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Register a new userOnline Learning with Radial Basis Function Networks
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Added by
Gabriel Borrageiro Mr
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We investigate the benefits of feature selection, nonlinear modelling and online learning when forecasting in financial time series. We consider the sequential and continual learning sub-genres of online learning. The experiments we conduct show that there is a benefit to online transfer learning, in the form of radial basis function networks, beyond the sequential updating of recursive least-squares models. We show that the radial basis function networks, which make use of clustering algorithms to construct a kernel Gram matrix, are more beneficial than treating each training vector as separate basis functions, as occurs with kernel Ridge regression. We demonstrate quantitative procedures to determine the very structure of the radial basis function networks. Finally, we conduct experiments on the log returns of financial time series and show that the online learning models, particularly the radial basis function networks, are able to outperform a random walk baseline, whereas the offline learning models struggle to do so.
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Radial basis function (RBF) network is a third layered neural network that is widely used in function approximation and data classification. Here we propose a quantum model of the RBF network. Similar to the classical case, we still use the radial basis functions as the activation functions. Quantum linear algebraic techniques and coherent states can be applied to implement these functions. Differently, we define the state of the weight as a tensor product of single-qubit states. This gives a simple approach to implement the quantum RBF network in the quantum circuits. Theoretically, we prove that the training is almost quadratic faster than the classical one. Numerically, we demonstrate that the quantum RBF network can solve binary classification problems as good as the classical RBF network. While the time used for training is much shorter.
Topology optimization by optimally distributing materials in a given domain requires gradient-free optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNNs prediction of the global optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.
We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several mode
Emotion recognition (ER) from facial images is one of the landmark tasks in affective computing with major developments in the last decade. Initial efforts on ER relied on handcrafted features that were used to characterize facial images and then feed to standard predictive models. Recent methodologies comprise end-to-end trainable deep learning methods that simultaneously learn both, features and predictive model. Perhaps the most successful models are based on convolutional neural networks (CNNs). While these models have excelled at this task, they still fail at capturing local patterns that could emerge in the learning process. We hypothesize these patterns could be captured by variants based on locally weighted learning. Specifically, in this paper we propose a CNN based architecture enhanced with multiple branches formed by radial basis function (RBF) units that aims at exploiting local information at the final stage of the learning process. Intuitively, these RBF units capture local patterns shared by similar instances using an intermediate representation, then the outputs of the RBFs are feed to a softmax layer that exploits this information to improve the predictive performance of the model. This feature could be particularly advantageous in ER as cultural / ethnicity differences may be identified by the local units. We evaluate the proposed method in several ER datasets and show the proposed methodology achieves state-of-the-art in some of them, even when we adopt a pre-trained VGG-Face model as backbone. We show it is the incorporation of local information what makes the proposed model competitive.
The radial basis function (RBF) approach has been used to improve the mass predictions of nuclear models. However, systematic deviations exist between the improved masses and the experimental data for nuclei with different odd-even parities of ($Z$, $N$), i.e., the (even $Z$, even $N$), (even $Z$, odd $N$), (odd $Z$, even $N$), and (odd $Z$, odd $N$). By separately training the RBF for these four different groups, it is found that the systematic odd-even deviations can be cured in a large extend and the predictive power of nuclear mass models can thus be further improved. Moreover, this new approach can better reproduce the single-nucleon separation energies. Based on the latest version of Weizsacker-Skyrme model WS4, the root-mean-square deviation of the improved masses with respect to known data falls to $135$ keV, approaching the chaos-related unpredictability limit ($sim 100$ keV).
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