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CURRENT RESEARCH
Advanced Deep Learning: Analytical, Fuzzy Theoretic, and Nonparametric
In the pursuit of machine intelligence, "Learning", i.e. computer algorithms improving automatically with the experience, is central to our research focus. In today’s era of Information Technology, there is an abundance of data being generated by different sources. The development of computations based methodologies for learning data representation remains as our research aim. The data inherit uncertainties from their sources and thus prompting the researchers to apply probability and fuzzy theories in machine learning as means to handle uncertainties.
Probabilistic directed generative models, being potentially capable of uncertainty assessment, have been widely applied in machine learning. The data-driven parametric models have also received the most attention of the fuzzy/probabilistic machine learning researchers. However, the parametric approach suffers from the issues arising from a lack of knowledge regarding the optimal model structure. In contrast, the nonparametric approach facilitates the model structure to grow as necessary to fit the complexity of the data. Despite numerous research studies on deep learning, some of the fundamental issues that remained unaddressed are:
We introduce a novel approach to deep learning that not only addresses the aforementioned issues, but also facilitates to design fast, competent, and robust learning algorithms. A mathematical theory is provided to facilitate the application of deep models in prediction, filtering, and classification problems. The theoretical developments are supported by experiments on problems related to real-world applications.
Probabilistic directed generative models, being potentially capable of uncertainty assessment, have been widely applied in machine learning. The data-driven parametric models have also received the most attention of the fuzzy/probabilistic machine learning researchers. However, the parametric approach suffers from the issues arising from a lack of knowledge regarding the optimal model structure. In contrast, the nonparametric approach facilitates the model structure to grow as necessary to fit the complexity of the data. Despite numerous research studies on deep learning, some of the fundamental issues that remained unaddressed are:
- A mathematical theory is not available to study the propagation of non-statistical-uncertainty across the layers of a deep model by means of fuzzy membership functions.
- There does not exist an analytical solution to the learning of a deep model where fuzzy membership functions quantify the uncertainties on variables and nonlinear functions associated to layers of the deep model.
- The gradient-descent based learning of deep models requires a large time as a large number of model parameters are being estimated using ad-hoc iterative numerical algorithms.
- The state-of-art, in the context of nonparametric deep learning, doesn’t provide a fuzzy theoretic framework as elegant and powerful as the Bayesian framework in statistics and machine learning.
We introduce a novel approach to deep learning that not only addresses the aforementioned issues, but also facilitates to design fast, competent, and robust learning algorithms. A mathematical theory is provided to facilitate the application of deep models in prediction, filtering, and classification problems. The theoretical developments are supported by experiments on problems related to real-world applications.
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Competitive PerformanceA complete analytical solution to the learning of a deep model, referred to as deep-fuzzy-mapping, is provided. As the analytical approach allows to mathematically take into the uncertainties on variables and nonlinear functions associated to the deep model, a fast learning algorithm can be designed resulting in the building of robust deep models that should perform remarkable better than the classical methods such as convolutional neural networks.
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