Towards the Understanding of Kernel and Neural Learning Methods via Information-Theoretic Learning (ITL)

Dear Colleagues,

Kernel methods and neural networks have achieved great popularity as tools in pattern recognition and machine learning for the identification of nonlinear systems. The kernel function is a very flexible container under which to express knowledge about the problem as well as to capture the meaningful relations in input space. The choice of a proper kernel for a given problem is both an open issue and an appealing chance to boost research. Kernel methods are single-layer machines and usually involve solving a tractable convex problem. Contrary to neural models, they are able to handle nonvectorial data directly, leading to a higher (input) expressive power.

On the other hand, multilayer neural networks have experienced a rebirth in the data analysis field, displaying impressive results, extending even to classical artificial intelligence domains such as game playing, computer vision, natural language, and speech processing. The versatility of such methods has led deep (semi)-parametric models to overtake well-established methods like classical statistical techniques.

In this Special Issue, we aim to bring together contributions towards the understanding of such single and deep structures from the analysis of their information content, as well as contributions that apply or analyze such structures from inferential, probabilistic, or information-theoretic points of view. An additional natural field of research is given by their hybridization, which can be done in many fruitful ways. Many ideas from the deep learning field can be transferred to the kernel method framework and vice versa.

Of particular interest are works oriented towards increasing our current understanding on the following topics:

• Analysis of single or deep learning structures from an information-theoretic point of view;
• Links or dualities between ITL methods and kernel or neuronal methods;
• Characterization of the learning process from an information-theoretic point of view;
• Use of ITL methods to analyze the implications of the kernel or neuron model for the success of learning methods;
• Links between kernel or neuron model design and ITL methods for special or new application domains;
• New ideas to bridge the gap between the fields of deep and kernel learning;
• New ideas or tools to increase the understanding of their respective weak and strong points.

The scope of the contributions is rather broad, including theoretical studies and practical applications to any kind of machine learning or statistical task, such as regression, classification, system identification, unsupervised learning, density estimation, clustering, etc.

Prof. Dr. Lluís A. Belanche-Muñoz
Dr. Bruno Ordozgoiti-Rubio
Guest Editors

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