Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Geometry and Expressive Power of Conditional Restricted Boltzmann Machines

Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parametrized by interaction weights and biases. We address the representational power of these models, proving results their ability to represent conditional Markov random fields and conditional distributions with restricted supports, the minimal size of universal approximators, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional probability models, which allow us to improve the results that can be derived from existing work on restricted Boltzmann machine probability models.Comment: 30 pages, 5 figures, 1 algorith

Fast and deep deformation approximations

Character rigs are procedural systems that compute the shape of an animated character for a given pose. They can be highly complex and must account for bulges, wrinkles, and other aspects of a character's appearance. When comparing film-quality character rigs with those designed for real-time applications, there is typically a substantial and readily apparent difference in the quality of the mesh deformations. Real-time rigs are limited by a computational budget and often trade realism for performance. Rigs for film do not have this same limitation, and character riggers can make the rig as complicated as necessary to achieve realistic deformations. However, increasing the rig complexity slows rig evaluation, and the animators working with it can become less efficient and may experience frustration. In this paper, we present a method to reduce the time required to compute mesh deformations for film-quality rigs, allowing better interactivity during animation authoring and use in real-time games and applications. Our approach learns the deformations from an existing rig by splitting the mesh deformation into linear and nonlinear portions. The linear deformations are computed directly from the transformations of the rig's underlying skeleton. We use deep learning methods to approximate the remaining nonlinear portion. In the examples we show from production rigs used to animate lead characters, our approach reduces the computational time spent on evaluating deformations by a factor of 5×-10×. This significant savings allows us to run the complex, film-quality rigs in real-time even when using a CPU-only implementation on a mobile device

Deep Reinforcement Learning for Real-Time Optimization in NB-IoT Networks

NarrowBand-Internet of Things (NB-IoT) is an emerging cellular-based technology that offers a range of flexible configurations for massive IoT radio access from groups of devices with heterogeneous requirements. A configuration specifies the amount of radio resource allocated to each group of devices for random access and for data transmission. Assuming no knowledge of the traffic statistics, there exists an important challenge in "how to determine the configuration that maximizes the long-term average number of served IoT devices at each Transmission Time Interval (TTI) in an online fashion". Given the complexity of searching for optimal configuration, we first develop real-time configuration selection based on the tabular Q-learning (tabular-Q), the Linear Approximation based Q-learning (LA-Q), and the Deep Neural Network based Q-learning (DQN) in the single-parameter single-group scenario. Our results show that the proposed reinforcement learning based approaches considerably outperform the conventional heuristic approaches based on load estimation (LE-URC) in terms of the number of served IoT devices. This result also indicates that LA-Q and DQN can be good alternatives for tabular-Q to achieve almost the same performance with much less training time. We further advance LA-Q and DQN via Actions Aggregation (AA-LA-Q and AA-DQN) and via Cooperative Multi-Agent learning (CMA-DQN) for the multi-parameter multi-group scenario, thereby solve the problem that Q-learning agents do not converge in high-dimensional configurations. In this scenario, the superiority of the proposed Q-learning approaches over the conventional LE-URC approach significantly improves with the increase of configuration dimensions, and the CMA-DQN approach outperforms the other approaches in both throughput and training efficiency

On the Distribution of the Fourier Spectrum of Halfspaces

Bourgain showed that any noise stable Boolean function $f$ can be well-approximated by a junta. In this note we give an exponential sharpening of the parameters of Bourgain's result under the additional assumption that $f$ is a halfspace

Self-organizing nonlinear output (SONO): A neural network suitable for cloud patch-based rainfall estimation at small scales

Accurate measurement of rainfall distribution at various spatial and temporal scales is crucial for hydrological modeling and water resources management. In the literature of satellite rainfall estimation, many efforts have been made to calibrate a statistical relationship (including threshold, linear, or nonlinear) between cloud infrared (IR) brightness temperatures and surface rain rates (RR). In this study, an automated neural network for cloud patch-based rainfall estimation, entitled self-organizing nonlinear output (SONO) model, is developed to account for the high variability of cloud-rainfall processes at geostationary scales (i.e., 4 km and every 30 min). Instead of calibrating only one IR-RR function for all clouds the SONO classifies varied cloud patches into different clusters and then searches a nonlinear IR-RR mapping function for each cluster. This designed feature enables SONO to generate various rain rates at a given brightness temperature and variable rain/no-rain IR thresholds for different cloud types, which overcomes the one-to-one mapping limitation of a single statistical IR-RR function for the full spectrum of cloud-rainfall conditions. In addition, the computational and modeling strengths of neural network enable SONO to cope with the nonlinearity of cloud-rainfall relationships by fusing multisource data sets. Evaluated at various temporal and spatial scales, SONO shows improvements of estimation accuracy, both in rain intensity and in detection of rain/no-rain pixels. Further examination of the SONO adaptability demonstrates its potentiality as an operational satellite rainfall estimation system that uses the passive microwave rainfall observations from low-orbiting satellites to adjust the IR-based rainfall estimates at the resolution of geostationary satellites. Copyright 2005 by the American Geophysical Union