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The prediction has historically been a topic which is of great importance and will not lose interest in the future. The prediction was made with primitive methods in the past. However, with the introduction of large scale data to our lives, primitive methods have left its place to the machine learning algorithms. Prediction methods with machine learning are split into two sub-problems as classification and regression. In this thesis, three novel machine learning methods have been developed which target different problems that can work with large scale data. The proposed methods are mainly based on mathematical programming and optimization. The first method is ``Incremental Conic Functions (ICF) Algorithm for Large Scale Classification Problems'' which applies an efficient data reduction method to the data. Furthermore, it does not require to solve a linear programming (LP) problem in some cases. The second method is ``One-Class Polyhedral Conic Functions (O-PCF) Algorithm for One-Class Classification.'' This method can classify data points and detect outliers when the data is only available from one class. The last method is developed for ``clusterwise linear regression'' when the data size is large. These methods are tested on real-life datasets and compared with the well-known methods in the literature. It is possible to apply these three methods to real-life problems because of the short training and test times.