Derin sinir ağlarında aşırı öğrenmeyi engellemek için kullanılan kombinatöryel tasarımların etkisi

Combinatorial designs, as a mathematical subject, has deep connections with the fields such as combinatorics, graph theory, finite geometry, coding theory, cryptography and number theory and has attracted many researches from different fields. The combinatorial design found in the book Brhat Samhita, written by Varahamihira around 587 BC, was used to produce perfume by selecting 4 items from 16 different items with the help of a magic square. This is first known example of combinatorial designs. Combinatorial designs are used in widely known Kirkman's school girl problem. In the widely accepted view, modern study of block designs began in 1936 with the publication of an article by the statistician F. Yates. In this thesis, firstly, we provide an introduction about combinatorial designs and their properties. We will also introduce machine learning fundamentals that is required for our problem. Then, the problem that is being solved to generate BIBDs, exact covering problem will be mentioned. This NP-complete problem can be solved using Donald Knuth's Algorithm X. At this step, we will be explaining Algorithm X's algorithm and its implementation. Generated BIBDs will be used in neural networks, which have been built manually to prevent overfitting in machine learning. In this thesis, we show that it is possible to prevent overfitting in machine learning succesfully by using a known pattern (BIBDs) in dropout instead of randomness. Finally, we will share our results and compare them with widely known and used random dropout method. We will also compare our results with no-regularization applied models.