Browsing by Author "Akkaya, Deniz"

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1974 Kıbrıs Savaşı'nda Kıbrıslı bir mücahidin hikayesi
(Bilkent University, 2015) Akbaş, Ali Batuhan; Yüzer, Berkehan; Çelik, Damla; Akkaya, Deniz; Aydın, Doğukan
Open Access
Minimizers of sparsity regularized huber loss function
(Springer, 2020) Akkaya, Deniz; Pınar, Mustafa Ç.
We investigate the structure of the local and global minimizers of the Huber loss function regularized with a sparsity inducing L0 norm term. We characterize local minimizers and establish conditions that are necessary and sufficient for a local minimizer to be strict. A necessary condition is established for global minimizers, as well as non-emptiness of the set of global minimizers. The sparsity of minimizers is also studied by giving bounds on a regularization parameter controlling sparsity. Results are illustrated in numerical examples.
Open Access
Minimizers of sparsity regularized robust loss functions
(2021-06) Akkaya, Deniz
We study the structure of the local and global minimizers of the Huber loss and the sum of absolute deviations functions regularized with a sparsity penalty L0 norm term. We char-acterize local minimizers for both loss functions, and establish conditions that are necessary and sufficient for local minimizers to be strict. A necessary condition is established for global minimizers, as well as non-emptiness of the set of global minimizers. The sparsity of minimizers is also studied by giving bounds on a regularization parameter controlling sparsity. Results are illustrated in numerical examples.
Open Access
Subset based error recovery
(Elsevier BV, 2021-10-12) Ekmekcioğlu, Ömer; Akkaya, Deniz; Pınar, Mustafa Çelebi
We propose a data denoising method using Extreme Learning Machine (ELM) structure which allows us to use Johnson-Lindenstrauß Lemma (JL) for preserving Restricted Isometry Property (RIP) in order to give theoretical guarantees for recovery. Furthermore, we show that the method is equivalent to a robust two-layer ELM that implicitly benefits from the proposed denoising algorithm. Current robust ELM methods in the literature involve well-studied L1, L2 regularization techniques as well as the usage of the robust loss functions such as Huber Loss. We extend the recent analysis on the Robust Regression literature to be effectively used in more general, non-linear settings and to be compatible with any ML algorithm such as Neural Networks (NN). These methods are useful under the scenario where the observations suffer from the effect of heavy noise. We extend the usage of ELM as a general data denoising method independent of the ML algorithm. Tests for denoising and regularized ELM methods are conducted on both synthetic and real data. Our method performs better than its competitors for most of the scenarios, and successfully eliminates most of the noise.