MODELLING OF KERNEL MACHINES BY INFINITE AND SEMI-INFINITE PROGRAMMING

2009-06-03
Ozogur-Akyuz, S.
Weber, Gerhard Wilhelm
In Machine Learning (ML) algorithms, one of the crucial issues is the representation of the data. As the data become heterogeneous and large-scale, single kernel methods become insufficient to classify nonlinear data. The finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, we propose a novel method of "infinite" kernel combinations for learning problems with the help of infinite and semi-infinite programming regarding all elements in kernel space. Looking at all infinitesimally fine convex combinations of the kernels from the infinite kernel set, the margin is maximized subject to an infinite number of constraints with a compact index set and an additional (Riemann-Stieltjes) integral constraint due to the combinations. After a parametrization in the space of probability measures, it becomes semi-infinite. We analyze the regularity conditions which satisfy the Reduction Ansatz and discuss the type of distribution functions within the structure of the constraints and our bi-level optimization problem.

Suggestions

On numerical optimization theory of infinite kernel learning
Ozogur-Akyuz, S.; Weber, Gerhard Wilhelm (2010-10-01)
In Machine Learning algorithms, one of the crucial issues is the representation of the data. As the given data source become heterogeneous and the data are large-scale, multiple kernel methods help to classify "nonlinear data". Nevertheless, the finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, a novel method of "infinite" kernel combinations is proposed with the help of infinite and semi-infinite programming regarding all elements in kernel space. Look...
Adapted Infinite Kernel Learning by Multi-Local Algorithm
Akyuz, Sureyya Ozogur; Ustunkar, Gurkan; Weber, Gerhard Wilhelm (2016-05-01)
The interplay of machine learning (ML) and optimization methods is an emerging field of artificial intelligence. Both ML and optimization are concerned with modeling of systems related to real-world problems. Parameter selection for classification models is an important task for ML algorithms. In statistical learning theory, cross-validation (CV) which is the most well-known model selection method can be very time consuming for large data sets. One of the recent model selection techniques developed for supp...
Machine Learning over Encrypted Data With Fully Homomorphic Encyption
Kahya, Ayşegül; Cenk, Murat; Department of Cryptography (2022-8-26)
When machine learning algorithms train on a large data set, the result will be more realistic. Big data, distribution of big data, and the study of learning algorithms on distributed data are popular research topics of today. Encryption is a basic need, especially when storing data with a high degree of confidentiality, such as medical data. Classical encryption methods cannot meet this need because when texts encrypted with classical encryption methods are distributed, and the distributed data set is decry...
Optimization of well placement geothermal reservoirs using artificial intelligence
Akın, Serhat; Kök, Mustafa Verşan (2010-06-01)
This research proposes a framework for determining the optimum location of an injection well using an inference method, artificial neural networks and a search algorithm to create a search space and locate the global maxima. A complex carbonate geothermal reservoir (Kizildere Geothermal field, Turkey) production history is used to evaluate the proposed framework. Neural networks are used as a tool to replicate the behavior of commercial simulators, by capturing the response of the field given a limited numb...
Multiobjective evolutionary feature subset selection algorithm for binary classification
Deniz Kızılöz, Firdevsi Ayça; Coşar, Ahmet; Dökeroğlu, Tansel; Department of Computer Engineering (2016)
This thesis investigates the performance of multiobjective feature subset selection (FSS) algorithms combined with the state-of-the-art machine learning techniques for binary classification problem. Recent studies try to improve the accuracy of classification by including all of the features in the dataset, neglecting to determine the best performing subset of features. However, for some problems, the number of features may reach thousands, which will cause too much computation power to be consumed during t...
Citation Formats
S. Ozogur-Akyuz and G. W. Weber, “MODELLING OF KERNEL MACHINES BY INFINITE AND SEMI-INFINITE PROGRAMMING,” 2009, vol. 1159, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55001.