The document summarizes research on heuristic search based stacking of classifiers. It discusses ensemble methods like bagging and boosting that combine multiple classifiers, and stacking which uses a meta-classifier to combine classifiers from different learning algorithms. The authors propose using genetic algorithms to optimize the combination of learning methods in a stacking system, selecting the ideal base classifiers and meta-classifier through heuristic search.
This document discusses maximum entropy models and their application to natural language processing tasks. It introduces maximum entropy modeling, describing how the approach works by choosing a probability distribution with maximum entropy subject to constraints from observed data. Training involves using algorithms like generalized iterative scaling to find optimal feature weights that satisfy the constraints. Maximum entropy models have been applied successfully to tasks like part-of-speech tagging, machine translation, and language modeling.
Considerate Approaches to ABC Model SelectionMichael Stumpf
The document discusses using approximate Bayesian computation (ABC) for model selection when directly evaluating likelihoods is computationally intractable, noting that ABC involves simulating data from models and comparing simulated and observed summary statistics, and that constructing minimally sufficient summary statistics is important for accurate ABC model selection.
The document discusses the principle of maximum entropy. It explains that maximum entropy is an approach for making probability assignments where the assigned probability distribution should have the largest entropy or uncertainty possible, subject to whatever information is known. It describes applications of maximum entropy modeling such as part-of-speech tagging and logistic regression. Maximum entropy and maximum likelihood methods are related as they both aim to make distributions as uniform as possible based on available information.
A Maximum Entropy Approach to the Loss Data Aggregation ProblemErika G. G.
This document discusses using a maximum entropy approach to model loss distributions for operational risk modeling. It begins by motivating the need to accurately model loss distributions given challenges with limited datasets, including heavy tails and dependence between risks. It then provides an overview of the loss distribution approach commonly used in operational risk modeling and its limitations. The document introduces the maximum entropy approach, which frames the problem as maximizing entropy subject to moment constraints. It discusses using the Laplace transform of loss distributions to compress information into moments and how these can be estimated from sample data or fitted distributions to serve as constraints for the maximum entropy approach.
SemiBoost: Boosting for Semi-supervised Learningbutest
SemiBoost is a boosting algorithm for semi-supervised learning that utilizes both labeled and unlabeled data. It works by iteratively selecting the most confidently labeled unlabeled examples based on pairwise similarities, assigning labels, and training a classifier. The algorithm aims to minimize inconsistencies between labeled examples and unlabeled example labels implied by similarities. It formulates the problem as optimizing an objective function balancing these inconsistencies. Experimental results show SemiBoost improves classification accuracy over other semi-supervised and supervised methods on benchmark datasets.
Meta-learning of exploration-exploitation strategies in reinforcement learningUniversité de Liège (ULg)
The document discusses meta-learning of exploration-exploitation strategies in reinforcement learning. It proposes learning exploration strategies rather than relying on predefined formulas. The approach involves defining training problems, candidate strategies, a performance criterion, and optimizing strategies on the training problems using an optimization tool. Simulation results show learned strategies outperform strategies based on predefined formulas when the test problems match the training problems. The document provides examples applying this approach to multi-armed bandits and tree search problems.
Learning for exploration-exploitation in reinforcement learning. The dusk of ...Université de Liège (ULg)
The document discusses reinforcement learning and the exploration-exploitation tradeoff that agents face. It proposes learning exploration-exploitation strategies rather than relying on predefined formulas. The approach defines training problems, candidate strategies parameterized by formulas, a performance criterion, and optimizes strategies on training problems using an estimation of distribution algorithm. Simulation results show learned strategies outperform strategies from common formulas on matching test problems.
Here a Review of the Combination of Machine Learning models from Bayesian Averaging, Committees to Boosting... Specifically An statistical analysis of Boosting is done
This document discusses maximum entropy models and their application to natural language processing tasks. It introduces maximum entropy modeling, describing how the approach works by choosing a probability distribution with maximum entropy subject to constraints from observed data. Training involves using algorithms like generalized iterative scaling to find optimal feature weights that satisfy the constraints. Maximum entropy models have been applied successfully to tasks like part-of-speech tagging, machine translation, and language modeling.
Considerate Approaches to ABC Model SelectionMichael Stumpf
The document discusses using approximate Bayesian computation (ABC) for model selection when directly evaluating likelihoods is computationally intractable, noting that ABC involves simulating data from models and comparing simulated and observed summary statistics, and that constructing minimally sufficient summary statistics is important for accurate ABC model selection.
The document discusses the principle of maximum entropy. It explains that maximum entropy is an approach for making probability assignments where the assigned probability distribution should have the largest entropy or uncertainty possible, subject to whatever information is known. It describes applications of maximum entropy modeling such as part-of-speech tagging and logistic regression. Maximum entropy and maximum likelihood methods are related as they both aim to make distributions as uniform as possible based on available information.
A Maximum Entropy Approach to the Loss Data Aggregation ProblemErika G. G.
This document discusses using a maximum entropy approach to model loss distributions for operational risk modeling. It begins by motivating the need to accurately model loss distributions given challenges with limited datasets, including heavy tails and dependence between risks. It then provides an overview of the loss distribution approach commonly used in operational risk modeling and its limitations. The document introduces the maximum entropy approach, which frames the problem as maximizing entropy subject to moment constraints. It discusses using the Laplace transform of loss distributions to compress information into moments and how these can be estimated from sample data or fitted distributions to serve as constraints for the maximum entropy approach.
SemiBoost: Boosting for Semi-supervised Learningbutest
SemiBoost is a boosting algorithm for semi-supervised learning that utilizes both labeled and unlabeled data. It works by iteratively selecting the most confidently labeled unlabeled examples based on pairwise similarities, assigning labels, and training a classifier. The algorithm aims to minimize inconsistencies between labeled examples and unlabeled example labels implied by similarities. It formulates the problem as optimizing an objective function balancing these inconsistencies. Experimental results show SemiBoost improves classification accuracy over other semi-supervised and supervised methods on benchmark datasets.
Meta-learning of exploration-exploitation strategies in reinforcement learningUniversité de Liège (ULg)
The document discusses meta-learning of exploration-exploitation strategies in reinforcement learning. It proposes learning exploration strategies rather than relying on predefined formulas. The approach involves defining training problems, candidate strategies, a performance criterion, and optimizing strategies on the training problems using an optimization tool. Simulation results show learned strategies outperform strategies based on predefined formulas when the test problems match the training problems. The document provides examples applying this approach to multi-armed bandits and tree search problems.
Learning for exploration-exploitation in reinforcement learning. The dusk of ...Université de Liège (ULg)
The document discusses reinforcement learning and the exploration-exploitation tradeoff that agents face. It proposes learning exploration-exploitation strategies rather than relying on predefined formulas. The approach defines training problems, candidate strategies parameterized by formulas, a performance criterion, and optimizes strategies on training problems using an estimation of distribution algorithm. Simulation results show learned strategies outperform strategies from common formulas on matching test problems.
Here a Review of the Combination of Machine Learning models from Bayesian Averaging, Committees to Boosting... Specifically An statistical analysis of Boosting is done
This document provides an overview of machine learning techniques using R. It discusses regression, classification, linear models, decision trees, neural networks, genetic algorithms, support vector machines, and ensembling methods. Evaluation metrics and algorithms like lm(), rpart(), nnet(), ksvm(), and ga() are presented for different machine learning tasks. The document also compares inductive learning, analytical learning, and explanation-based learning approaches.
This document provides an overview of various techniques for text categorization, including decision trees, maximum entropy modeling, perceptrons, and K-nearest neighbor classification. It discusses the data representation, model class, and training procedure for each technique. Key aspects covered include feature selection, parameter estimation, convergence criteria, and the advantages/limitations of each approach.
better together? statistical learning in models made of modulesChristian Robert
The document discusses statistical models composed of modular components called modules. Each module may be developed independently and represent different data modalities or domains of knowledge. Joint Bayesian updating treats all modules simultaneously but misspecification of one module can impact the others. Alternative approaches are proposed to allow uncertainty propagation between modules while preventing feedback that could lead to misspecification. Candidate distributions for the modules are discussed, along with strategies for choosing among them based on predictive performance.
SVMs are classifiers derived from statistical learning theory that maximize the margin between decision boundaries. They work by mapping data to a higher dimensional space using kernels to allow for nonlinear decision boundaries. SVMs find the linear decision boundary that maximizes the margin between the closest data points of each class by solving a quadratic programming optimization problem.
The document discusses several computational methods for Bayesian model choice, including importance sampling, bridge sampling, nested sampling, and approximate Bayesian computation (ABC) model choice. Importance sampling can be used to approximate Bayes factors by sampling from an importance function. Bridge sampling provides an alternative estimator that performs better when the models being compared have little overlap. Nested sampling and ABC can also be applied to Bayesian model choice by approximating the marginal likelihood of each model.
This document describes a new method called component-wise approximate Bayesian computation (ABCG or ABC-Gibbs) that combines approximate Bayesian computation (ABC) with Gibbs sampling. ABCG aims to more efficiently explore parameter spaces when the number of parameters is large. It works by alternately sampling each parameter from its ABC-approximated conditional distribution given current values of other parameters. The document provides theoretical analysis showing ABCG converges to a stationary distribution under certain conditions. It also presents examples demonstrating ABCG can better separate estimates from the prior compared to simple ABC, especially for hierarchical models.
Dictionary Learning for Massive Matrix Factorizationrecsysfr
The document presents a new algorithm called Subsampled Online Dictionary Learning (SODL) for solving very large matrix factorization problems with missing values efficiently. SODL adapts an existing online dictionary learning algorithm to handle missing values by only using the known ratings for each user, allowing it to process large datasets with billions of ratings in linear time with respect to the number of known ratings. Experiments on movie rating datasets show that SODL achieves similar prediction accuracy as the fastest existing solver but with a speed up of up to 6.8 times on the largest Netflix dataset tested.
The document summarizes Approximate Bayesian Computation (ABC). It discusses how ABC provides a way to approximate Bayesian inference when the likelihood function is intractable or too computationally expensive to evaluate directly. ABC works by simulating data under different parameter values and accepting simulations that are close to the observed data according to a distance measure and tolerance level. Key points discussed include:
- ABC provides an approximation to the posterior distribution by sampling from simulations that fall within a tolerance of the observed data.
- Summary statistics are often used to reduce the dimension of the data and improve the signal-to-noise ratio when applying the tolerance criterion.
- Random forests can help select informative summary statistics and provide semi-automated ABC
1. The document discusses Bayesian model choice and compares multiple computational methods for approximating model evidence, including importance sampling, bridge sampling, and nested sampling.
2. It explains that Bayesian model choice involves probabilizing models and parameters, and computing the evidence for each model, which is proportional to the marginal likelihood.
3. One method covered is bridge sampling, which uses importance functions to approximate the Bayes factor for comparing two models. Optimal bridge sampling chooses an auxiliary function that minimizes the variance of the estimate.
The document describes a new method called component-wise approximate Bayesian computation (ABC) that combines ABC with Gibbs sampling. It aims to improve ABC's ability to efficiently explore parameter spaces when the number of parameters is large. The method works by alternating sampling from each parameter's ABC posterior conditional distribution given current values of other parameters and the observed data. The method is proven to converge to a stationary distribution under certain assumptions, especially for hierarchical models where conditional distributions are often simplified. Numerical experiments on toy examples demonstrate the method can provide a better approximation of the true posterior than vanilla ABC.
This document discusses regularization and model selection techniques for machine learning models. It describes cross-validation methods like hold-out validation and k-fold cross validation that evaluate models on held-out data to select models that generalize well. Feature selection is discussed as an important application of model selection. Bayesian statistics and placing prior distributions on parameters is introduced as a regularization technique that favors models with smaller parameter values.
Approximate Bayesian model choice via random forestsChristian Robert
The document describes approximate Bayesian computation (ABC) methods for model choice when likelihoods are intractable. ABC generates parameter-dataset pairs from the prior and retains those where the simulated and observed datasets are similar according to a distance measure on summary statistics. For model choice, ABC approximates posterior model probabilities by the proportion of simulations from each model that are retained. Machine learning techniques can also be used to infer the most likely model directly from the simulated summary statistics.
Machine Learning: Decision Trees Chapter 18.1-18.3butest
The document discusses machine learning and decision trees. It provides an overview of different machine learning paradigms like rote learning, induction, clustering, analogy, discovery, and reinforcement learning. It then focuses on decision trees, describing them as trees that classify examples by splitting them along attribute values at each node. The goal of learning decision trees is to build a tree that can accurately classify new examples. It describes the ID3 algorithm for constructing decision trees in a greedy top-down manner by choosing the attribute that best splits the training examples at each node.
Eagle Strategy Using Levy Walk and Firefly Algorithms For Stochastic Optimiza...Xin-She Yang
This document proposes a new two-stage hybrid search method called the Eagle Strategy for solving stochastic optimization problems. The Eagle Strategy combines random search using Lévy walk with intensive local search using the Firefly Algorithm. It first uses Lévy walk to randomly explore the search space, then switches to the Firefly Algorithm to intensively search locally around good solutions. Numerical results suggest the Eagle Strategy is efficient for stochastic optimization problems.
These are the slides I gave during three lectures at the YES III meeting in Eindhoven, October 5-7, 2009. They include a presentation of the Savage-Dickey paradox and a comparison of major importance sampling solution, both obtained in collaboration with Jean-Michel Marin.
This document discusses approximate Bayesian computation (ABC) methods for Bayesian model choice. It begins by introducing ABC as a technique for performing Bayesian inference when the likelihood function is intractable. It then describes how ABC can be used for model choice by sampling models from their prior and parameters from the prior conditional on the model. The document outlines the generic ABC algorithm for model choice and discusses how it estimates posterior model probabilities. It also discusses applications of ABC for model choice in Gibbs random fields and Potts models.
The document discusses approximate Bayesian computation (ABC), a simulation-based method for conducting Bayesian inference when the likelihood function is intractable or impossible to compute directly. ABC works by simulating data under different parameter values, and accepting simulations that are close to the observed data according to some distance measure. The document covers the basic ABC algorithm, convergence properties as the tolerance approaches zero, examples of ABC for probit models and MA time series models, and advances such as modifying the proposal distribution to increase efficiency.
This document discusses approximate Bayesian computation (ABC) techniques for performing Bayesian inference when the likelihood function is not available in closed form. It covers the basic ABC algorithm and discusses challenges with high-dimensional data. It also summarizes recent advances in ABC that incorporate nonparametric regression, reproducing kernel Hilbert spaces, and neural networks to help address these challenges.
This document summarizes an incremental machine learning algorithm applied to robot navigation. The algorithm learns a set of declarative rules by executing random actions and observing the results. The rules are then pruned to remove useless rules. Initially, crisp conditions are used in the rules, but fuzzy conditions learned from a human expert produce better results. The algorithm is demonstrated through a robot simulation navigating an obstacle-free path, first with crisp and then fuzzy rules. The fuzzy rules improve performance by better handling uncertainties close to the goal direction.
The document contains a series of worksheets for students to practice writing numbers from 1 to 100. Each worksheet provides different sequences or patterns for the numbers to follow, such as by 5s, 10s, odds and evens. The final worksheet provides the complete sequence from 1 to 100. The document encourages downloading more free teaching resources and provides contact information for the creator.
This document provides an overview of machine learning techniques using R. It discusses regression, classification, linear models, decision trees, neural networks, genetic algorithms, support vector machines, and ensembling methods. Evaluation metrics and algorithms like lm(), rpart(), nnet(), ksvm(), and ga() are presented for different machine learning tasks. The document also compares inductive learning, analytical learning, and explanation-based learning approaches.
This document provides an overview of various techniques for text categorization, including decision trees, maximum entropy modeling, perceptrons, and K-nearest neighbor classification. It discusses the data representation, model class, and training procedure for each technique. Key aspects covered include feature selection, parameter estimation, convergence criteria, and the advantages/limitations of each approach.
better together? statistical learning in models made of modulesChristian Robert
The document discusses statistical models composed of modular components called modules. Each module may be developed independently and represent different data modalities or domains of knowledge. Joint Bayesian updating treats all modules simultaneously but misspecification of one module can impact the others. Alternative approaches are proposed to allow uncertainty propagation between modules while preventing feedback that could lead to misspecification. Candidate distributions for the modules are discussed, along with strategies for choosing among them based on predictive performance.
SVMs are classifiers derived from statistical learning theory that maximize the margin between decision boundaries. They work by mapping data to a higher dimensional space using kernels to allow for nonlinear decision boundaries. SVMs find the linear decision boundary that maximizes the margin between the closest data points of each class by solving a quadratic programming optimization problem.
The document discusses several computational methods for Bayesian model choice, including importance sampling, bridge sampling, nested sampling, and approximate Bayesian computation (ABC) model choice. Importance sampling can be used to approximate Bayes factors by sampling from an importance function. Bridge sampling provides an alternative estimator that performs better when the models being compared have little overlap. Nested sampling and ABC can also be applied to Bayesian model choice by approximating the marginal likelihood of each model.
This document describes a new method called component-wise approximate Bayesian computation (ABCG or ABC-Gibbs) that combines approximate Bayesian computation (ABC) with Gibbs sampling. ABCG aims to more efficiently explore parameter spaces when the number of parameters is large. It works by alternately sampling each parameter from its ABC-approximated conditional distribution given current values of other parameters. The document provides theoretical analysis showing ABCG converges to a stationary distribution under certain conditions. It also presents examples demonstrating ABCG can better separate estimates from the prior compared to simple ABC, especially for hierarchical models.
Dictionary Learning for Massive Matrix Factorizationrecsysfr
The document presents a new algorithm called Subsampled Online Dictionary Learning (SODL) for solving very large matrix factorization problems with missing values efficiently. SODL adapts an existing online dictionary learning algorithm to handle missing values by only using the known ratings for each user, allowing it to process large datasets with billions of ratings in linear time with respect to the number of known ratings. Experiments on movie rating datasets show that SODL achieves similar prediction accuracy as the fastest existing solver but with a speed up of up to 6.8 times on the largest Netflix dataset tested.
The document summarizes Approximate Bayesian Computation (ABC). It discusses how ABC provides a way to approximate Bayesian inference when the likelihood function is intractable or too computationally expensive to evaluate directly. ABC works by simulating data under different parameter values and accepting simulations that are close to the observed data according to a distance measure and tolerance level. Key points discussed include:
- ABC provides an approximation to the posterior distribution by sampling from simulations that fall within a tolerance of the observed data.
- Summary statistics are often used to reduce the dimension of the data and improve the signal-to-noise ratio when applying the tolerance criterion.
- Random forests can help select informative summary statistics and provide semi-automated ABC
1. The document discusses Bayesian model choice and compares multiple computational methods for approximating model evidence, including importance sampling, bridge sampling, and nested sampling.
2. It explains that Bayesian model choice involves probabilizing models and parameters, and computing the evidence for each model, which is proportional to the marginal likelihood.
3. One method covered is bridge sampling, which uses importance functions to approximate the Bayes factor for comparing two models. Optimal bridge sampling chooses an auxiliary function that minimizes the variance of the estimate.
The document describes a new method called component-wise approximate Bayesian computation (ABC) that combines ABC with Gibbs sampling. It aims to improve ABC's ability to efficiently explore parameter spaces when the number of parameters is large. The method works by alternating sampling from each parameter's ABC posterior conditional distribution given current values of other parameters and the observed data. The method is proven to converge to a stationary distribution under certain assumptions, especially for hierarchical models where conditional distributions are often simplified. Numerical experiments on toy examples demonstrate the method can provide a better approximation of the true posterior than vanilla ABC.
This document discusses regularization and model selection techniques for machine learning models. It describes cross-validation methods like hold-out validation and k-fold cross validation that evaluate models on held-out data to select models that generalize well. Feature selection is discussed as an important application of model selection. Bayesian statistics and placing prior distributions on parameters is introduced as a regularization technique that favors models with smaller parameter values.
Approximate Bayesian model choice via random forestsChristian Robert
The document describes approximate Bayesian computation (ABC) methods for model choice when likelihoods are intractable. ABC generates parameter-dataset pairs from the prior and retains those where the simulated and observed datasets are similar according to a distance measure on summary statistics. For model choice, ABC approximates posterior model probabilities by the proportion of simulations from each model that are retained. Machine learning techniques can also be used to infer the most likely model directly from the simulated summary statistics.
Machine Learning: Decision Trees Chapter 18.1-18.3butest
The document discusses machine learning and decision trees. It provides an overview of different machine learning paradigms like rote learning, induction, clustering, analogy, discovery, and reinforcement learning. It then focuses on decision trees, describing them as trees that classify examples by splitting them along attribute values at each node. The goal of learning decision trees is to build a tree that can accurately classify new examples. It describes the ID3 algorithm for constructing decision trees in a greedy top-down manner by choosing the attribute that best splits the training examples at each node.
Eagle Strategy Using Levy Walk and Firefly Algorithms For Stochastic Optimiza...Xin-She Yang
This document proposes a new two-stage hybrid search method called the Eagle Strategy for solving stochastic optimization problems. The Eagle Strategy combines random search using Lévy walk with intensive local search using the Firefly Algorithm. It first uses Lévy walk to randomly explore the search space, then switches to the Firefly Algorithm to intensively search locally around good solutions. Numerical results suggest the Eagle Strategy is efficient for stochastic optimization problems.
These are the slides I gave during three lectures at the YES III meeting in Eindhoven, October 5-7, 2009. They include a presentation of the Savage-Dickey paradox and a comparison of major importance sampling solution, both obtained in collaboration with Jean-Michel Marin.
This document discusses approximate Bayesian computation (ABC) methods for Bayesian model choice. It begins by introducing ABC as a technique for performing Bayesian inference when the likelihood function is intractable. It then describes how ABC can be used for model choice by sampling models from their prior and parameters from the prior conditional on the model. The document outlines the generic ABC algorithm for model choice and discusses how it estimates posterior model probabilities. It also discusses applications of ABC for model choice in Gibbs random fields and Potts models.
The document discusses approximate Bayesian computation (ABC), a simulation-based method for conducting Bayesian inference when the likelihood function is intractable or impossible to compute directly. ABC works by simulating data under different parameter values, and accepting simulations that are close to the observed data according to some distance measure. The document covers the basic ABC algorithm, convergence properties as the tolerance approaches zero, examples of ABC for probit models and MA time series models, and advances such as modifying the proposal distribution to increase efficiency.
This document discusses approximate Bayesian computation (ABC) techniques for performing Bayesian inference when the likelihood function is not available in closed form. It covers the basic ABC algorithm and discusses challenges with high-dimensional data. It also summarizes recent advances in ABC that incorporate nonparametric regression, reproducing kernel Hilbert spaces, and neural networks to help address these challenges.
This document summarizes an incremental machine learning algorithm applied to robot navigation. The algorithm learns a set of declarative rules by executing random actions and observing the results. The rules are then pruned to remove useless rules. Initially, crisp conditions are used in the rules, but fuzzy conditions learned from a human expert produce better results. The algorithm is demonstrated through a robot simulation navigating an obstacle-free path, first with crisp and then fuzzy rules. The fuzzy rules improve performance by better handling uncertainties close to the goal direction.
The document contains a series of worksheets for students to practice writing numbers from 1 to 100. Each worksheet provides different sequences or patterns for the numbers to follow, such as by 5s, 10s, odds and evens. The final worksheet provides the complete sequence from 1 to 100. The document encourages downloading more free teaching resources and provides contact information for the creator.
This document contains information about Dr. Saeed Shafi including his qualifications, positions, and contact information. It also contains 48 multiple choice questions related to anatomy with corresponding answers. The questions cover topics like nerves, muscles, lymphatic drainage patterns, and anatomical structures of the head and neck region.
An army cadet injured his foot on a barbed wire during a military drill, resulting in pain in his foot, leg, and thigh. A week later, he developed enlarged lymph nodes in his groin.
A chukidar was brought to the emergency department after sustaining a bullet injury to his left femoral sheath. The damaged femoral artery was ligated. His postoperative recovery was smooth.
A football player twisted his leg while kicking, fully extending his knee. He was unable to flex his extended knee after falling to the ground.
El lila es un color que se obtiene de la mezcla del rojo y el azul. Es un tono que transmite elegancia y sofisticación. El lila se asocia con la creatividad, la imaginación y la intuición.
Active learning aims to improve machine learning models using less training data by strategically selecting the most informative data points to be labeled. It is important because manually labeling data can be time-consuming and expensive. The core problem is how to actively select the most informative training points to query labels for. Different active learning methods, such as using neural networks, Bayesian models, and support vector machines, aim to query points that the current model is most uncertain about. Combining active learning with expectation maximization using a large pool of unlabeled data can improve text classification when only a small amount of labeled training data is available.
Machine learning solutions for transportation networksbutest
This dissertation proposes machine learning solutions for problems in transportation networks. There are four main contributions: 1) A probabilistic graphical model called a Gaussian Tree Model to describe multivariate traffic patterns using fewer parameters than standard models. 2) A dynamic probabilistic traffic flow model combined with a particle filter for medium- and long-term traffic prediction. 3) Two new optimization algorithms for vehicle routing that incorporate the dynamic traffic flow model. 4) A method for detecting traffic incidents using a support vector machine that is improved through a dynamic Bayesian network framework for learning and correcting data biases. The dissertation addresses both static description of traffic patterns and dynamic probabilistic traffic prediction and routing.
This document summarizes kernel methods in machine learning. It begins with an introductory example of using a kernel function to perform binary classification in a reproducing kernel Hilbert space. It then defines positive definite kernels and shows how they allow representing algorithms as operating in linear dot product spaces while using nonlinear kernel functions. The document covers fundamental properties of kernels, provides examples, and discusses how kernels define reproducing kernel Hilbert spaces for regularization. It overviews various kernel-based machine learning approaches and modeling structured responses using statistical models in reproducing kernel Hilbert spaces.
Enjoy your sleep time with this printed night wear gown for women from Indiatrendzs. Made from Cotton, this nighty or night dress as we may call it is easy on the skin and features short sleeve. Look good and feel relaxed by wearing this Printed Sleepwear.
"Development Methods for Intelligent Systems"butest
This chapter discusses three mathematical models for intelligent learning agents: Markov Decision Processes (MDPs), Partially Observable Markov Decision Processes (POMDPs), and Hidden Markov Models (HMMs). MDPs and POMDPs are widely used in reinforcement learning to model environments as finite state machines. HMMs generalize MDPs by adding hidden states and are presented as a tool for modeling intelligent agent environments, with the potential to be useful for problems involving perception and learning from experiences.
Data.Mining.C.6(II).classification and predictionMargaret Wang
The document summarizes different machine learning classification techniques including instance-based approaches, ensemble approaches, co-training approaches, and partially supervised approaches. It discusses k-nearest neighbor classification and how it works. It also explains bagging, boosting, and AdaBoost ensemble methods. Co-training uses two independent views to label unlabeled data. Partially supervised approaches can build classifiers using only positive and unlabeled data.
2013-1 Machine Learning Lecture 06 - Artur Ferreira - A Survey on Boosting…Dongseo University
This document summarizes a survey on boosting algorithms for supervised learning. It begins with an introduction to ensembles of classifiers and boosting, describing how boosting builds ensembles by combining simple classifiers with associated contributions. The AdaBoost algorithm and its variants are then explained in detail. Experimental results on synthetic and standard datasets are presented, comparing boosting with generative and RBF weak learners. The results show that boosting algorithms can achieve low error rates, with AdaBoost performing well when weak learners are only slightly better than random.
Fuzzy clustering has been widely studied and applied in a variety of key areas of science and
engineering. In this paper the Improved Teaching Learning Based Optimization (ITLBO)
algorithm is used for data clustering, in which the objects in the same cluster are similar. This
algorithm has been tested on several datasets and compared with some other popular algorithm
in clustering. Results have been shown that the proposed method improves the output of
clustering and can be efficiently used for fuzzy clustering.
This presentation provides an overview of boosting approaches for classification problems. It discusses combining classifiers through bagging and boosting to create stronger classifiers. The AdaBoost algorithm is explained in detail, including its training and classification phases. An example is provided to illustrate how AdaBoost works over multiple rounds, increasing the weights of misclassified examples to improve classification accuracy. In conclusion, AdaBoost is highlighted as an effective approach for classification problems where misclassification has severe consequences by producing highly accurate strong classifiers.
An Automatic Medical Image Segmentation using Teaching Learning Based Optimiz...idescitation
Nature inspired population based evolutionary algorithms are very popular with
their competitive solutions for a wide variety of applications. Teaching Learning based
Optimization (TLBO) is a very recent population based evolutionary algorithm evolved
on the basis of Teaching Learning process of a class room. TLBO does not require any
algorithmic specific parameters. This paper proposes an automatic grouping of pixels into
different homogeneous regions using the TLBO. The experimental results have
demonstrated the effectiveness of TLBO in image segmentation.
This document discusses machine learning concepts of concept learning and decision-tree learning. It describes concept learning as inferring a boolean function from training examples and using algorithms like Candidate Elimination to search the hypothesis space. Decision tree learning is explained as representing classification functions as trees with nodes testing attributes, allowing disjunctive concepts. The ID3 algorithm is presented as a greedy top-down search that selects the best attribute at each node using information gain, potentially overfitting data without pruning or a validation set.
A baseline for_few_shot_image_classificationDongHeeKim39
This paper proposes a simple baseline approach for few-shot learning without requiring specialized training or hyperparameter tuning. The approach uses support-based initialization to construct a classifier for novel classes based on a pretrained model. It also proposes a transductive fine-tuning method where the model is fine-tuned on both support and query sets simultaneously to predict query labels. Experimental results on benchmark datasets show the approach is competitive with more complex meta-learning models. The paper also introduces a "hardness" metric to directly compare different few-shot learning algorithms.
This document discusses various methods for evaluating and improving the accuracy of classification models, including:
- Confusion matrices and measures like accuracy, sensitivity, and precision to evaluate classifier performance.
- Ensemble methods like bagging and boosting that combine multiple models to improve accuracy. Bagging averages predictions from models trained on bootstrap samples, while boosting gives higher weight to instances harder to classify.
- Model selection techniques like statistical tests and ROC curves to compare models and determine the best performing one. ROC curves show the tradeoff between true and false positives for threshold-based classifiers.
Machine Learning and Data Mining: 16 Classifiers EnsemblesPier Luca Lanzi
This document discusses ensemble machine learning methods. It introduces classifiers ensembles and describes three common ensemble methods: bagging, boosting, and random forests. For each method, it explains the basic idea, how the method works, advantages and disadvantages. Bagging constructs multiple classifiers from bootstrap samples of the training data and aggregates their predictions through voting. Boosting builds classifiers sequentially by focusing on misclassified examples. Random forests create decision trees with random subsets of features and samples. Ensembles can improve performance over single classifiers by reducing variance.
Machine Learning and Artificial Neural Networks.pptAnshika865276
Machine learning and neural networks are discussed. Machine learning investigates how knowledge is acquired through experience. A machine learning model includes what is learned (the domain), who is learning (the computer program), and the information source. Techniques discussed include k-nearest neighbors algorithm, Winnow algorithm, naive Bayes classifier, decision trees, and reinforcement learning. Reinforcement learning involves an agent interacting with an environment to optimize outcomes through trial and error.
Binary Class and Multi Class Strategies for Machine LearningPaxcel Technologies
This presentation discusses the following -
Possible strategies to follow when working on a new machine learning problem.
The common problems with classifiers (how to detect them and eliminate them).
Popular approaches on how to use binary classifiers to problems with multi class classification.
The document discusses genetic algorithms and genetic programming. It explains that genetic algorithms perform a parallel search of the hypothesis space to optimize a fitness function, mimicking biological evolution. New hypotheses are generated through mutation and crossover of existing hypotheses. Genetic programming similarly evolves computer programs represented as trees through genetic operators. An example shows a genetic programming approach for stacking blocks to spell a word.
Genetic Programming for Generating Prototypes in Classification ProblemsTarundeep Dhot
This document summarizes a research paper that proposes using genetic programming to generate prototypes for classification problems. It describes encoding prototypes as variable-length logical expressions and using a multi-tree representation. The approach evolves a population of these prototypes using genetic operators like crossover and mutation. Classification involves matching samples to prototypes, and fitness is based on recognition rate on a training set. The method was tested on several datasets and achieved higher recognition rates than an alternative genetic programming approach.
Operations management chapter 03 homework assignment use thisPOLY33
This document contains homework assignments related to operations management, machine learning algorithms, and product life cycles. It includes questions about breaking even on a new product line, calculating process velocity and efficiency, analyzing the Perceptron algorithm and stochastic gradient descent, weak learners for concept classes, and AdaBoost iterations. The key details are calculating metrics like break even point, profit/loss, process velocity and efficiency based on given costs, sales, time estimates. It also involves explaining relationships between algorithms, finding weak learners to approximate complex concepts, and ensuring classifiers have 50% accuracy for AdaBoost iterations.
This document provides an overview of machine learning and neural network techniques. It defines machine learning as the field that focuses on algorithms that can learn. The document discusses several key components of a machine learning model, including what is being learned (the domain) and from what information the learner is learning. It then summarizes several common machine learning algorithms like k-NN, Naive Bayes classifiers, decision trees, reinforcement learning, and the Rocchio algorithm for relevance feedback in information retrieval. For each technique, it provides a brief definition and examples of applications.
The document discusses various machine learning techniques including k-nearest neighbors, which classifies new data based on its similarity to existing examples; Naive Bayes classifiers, which use Bayes' theorem to classify items based on the presence or absence of features; and decision trees, which classify items by sorting them based on the results of tests on their features and dividing them into branches. Reinforcement learning is also covered, where an agent learns through trial-and-error interactions with an environment by receiving rewards or penalties for actions.
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1. Heuristic Search Based Stacking of Classifiers
By Ricardo Aler, Daniel Borrajo, and Agapito Ledezma.
Universidad Carlos III
Avda. Universidad, 30
28911 Leganés (Madrid)
Spain
e-mails: aler@inf.uc3m.es, dborrajo@ia.uc3m.es, ledezma@elrond.uc3m.es
fax: +34-91-624 9430
INTRODUCTION
One of the most active and promising fields in inductive Machine Learning is the
ensemble of classifiers approach. An ensemble of classifiers is a set of classifiers whose
individual decisions are combined in some way to classify new examples (Dietterich,
1997). The purpose of combining classifiers consists on improving the accuracy of a
single classifier. Experimental results show that this is usually achieved.
There are several ways to construct such ensembles, but currently the most used ones
are bagging (Breiman, 1996), boosting (Freund & Schapire, 1995) and less widely used,
stacking (Wolpert, 1992). Bagging constructs a set of classifiers by subsampling the
training examples to generate different hypotheses. After the different hypotheses are
generated, they are combined by a voting mechanism. Boosting also uses the voting
system to combine the classifiers. But, instead of subsampling the training examples, it
generates the hypotheses sequentially. In each repetition, a new classifier is generated
which focus in those instances that were handled incorrectly by the previous classifier.
This is achieved by giving a weight to each instance in the training examples and
adjusting these weights according to its importance after every iteration. Both, bagging
and boosting use classifiers generated by the same base-learning algorithm and obtained
from the same data. Finally, stacking can combine classifiers obtained from different
learning algorithms using a high level classifier –the metaclassifier- to combine the
lower level models. This is based on the fact that different classifiers are obtained from
the same data and different learning algorithms use different biases to search the
hypothesis space. This approach expects that the metaclassifier will be able to learn how
to decide between the predictions provided by the base classifiers, in order to get
accuracies better than any of them, much in the same way as a committee of experts.
One problem of stacked generalization consists in identifying which learning algorithm
should be used to obtain the metaclassifier, and which ones should be the base
classifiers. The approach we present in this chapter consists to pose this problem as an
optimization task, and then use optimization techniques based on heuristic search to
solve it. In particular, we apply genetic algorithms (Holland, 1975) to automatically
obtain the ideal combination of learning methods for the stacking system.
BACKGROUND
The purpose of this section is to give enough background to understand the rest of the
paper. Here, we will explain concepts related to ensembles of classifiers, bagging,
boosting, stacking, and genetic algorithms.
2. Ensemble of Classifiers
The combination of multiple classifiers to improve the accuracy of a single classifier
has had good results over several datasets that appear in recent papers about ensembles
of classifiers (Bauer & Kohavi, 1999; Breiman, 1996; Freund & Schapire, 1996;
Quinlan, 1996). According to Dietterich (1997), an ensemble of classifiers is a set of
classifiers whose individual decisions are combined in some way to classify new
examples. There are many ways to construct an ensemble of classifiers. Bauer and
Kohavi (1999) have made a comparison of algorithms based in voting systems.
Dietterich (2000) carried out a survey of the main methods to construct an ensemble of
classifiers. One way to construct an ensemble of classifiers is based on subsampling the
training set to generate a different set of hypotheses and then combine them. This is
called bagging (Breiman, 1996). The second way is to create classifiers sequentially,
giving more importance to examples that missclassified the previous classifier. The
latter is called boosting (Schapire, 1990). Both bagging and boosting use a single
learning algorithm to generate all the classifiers, whereas stacking combines classifiers
from different learning algorithm.
There are other methods to combine a set of classifiers (Dietterich, 2000), but for
experimental purposes in this study we consider here the most well known methods,
bagging, boosting and stacking.
Bagging
Breiman (1996) introduced the Bootstrap aggregating Algorithm (Bagging) that
generates different classifiers from different bootstrap samples and combines decisions
from the different classifiers into a single prediction by voting (the class that gets more
votes from the classifiers wins). Figure 1 shows the bagging algorithm.
Each bootstrap sample is generated by sampling uniformly (with replacement) the m-
sized training set, until a new set with m instances is obtained. Obviously, some of the
instances of the training set will be cloned in the bootstrap sample, and some will be
missing. Then, a classifier Ci is built from each of the bootstrap samples B1, B2, … BT.
Each classifier corresponding to each bootstrap sample will focus on some instances of
the training set, and therefore the resulting classifiers will usually differ from each
other. The final classifier C* is the ensemble of the Ci classifiers combined by means of
the uniform voting system (all classifiers have equal weight).
The Bagging Algorithm
Input:
Training set S
Base Learning Algorithm B
Number of bootstrap samples T
Procedure:
For i = 1 to T {
S' = bootstrap sample from S (S' is a sample with replacement from S)
Ci = B (S') (create a new classifier from S')
}
C*(x) = arg max
y∈Y
∑(the most often predicted label y)
1
i:Ci( x) =y
Output
Classifier C*
Figure 1. The Bagging Algorithm
3. Since an instance has probability 1-(1-1/m) m of being in the bootstrap sample, each
bootstrap replicate has, in average, 63.2% of unique training instances (1 - 1/e = 63.2%).
For this reason the generated classifiers will be different if the base learning algorithm
is unstable (e.g. decision tree or neural networks). If the generated classifiers are good
and do not correlate, the performance will be improved. This will occur if they make
few mistakes and different classifiers do not missclassify the same instances frequently.
Boosting
Another method to construct an ensemble of classifiers is know as boosting (Schapire,
1990), which is used to boost the performance of a weak learner. A weak learner is a
simple classifier whose error is less than 50% on training instances. There are many
variants of the boosting idea, but in this study we will describe the widely used
AdaBoost Algorithm (Adaptive Boosting) that was introduced by Freund & Schapire
(1995). Sometimes the AdaBoost algorithm is also known as AdaBoostM1.
Similarly to bagging, boosting manipulates the training set to generate a set of
classifiers of the same type (e.g. decision trees). But while in bagging classifiers are
generated independently from each other, in boosting they are generated sequentially, in
such a way that each one complements the previous one. First, a classifier is generated
using the original training set. Then, those instances misclassified by this classifier are
given a larger weight (therefore, missclassifying this instance makes the error larger).
Next, a new classifier is obtained by using the previously weighted training set. The
training error is calculated and a weight is assigned to the classifier in accordance with
its performance on the training set. Therefore, the new classifier should do better on the
misclassified instances than the previous one, hence complementing it. This process is
repeated several times. Finally, to combine the set of classifiers in the final classifier,
AdaBoost (like bagging) uses the voting method. But unlike bagging that use equal
weights for all classifiers, in boosting the classifiers with lower training error have a
higher weight in the final decision.
More formally, let S be the training set and T the number of trials, the classifiers C 1, C2,
…. CT are built in sequence from the weighted training samples (S1, S2,…,ST). The final
classifier is the combination of the set of classifiers in which the weight of each
classifier is calculated by its accuracy on its training sample. The AdaBoost algorithm is
displayed in Figure 2
4. The AdaBoostM1 Algorithm
Input:
Training set S, of labelled instances: S = {(xi , yi), i = 1,2, …, m},
classes yi ∈ Y = {1, …, K}
Base Learning Algorithm (weak learner) B
Number of iteration T
Procedure:
Initialise for all i: w1 (i) = 1/m Assign equal weights to
all training instances
For t = 1 to T {
for i: pt (i) = w t(i)/(Σ i wt (i)) Normalise the weight
of the instances
C t = B(p t ) Apply the base learning
algorithm with the normalised
weights
εi =
m
1
∑ weight(x) weighted error on training set
xj ∈ S ':Ci ( xj ) ≠ yj
If ε i > 1/2 then
T= t -1
exit
βt = εi/(1- ε i)
1− [Ci ( xi ) ≠ yi ]
for all i: wt+1 (i) = wt(i) β t Compute the new weights
}
T
1
Classifier C* = argmax
y∈Y
∑ log βt [C ( x) = y]
t
t =1
Output
Classifier C*
.
Figure 2 AdaBoostM1 Algorithm.
An important characteristic of the AdaBoost algorithm is that it can combine some
weak learners to produce a strong learner, so long as the error on the weighted training
set is smaller than 0.5. If the error is greater than 0.5, the algorithm finishes the
execution. Were it not so, the final prediction of the ensemble would be random.
Stacking
Stacking is the abbreviation to refer to Stacked Generalization (Wolpert, 1992). Unlike
bagging and boosting, it uses different learning algorithms to generate the ensemble of
classifiers. The main idea of stacking is to combine classifiers from different learners
such as decision trees, instance-based learners, etc. Since each one uses different
knowledge representation and different learning biases, the hypothesis space will be
explored differently, and different classifiers will be obtained. Thus, it is expected that
they will not be correlated.
Once the classifiers have been generated, they must be combined. Unlike bagging and
boosting, stacking does not use a voting system because, for example, if the majority of
the classifiers make bad predictions this will lead to a final bad classification. To solve
this problem, stacking uses the concept of meta learner. The meta learner (or level-1
model), tries to learn, using a learning algorithm, how the decisions of the base
classifiers (or level-0 models) should be combined.
5. Given a data set S, stacking first generates a subset of training sets S1,…,ST and then
follows something similar to a cross-validation process: it leaves one of the subsets out
(e.g. Sj ) to use later. The remaining instances S(-j)= S - Sj are used to generate the
level-0 classifiers by applying K different learning algorithms, k = 1, …, K, to obtain K
classifiers. After the level-0 models have been generated, the Sj set is used to train the
meta learner (level-1 classifier). Level-1 training data is built from the predictions of the
level-0 models over the instances in Sj , that were left out for this purpose. Level-1 data
has K attributes, whose values are the predictions of each one of the K level-0
classifiers for every instance in Sj . Therefore, a level-1 training example is made of K
attributes (the K predictions) and the target class, which is the right class for every
particular instance in Sj. Once the level-1 data has been built from all instances in Sj,
any learning algorithm can be used to generate the level-1 model. To complete the
process, the level-0 models are re-generated from the whole data set S (this way, it is
expected that classifiers will be slightly more accurate). To classify a new instance, the
level-0 models produce a vector of predictions that is the input to the level-1 model,
which in turn predicts the class.
There are many ways to apply the general idea of stacked generalization. Ting and
Witten (1997) use probability outputs from level-0 models instead a of simple class
prediction as inputs to the level-1 model. LeBlanc and Tibshirani (1993) analyze the
stacked generalization with some regularization (non-negative constraint) to improve
the prediction performance on one artificial dataset. Other works on stacked
generalization have developed a different focus (Chan & Stolfo, 1995; Fan, Chan &
Stolfo, 1996).
Genetic Algorithms for Optimization Problems
Genetic algorithms (GA's) are search procedures loosely connected to the theory of
evolution by means of artificial selection (Holland, 1975). In classical search terms,
GA's can be viewed as a kind of beam search procedure. Its main three components are:
• The beam (or population). It contains the set of points (candidate solutions or
individuals) in the search space that the algorithm is currently exploring. All points
are usually represented by means of bit strings. This domain independent
representation of candidate solutions makes GA's very flexible.
• The search operators. They transform current candidate solutions into new candidate
solutions. Their main characteristic is that, as they operate on bit strings, they are
also domain independent. That is, they can be used to search in any domain. GA's
operators are also based in biological analogies. The three most frequently used
operators are:
• Reproduction: it just copies the candidate solution without modification.
• Crossover: it takes two candidate solutions, mixes them and generates two new
candidate solutions. There are many variations of this operator (mainly, single
point, two point and uniform). See Figure 3 .
6. 00110000100 00110000100
11100100010 11100100010
00100100010 00100100100
11110000100 11110000010
One point crossover Two point crossover
Figure 3 One and Two Point Crossover Operations
• Mutation: it flips a single bit of a candidate solution (it mutates from 0 to 1, or
from 1 to 0). The bit is selected randomly from the bits in the individual.
• The heuristic function (or fitness function). This function measures the worth of a
candidate solution. The goal of a GA is to find candidate solutions that maximize
this function.
GA's start from a population made of randomly generated bit strings. Then, genetic
operators are applied to worthy candidate solutions (according to the heuristic function)
until a new population is built (the new generation). A GA continues producing new
generations until a candidate solution is found that is considered to be good enough, or
when the algorithm seems to be unable to improve candidate solutions (or until the
number of generations reaches a predefined limit). More exactly, a GA follows the
algorithm below:
1. Randomly generate initial population G(0)
2. Evaluate candidate solutions in G(0) with the heuristic function
3. Repeat until a solution is found or population converges
3.1. Apply selection-reproduction: G(i) -> Ga(0)
3.2. Apply crossover: Ga(i) -> Gb(i)
3.3. Apply mutation: Gb(i) -> Gc(i)
3.4. Obtain new generation G(i+1) = Gc(i)
3.5. Evaluate new generation G(i+1)
3.6. Let i=i+1
The production of a new generation G(i+1) from G(i) (steps 3.1, 3.2, and 3.3) is as
follows. First, a new population (Ga(i)) is generated by means of selection. In order to
fill up a population of n individuals for Ga(0), candidate solutions are stochastically
selected with replacement from G(i) n times. The probability for selecting a candidate
solution is the ratio between its fitness and the total fitness of the population. This
means that there will be several copies of very good candidate solutions in Ga(0),
whereas there might be none of those whose heuristic evaluation is poor. However, due
to stochasticity, even bad candidate solutions have a chance of being present in Ga(0).
This method is called ‘selection proportional to fitness’, but there are several more, like
tournament and ranking (Goldberg,1989).
7. Gb(i) is produced by applying crossover to a fixed percentage pc of randomly selected
candidate solutions in Ga(i). As each crossover event takes two parents and produces
two offspring, crossover happens pc/2 times. In a similar manner, Gc(i) is obtained from
Gb(0) by applying mutation to a percentage pm of candidate solutions.
GA-STACKING APPROACH
In this section, the approach we have taken to build stacking systems will be explained.
Given that stacked generalization is composed by a set of classifiers from a different set
of learning algorithms, the question is: what algorithm should be used to generate the
level-0 and the level-1 models? In principle, any algorithm can be used to generate
them. For instance, Ting and Witten (1997) showed that a linear model is useful to
generate the level-1 model using probabilistic outputs from level-0 models. In our work
we start from the original stacked generalization idea proposed by Wolpert (1992), in
which the outputs from level-0 models are nominal (predictions). Also, our classifiers at
level-0 are hetereogeneous, and any algorithm can be used to build the metaclassifier. In
the present study, to determine the optimum distribution of learning algorithms for the
level-0 and level-1 models, we have used a GA.
GA-Stacking
Two sets of experiment have been carried out to determine whether stacked
generalization combinations of classifiers can be successfully found by genetic
algorithms. We also wanted to know whether GA stacking can obtain improvements
over the most popular ensemble techniques (bagging and boosting) as well as any of the
standalone learning algorithms.
As indicated previously, the application of genetic algorithms to optimization problems
requires to define:
• the representation of the individuals (candidate solutions)
• the fitness function that is used to evaluate the individuals
• the selection-scheme (e.g., selection proportional to fitness)
• the genetic operators that will be used to evolve the individuals
• the parameters (e.g., size of population, generations, probability of crossover, etc.)
In the two sets of performed experiments, the representation of the possible solutions
(individuals) are chromosomes with five genes (see Figure 4). They contain the codes of
the four algorithms to build the level-0 classifiers (firsts 4 genes) and the metaclassifier
(last gene). A gene has 3 bits, because we want to use 7 possible learning algorithms.
To evaluate every individual, we used the classification accuracy of the stacking system
as the fitness function.
level-1 model
010111000110001
level-0 models
Figure 4. Individual description.
8. EXPERIMENTAL RESULTS
Introduction
In this section, we present the empirical results for our GA-Stacking system. GA-
Stacking has been evaluated in several domains of the well-known UCI database (Blake
& Merz, 1998). There are two sets of experiments. In the first one, we show some
preliminary results, which are quite good but suffer some overfitting. In the second set
of experiments, steps are taken to avoid said overfitting. Both sets of experiments differ
only in the way GA individuals are tested (i.e. the fitness function). In this work, we
have used the algorithms implemented in Weka (Witten & Frank, 2000). This includes
all the classifiers above, bagging, boosting and stacking.
Basically, the implementation of GA-Stacking combines two parts: a part coming from
Weka that includes all the base learning algorithms and another part, which was
integrated into Weka, that implements a GA. The parameters used for the GA in the
experiments are shown in Table 1. The elite rate is the proportion of the population
carried forward unchanged from each generation. Cull rate refers to the proportion of
the population that is deemed unfit for reproduction. Finally, the mutation rate is the
proportion of the population that can suffer change in configuration at random.
Parameters Values
Population size 10
Generations 10
Elite rate 0.1
Cull rate 0.4
Mutation rate 0.067
Table 1. Genetic algorithms parameters.
For the experimental test of our approach we have used seven data sets from the
repository of machine learning databases at UCI. Table 2 shows the data sets
characteristics.
Dataset Attributes Attributes Type Instances Classes
Heart disease 13 Numeric-nominal 303 2
Sonar classification 60 Numeric 208 2
Musk 166 Numeric 476 2
Ionosphere 34 Numeric 351 2
Dermatology 34 Numeric-nominal 366 6
DNA splice 60 Nominal 3190 3
Satellite images 36 Numeric 6435 6
Table 2. Datasets description.
The candidate learning algorithms for GA stacking we used were:
• C4.5 (Quinlan, 1993). It generates decision trees - (C4.5)
• PART (Frank & Witten, 1998). It forms a decision list from pruned partial decision
trees generated using the C4.5 heuristic - (PART)
• A probabilistic Naive Bayesian classifier (John & Langley, 1995) - (NB)
• IB1. This is Aha’s instance based learning algorithm (Aha & Kibler, 1991) - (IB1)
• Decision Table. It is a simple decision table majority classifier (Kohavi, 1995) -
(DT)
9. • Decision Stump. It generates single-level decision trees - (DS)
Preliminary Experiments
Experiments in this subsection are a first evaluation of GA-Stacking. They use the GA-
Stacking scheme described in previous sections. Here, we will describe in more detail
how individuals are tested (the fitness function), and how the whole system is tested.
Each data set was split randomly in two sets. One of them was used as the training set
for the GA fitness function. It contained about 85% of all the instances. Individual
fitness was measured as the accuracy of the stacking system codified in it. The rest was
used as testing set to validate the stacked hypothesis obtained. In these experiments we
used only two of the data sets shown in Table 2 (dermatology and ionosphere).
Table 3 shows the results for this preliminary approach. Training and test accuracy
columns display how many instances in the training and testing sets were correctly
predicted for each of the systems. The first part of the table contains the standalone
algorithms. The second part shows results corresponding to traditional bagging and
boosting approaches (with C4.5 as the base classifier). Finally, results for GA-Stacking
are shown. The best GA-Stacking individual in the last generation has a 100% in the
training set in both domains, but drops to 85.71% and 95.45% in testing. On the other
hand, some individuals from previous generations manage to get a 94.29% and 98.48%
testing accuracies. This means that, GA-Stacking overfits the data as generations pass
on. Despite this overfitting, GA-Stacking found individuals which are better than most
of the base classifiers. Only in the Ionosphere domain, the Decision Table is better in
testing than the overfitted individual (88.57 vs. 85.71). Also, performance of GA-
Stacking is very close to bagging and boosting (both using C4.5 to generated base
classifiers). Non-overfitted individuals (those obtained in previous generations) show an
accuracy better than any of the other ensemble systems. In addition, stacking systems
only use four level-0 classifiers whereas bagging and boosting use at least 10 base
classifiers. This shows that the approach is solid. Next section will show how we
overcame the problem of overfitting.
10. Ionosphere Dermatology
Algorithm Training Test Accuracy Training Test
Accuracy Accuracy Accuracy
C4.5 98.42 82.86 96.67 92.42
Naive Bayes 85.13 82.86 98.67 96.97
PART 98.73 88.57 96.67 93.94
IBk (one neighbor) 100.00 82.86 100.00 92.42
IB1 100.00 82.86 100.00 92.42
Decision Stump 84.18 80.00 51.33 45.45
Decision Table 94.94 88.57 96.67 87.88
Ensembles
Bagging with C4.5 97.78 85.71 97.00 93.94
Boosting with C4.5 100.00 91.43 100.00 96.97
GA-Stacking (last
100.00 85.71 100.00 95.45
generation solutions)
GA-Stacking (solutions of
97.78 94.29 98.67 98.48
previous generations)
Table 3. Preliminary Results.
Main Experiments
In the preliminary experiments, individuals overfit because they are evaluated with the
same training instances that were used to build the stacking associated with the
individual. Obviously, the individual will do very well with the instances it has been
trained with. Therefore, in order to avoid the overfitting, the fitness value was
calculated with a separate validation set (different from the testing set used to evaluate
GA-Stacking itself). To do so, the set of training instances was partitioned randomly
into two parts. 80% of training instances were used to build the stacking system
associated with each individual, and the remaining 20% –the validation set- was used to
give a non-biased estimation of the individual accuracy. The latter was used as the
fitness of the individual. It is important to highlight that now fewer instances are used to
build the stacking systems, as some of them are used to ward off overfitting.
For testing all the systems we used the testing data set, just as we did in the preliminary
experiments. However, now a five-fold cross-validation was used. Therefore, results
shown are the average of the five cross-validation iterations. In the satellite images
domain no cross-validation was carried out because the sets for training and testing are
available separately and the data set donor indicated that it is better not to use cross-
validation.
Results are divided in two tables. Table 4 shows the testing accuracy of all the base
algorithms over the data sets. Table 5 displays testing results for the three ensemble
methods, including GA-Stacking. The best results for each domain are highlighted in
bold. The configuration of the stacked generalization found by the genetic algorithms
obtained more accuracy in four of the seven domains used in the experiment with
comparison with others ensemble methods. Boosting only won two times, and Bagging
once.
Dataset C4.5 PART NB IB1 DT DS
11. Heart 74.00 82.00 83.00 78.00 76.33 70.67
Sonar 72.38 73.81 67.62 79.52 71.90 73.93
Musk 83.33 85.21 74.38 86.46 82.08 71.46
Ionosphere 90.14 89.30 82.82 87.61 89.30 82.82
Dermatology 94.33 94.59 97.03 94.59 87.83 50.40
DNA splice 94.12 92.11 95.63 75.62 92.49 62.42
Satellite images* 85.20 84.10 79.60 89.00 80.70 41.75
Table 4. Average accuracy rate of independent classifiers. *not cross-validation.
Dataset Bagging Boosting GA-Stacking
Heart 76.33 79.67 80.67
Sonar 80.00 79.05 80.47
Musk 87.29 88.96 83.96
Ionosphere 92.11 91.83 90.42
Dermatology 94.59 97.03 98.11
DNA splice 94.56 94.43 95.72
Satellite images 88.80 89.10 88.60
Table 5. Average accuracy rate of ensemble methods
.
CONCLUSIONS
In this chapter, we have presented a new way of building hetereogeneous stacking
systems. To do so, a search on the space of stacking systems is carried out by means of
a genetic algorithm. Empirical results show that GA-Stacking is competitive with more
sophisticated ensemble systems such as Bagging and Boosting. Also, our simple
approach is able to obtain high accuracy classifiers which are very small (they contain
only 5 classifiers) in comparison with other ensemble approaches.
12. Even though the GA-Stacking approach has already produced very good results, we
believe that future research will show its worth even more clearly:
• Currently, GA-Stacking searches the space of stacked configurations. However, the
behavior of some learning algorithms is controlled by parameters. For instance, the
rules produced by C4.5 can be very different depending on the degree of pruning
carried out. Our GA-Stacking approach would only have to include a binary coding
of the desired parameters in the chromosome.
• Search depends on the representation of candidate hypothesis. Therefore, it would
be interesting to use other representations for our chromosomes. For instance, the
chromosome could be divided into two parts, one for the level 0 learners and
another for the level 1 metaclassifier. A bit in the first part would indicate whether a
particular classifier is included in level 0 or not. The metaclassifier would be coded
in the same way we have done in this paper (i.e. if there are 8 possible
metaclassifiers, 3 bits would be used).
• Different classifiers could be better suited for certain regions of the instance space.
Therefore, instead of having a metaclassifer that determines what output is
appropriate according to the level 0 outputs (as currently), it would be interesting to
have a metaclassifier that knows what level 0 classifier to trust according to some
features of the instance to be classified. In that case, the inputs to the metaclassifier
would be the attributes of the instance and the output the right level 0 classifier to
use.
• We would like to test our approach in domains where the cooperation between
hetereogeneous learning systems is required.
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