A Comprehensive Approach to Universal Piecewise Nonlinear Regression Based on Trees

Cataloged from PDF version of article.In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We use a tree notion in order to partition the space of regressors in a nested structure. The introduced algorithms adapt not only their regression functions but also the complete tree structure while achieving the performance of the “best” linear mixture of a doubly exponential number of partitions, with a computational complexity only polynomial in the number of nodes of the tree. While constructing these algorithms, we also avoid using any artificial “weighting” of models (with highly data dependent parameters) and, instead, directly minimize the final regression error, which is the ultimate performance goal. The introduced methods are generic such that they can readily incorporate different tree construction methods such as random trees in their framework and can use different regressor or partitioning functions as demonstrated in the paper

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

Crop Yield Prediction Using Deep Neural Networks

Crop yield is a highly complex trait determined by multiple factors such as genotype, environment, and their interactions. Accurate yield prediction requires fundamental understanding of the functional relationship between yield and these interactive factors, and to reveal such relationship requires both comprehensive datasets and powerful algorithms. In the 2018 Syngenta Crop Challenge, Syngenta released several large datasets that recorded the genotype and yield performances of 2,267 maize hybrids planted in 2,247 locations between 2008 and 2016 and asked participants to predict the yield performance in 2017. As one of the winning teams, we designed a deep neural network (DNN) approach that took advantage of state-of-the-art modeling and solution techniques. Our model was found to have a superior prediction accuracy, with a root-mean-square-error (RMSE) being 12% of the average yield and 50% of the standard deviation for the validation dataset using predicted weather data. With perfect weather data, the RMSE would be reduced to 11% of the average yield and 46% of the standard deviation. We also performed feature selection based on the trained DNN model, which successfully decreased the dimension of the input space without significant drop in the prediction accuracy. Our computational results suggested that this model significantly outperformed other popular methods such as Lasso, shallow neural networks (SNN), and regression tree (RT). The results also revealed that environmental factors had a greater effect on the crop yield than genotype.Comment: 9 pages, Presented at 2018 INFORMS Conference on Business Analytics and Operations Research (Baltimore, MD, USA). One of the winning solutions to the 2018 Syngenta Crop Challeng

From patterned response dependency to structured covariate dependency: categorical-pattern-matching

Data generated from a system of interest typically consists of measurements from an ensemble of subjects across multiple response and covariate features, and is naturally represented by one response-matrix against one covariate-matrix. Likely each of these two matrices simultaneously embraces heterogeneous data types: continuous, discrete and categorical. Here a matrix is used as a practical platform to ideally keep hidden dependency among/between subjects and features intact on its lattice. Response and covariate dependency is individually computed and expressed through mutliscale blocks via a newly developed computing paradigm named Data Mechanics. We propose a categorical pattern matching approach to establish causal linkages in a form of information flows from patterned response dependency to structured covariate dependency. The strength of an information flow is evaluated by applying the combinatorial information theory. This unified platform for system knowledge discovery is illustrated through five data sets. In each illustrative case, an information flow is demonstrated as an organization of discovered knowledge loci via emergent visible and readable heterogeneity. This unified approach fundamentally resolves many long standing issues, including statistical modeling, multiple response, renormalization and feature selections, in data analysis, but without involving man-made structures and distribution assumptions. The results reported here enhance the idea that linking patterns of response dependency to structures of covariate dependency is the true philosophical foundation underlying data-driven computing and learning in sciences.Comment: 32 pages, 10 figures, 3 box picture

Kernel methods in machine learning

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org