Online Learning of Single- and Multivalued Functions with an Infinite Mixture of Linear Experts

2013 ◽  
Vol 25 (11) ◽  
pp. 3044-3091 ◽  
Author(s):  
Bruno Damas ◽  
José Santos-Victor
Keyword(s):  
Function Approximation ◽  
Learning Algorithm ◽  
Target Function ◽  
Algorithm Performance ◽  
Learning Domains ◽  
Input Domain ◽  
Expert Input ◽  
Multivalued Functions ◽  
Fully Bayesian ◽  
Localized Learning

We present a supervised learning algorithm for estimation of generic input-output relations in a real-time, online fashion. The proposed method is based on a generalized expectation-maximization approach to fit an infinite mixture of linear experts (IMLE) to an online stream of data samples. This probabilistic model, while not fully Bayesian, can efficiently choose the number of experts that are allocated to the mixture, this way effectively controlling the complexity of the resulting model. The result is an incremental, online, and localized learning algorithm that performs nonlinear, multivariate regression on multivariate outputs by approximating the target function by a linear relation within each expert input domain and that can allocate new experts as needed. A distinctive feature of the proposed method is the ability to learn multivalued functions: one-to-many mappings that naturally arise in some robotic and computer vision learning domains, using an approach based on a Bayesian generative model for the predictions provided by each of the mixture experts. As a consequence, it is able to directly provide forward and inverse relations from the same learned mixture model. We conduct an extensive set of experiments to evaluate the proposed algorithm performance, and the results show that it can outperform state-of-the-art online function approximation algorithms in single-valued regression, while demonstrating good estimation capabilities in a multivalued function approximation context.

Machine Learning Algorithm Performance on the Lucata Computer

2020 ◽  
Author(s):  
Paul L. Springer ◽  
Thomas Schibler ◽  
Geraud Krawezik ◽  
Jack Lightholder ◽  
Peter M. Kogge
Keyword(s):  
Machine Learning ◽  
Learning Algorithm ◽  
Machine Learning Algorithm ◽  
Algorithm Performance

Convergence analysis of distributed multi-penalty regularized pairwise learning

2019 ◽  
Vol 18 (01) ◽  
pp. 109-127
Author(s):  
Ting Hu ◽  
Jun Fan ◽  
Dao-Hong Xiang
Keyword(s):  
Single Machine ◽  
Learning Algorithm ◽  
Target Function ◽  
Distributed Learning ◽  
Divide And Conquer ◽  
Learning Performance ◽  
Manifold Regularization ◽  
Optimal Learning ◽  
Pairwise Learning ◽  
Optimal Learning Rate

In this paper, we establish the error analysis for distributed pairwise learning with multi-penalty regularization, based on a divide-and-conquer strategy. We demonstrate with [Formula: see text]-error bound that the learning performance of this distributed learning scheme is as good as that of a single machine which could process the whole data. With semi-supervised data, we can relax the restriction of the number of local machines and enlarge the range of the target function to guarantee the optimal learning rate. As a concrete example, we show that the work in this paper can apply to the distributed pairwise learning algorithm with manifold regularization.

scholarly journals Visual Tracking Using Wang–Landau Reinforcement Sampler

2020 ◽  
Vol 10 (21) ◽  
pp. 7780
Author(s):  
Dokyeong Kwon ◽  
Junseok Kwon
Keyword(s):  
Visual Tracking ◽  
Deep Neural Network ◽  
Learning Algorithm ◽  
State Of The Art ◽  
Tracking System ◽  
Network Architectures ◽  
Tracking Accuracy ◽  
Algorithm Performance ◽  
Q Learning ◽  
Number Of Visits

In this study, we present a novel tracking system, in which the tracking accuracy can be considerably enhanced by state prediction. Accordingly, we present a new Q-learning-based reinforcement method, augmented by Wang–Landau sampling. In the proposed method, reinforcement learning is used to predict a target configuration for the subsequent frame, while Wang–Landau sampler balances the exploitation and exploration degrees of the prediction. Our method can adapt to control the randomness of policy, using statistics on the number of visits in a particular state. Thus, our method considerably enhances conventional Q-learning algorithm performance, which also enhances visual tracking performance. Numerical results demonstrate that our method substantially outperforms other state-of-the-art visual trackers and runs in realtime because our method contains no complicated deep neural network architectures.

AVERAGE CASE ANALYSIS OF AN HEBB-TYPE RULE THAT FINDS THE NETWORK CONNECTIVITY

1994 ◽  
Vol 05 (02) ◽  
pp. 115-122
Author(s):  
MOSTEFA GOLEA
Keyword(s):  
Network Architecture ◽  
Learning Algorithm ◽  
Target Function ◽  
Network Connectivity ◽  
Case Analysis ◽  
Average Case Analysis ◽  
Training Set ◽  
Average Case ◽  
Input Variables ◽  
Training Examples

We describe an Hebb-type algorithm for learning unions of nonoverlapping perceptrons with binary weights. Two perceptrons are said to be nonoverlapping if they do not share any input variables. The learning algorithm is able to find both the network architecture and the weight values necessary to represent the target function. Moreover, the algorithm is local, homogeneous, and simple enough to be biologically plausible. We investigate the average behavior of this algorithm as a function of the size of the training set. We find that, as the size of the training set increases, the hypothesis network built by the algorithm “converges” to the target network, both in terms of the number of perceptrons and the connectivity. Moreover, the generalization rate converges exponentially to perfect generalization as a function of the number of training examples. The analytic expressions are in excellent agreement with the numerical simulations. To our knowledge, this is the first average case analysis of an algorithm that finds both the weight values and the network connectivity.

A CONSTRUCTIVE NEURAL NETWORK ALGORITHM FOR FUNCTION APPROXIMATION USING LOCALLY FIT SIGMOIDS

1998 ◽  
Vol 07 (03) ◽  
pp. 373-398
Author(s):  
TIM DRAELOS ◽  
DON HUSH
Keyword(s):  
Neural Network ◽  
Function Approximation ◽  
Piecewise Linear ◽  
Target Function ◽  
Approximation Problem ◽  
Sigmoidal Functions ◽  
Network Algorithm ◽  
Neural Network Algorithm ◽  
Training Error ◽  
Hidden Layer

A study of the function approximation capabilities of single hidden layer neural networks strongly motivates the investigation of constructive learning techniques as a means of realizing established error bounds. Learning characteristics employed by constructive algorithms provide ideas for development of new algorithms applicable to the function approximation problem. In addition, constructive techniques offer efficient methods for network construction and weight determination. The development of a novel neural network algorithm, the Constructive Locally Fit Sigmoids (CLFS) function approximation algorithm, is presented in detail. Basis functions of global extent (piecewise linear sigmoidal functions) are locally fit to the target function, resulting in a pool of candidate hidden layer nodes from which a function approximation is obtained. This algorithm provides a methodology of selecting nodes in a meaningful way from the infinite set of possibilities and synthesizes an n node single hidden layer network with empirical and analytical results that strongly indicate an O(1/n) mean squared training error bound under certain assumptions. The algorithm operates in polynomial time in the number of network nodes and the input dimension. Empirical results demonstrate its effectiveness on several multidimensional function approximate problems relative to contemporary constructive and nonconstructive algorithms.

GENERATING BALANCED LEARNING AND TEST SETS FOR FUNCTION APPROXIMATION PROBLEMS

2011 ◽  
Vol 21 (03) ◽  
pp. 247-263 ◽  
Author(s):  
J. P. FLORIDO ◽  
H. POMARES ◽  
I. ROJAS
Keyword(s):  
Function Approximation ◽  
Nearest Neighbor ◽  
Learning Algorithm ◽  
Original Data ◽  
Input Output ◽  
Output Data ◽  
Data Set ◽  
Out Of Sample ◽  
Test Sets ◽  
Approximation Problems

In function approximation problems, one of the most common ways to evaluate a learning algorithm consists in partitioning the original data set (input/output data) into two sets: learning, used for building models, and test, applied for genuine out-of-sample evaluation. When the partition into learning and test sets does not take into account the variability and geometry of the original data, it might lead to non-balanced and unrepresentative learning and test sets and, thus, to wrong conclusions in the accuracy of the learning algorithm. How the partitioning is made is therefore a key issue and becomes more important when the data set is small due to the need of reducing the pessimistic effects caused by the removal of instances from the original data set. Thus, in this work, we propose a deterministic data mining approach for a distribution of a data set (input/output data) into two representative and balanced sets of roughly equal size taking the variability of the data set into consideration with the purpose of allowing both a fair evaluation of learning's accuracy and to make reproducible machine learning experiments usually based on random distributions. The sets are generated using a combination of a clustering procedure, especially suited for function approximation problems, and a distribution algorithm which distributes the data set into two sets within each cluster based on a nearest-neighbor approach. In the experiments section, the performance of the proposed methodology is reported in a variety of situations through an ANOVA-based statistical study of the results.

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