processing. Apart from theoretical aspects, the project bears specific goals targeted to applications in principal subspace estimation, low-rank matrix factorization, tensor decomposition and deep learning for largescale systems. Specifically, this novel approach brings together several attractive features:

• The emerging concept of online-learning will be adapted to a distributed setting across a decentralized network topology.
• The exact dynamics of the algorithms will be extracted by a stochastic process analysis method; which current state-of-the-art methods are not able to deliver.
• Studying the extracted dynamics, the learning capabilities and performances of large-scale systems will be improved to match the current needs and challenges of the modern data-driven applications.

Keywords: Data processing, machine learning, non-convex optimization, Markov processes, online-learning, distributed-learning, deep-learning, neural network, artificial intelligence

This project is funded by the Scientific and Technological Research Council of Turkey – TÜBİTAK 2232 International Fellowship for Outstanding Researchers.