The objective of this paper is to define an effective strategy for building an ensemble of Genetic Programming (GP) models. Ensemble methods are widely used in machine learning due to their features: they average out biases, they reduce the variance and they usually generalize better than single models. Despite these advantages, building ensemble of GP models is not a well-developed topic in the evolutionary computation community. To fill this gap, we propose a strategy that blends individuals produced by standard syntax-based GP and individuals produced by geometric semantic genetic programming, one of the newest semantics-based method developed in GP. In fact, recent literature showed that combining syntax and semantics could improve the generalization ability of a GP model. Additionally, to improve the diversity of the GP models used to build up the ensemble, we propose different pruning criteria that are based on correlation and entropy, a commonly used measure in information theory. Experimental results,obtained over different complex problems, suggest that the pruning criteria based on correlation and entropy could be effective in improving the generalization ability of the ensemble model and in reducing the computational burden required to build it.
With respect to ensembles of regression models, a quite recent contribution was proposed in @cite_24 . The idea explored by the authors was to generate several regression models by concurrently executing multiple independent instances of a GP and, subsequently to analyze several strategies for fusing predictions from the multiple regression models. The study considered only small datasets due to memory constraints, but authors were able to draw interesting conclusions about the suitability of their approach in producing accurate predictions. Our study will differ from the one described in @cite_24 in several ways: we do not put any constraint on the size of the datasets, we will consider models produced by different GP algorithms (blend of STGP and GSGP) and we define and use different similarity-based criteria that, by taking into account the information related to all the populations evolved, aim at improving the generalization ability of the final ensemble as well as reducing the computational effort. Hence, in the experiments described in this contribution and as explained in , the populations evolved are not independent of each other.
@cite_24
2000292092 2491694318 2094248329 1599871777
Many machine learning and pattern classification methods have been applied to the diagnosis of Alzheimer’s disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI). Recently, rather than predicting categorical variables as in classification, several pattern regression methods have also been used to estimate continuous clinical variables from brain images. However, most existing regression methods focus on estimating multiple clinical variables separately and thus cannot utilize the intrinsic useful correlation information among different clinical variables. On the other hand, in those regression methods, only a single modality of data (usually only the structural MRI) is often used, without considering the complementary information that can be provided by different modalities. In this paper, we propose a general methodology, namely Multi-Modal Multi-Task (M3T) learning, to jointly predict multiple variables from multi-modal data. Here, the variables include not only the clinical variables used for regression but also the categorical variable used for classification, with different tasks corresponding to prediction of different variables. Specifically, our method contains two key components, i.e., (1) a multi-task feature selection which selects the common subset of relevant features for multiple variables from each modality, and (2) a multi-modal support vector machine which fuses the above-selected features from all modalities to predict multiple (regression and classification) variables. To validate our method, we perform two sets of experiments on ADNI baseline MRI, FDG-PET, and cerebrospinal fluid (CSF) data from 45 AD patients, 91 MCI patients, and 50 healthy controls (HC). In the first set of experiments, we estimate two clinical variables such as Mini Mental State Examination (MMSE) and Alzheimer’s Disease Assessment Scale - Cognitive Subscale (ADAS-Cog), as well as one categorical variable (with value of ‘AD’, ‘MCI’ or ‘HC’), from the baseline MRI, FDG-PET, and CSF data. In the second set of experiments, we predict the 2-year changes of MMSE and ADAS-Cog scores and also the conversion of MCI to AD from the baseline MRI, FDG-PET, and CSF data. The results on both sets of experiments demonstrate that our proposed M3T learning scheme can achieve better performance on both regression and classification tasks than the conventional learning methods. We study resource-limited online learning, motivated by the problem of conditional-branch outcome prediction in computer architecture. In particular, we consider (parallel) time and space-efficient ensemble learners for online settings, empirically demonstrating benefits similar to those shown previously for offline ensembles. Our learning algorithms are inspired by the previously published “boosting by filtering” framework as well as the offline Arc-x4 boosting-style algorithm. We train ensembles of online decision trees using a novel variant of the ID4 online decision-tree algorithm as the base learner, and show empirical results for both boosting and bagging-style online ensemble methods. Our results evaluate these methods on both our branch prediction domain and online variants of three familiar machine-learning benchmarks. Our data justifies three key claims. First, we show empirically that our extensions to ID4 significantly improve performance for single trees and additionally are critical to achieving performance gains in tree ensembles. Second, our results indicate significant improvements in predictive accuracy with ensemble size for the boosting-style algorithm. The bagging algorithms we tried showed poor performance relative to the boosting-style algorithm (but still improve upon individual base learners). Third, we show that ensembles of small trees are often able to outperform large single trees with the same number of nodes (and similarly outperform smaller ensembles of larger trees that use the same total number of nodes). This makes online boosting particularly useful in domains such as branch prediction with tight space restrictions (i.e., the available real-estate on a microprocessor chip). A hierarchical Bayes Gaussian Mixture Model (HBGMM) with adaptive sparsity is proposed.We impose our hierarchical Bayes prior on the entries of precision matrices in GMM to encourage sparsity.Our adaptive sparsity can reduce the dimensionality of the parameters in GMM to be estimated.Our HBGMM method does not involve any hyperparameters to be estimated, i.e., it is hyperparameter-free. Gaussian Mixture Model (GMM) has been widely used in statistics for its great flexibility. However, parameter estimation for GMM with high dimensionality is a challenge because of the large number of parameters and the lack of observation data. In this paper, we propose an effective method named hierarchical Bayes based Adaptive Sparsity in Gaussian Mixture Model (ASGMM) to estimate the parameters in a GMM by incorporating a two-layer hierarchical Bayes based adaptive sparsity prior. The prior we impose on the precision matrices can encourage sparsity and hence reduce the dimensionality of the parameters to be estimated. In contrast to the l 1 -norm penalty or Laplace prior, our approach does not involve any hyperparameters that must be tuned, and the sparsity adapts to the observation data. The proposed method is achieved by three steps: first, we formulate an adaptive hierarchical Bayes model of the precision matrices in the GMM with a Jeffrey's noninformative hyperprior, which expresses scale-invariance and, more importantly, is hyperparameter-free and unbiased. Second, we perform a Cholesky decomposition on the precision matrices to impose the positive definite property. Finally, we exploit the expectation maximization (EM) algorithm to obtain the final estimated parameters in the GMM. Experimental results on synthetic and real-world datasets demonstrate that ASGMM cannot only adapt the sparsity of high-dimensional data with small estimated error, but also achieve better clustering performance comparing with several classical methods. Breiman (2001a,b) has recently developed an ensemble classification and regression approach that displayed outstanding performance with regard prediction error on a suite of benchmark datasets. As the base constituents of the ensemble are tree-structured predictors, and since each of these is constructed using an injection of randomness, the method is called ‘random forests’. That the exceptional performance is attained with seemingly only a single tuning parameter, to which sensitivity is minimal, makes the methodology all the more remarkable. The individual trees comprising the forest are all grown to maximal depth. While this helps with regard bias, there is the familiar tradeoff with variance. However, these variability concerns were potentially obscured because of an interesting feature of those benchmarking datasets extracted from the UCI machine learning repository for testing: all these datasets are hard to overfit using tree-structured methods. This raises issues about the scope of the repository. With this as motivation, and coupled with experience from boosting methods, we revisit the formulation of random forests and investigate prediction performance on real-world and simulated datasets for which maximally sized trees do overfit. These explorations reveal that gains can be realized by additional tuning to regulate tree size via limiting the number of splits and or the size of nodes for which splitting is allowed. Nonetheless, even in these settings, good performance for random forests can be attained by using larger (than default) primary tuning parameter values.