The document discusses decision tree learning and the ID3 algorithm. It begins by introducing decision trees and how they are used to classify instances by sorting them from the root node to a leaf node. It then discusses how ID3 builds decision trees in a top-down greedy manner by selecting the attribute that best splits the data at each node based on information gain. The document also covers issues like overfitting, handling continuous attributes, and pruning decision trees.
1) The document discusses concept learning, which involves inferring a Boolean function from training examples. It focuses on a concept learning task where hypotheses are represented as vectors of constraints on attribute values.
2) It describes the FIND-S algorithm, which finds the most specific hypothesis consistent with positive examples by generalizing constraints. However, FIND-S has limitations like ignoring negative examples.
3) The Candidate-Elimination algorithm represents the version space of all hypotheses consistent with examples to address FIND-S limitations. It outputs the version space rather than a single hypothesis.
The document provides an overview of machine learning concepts including:
- Defining machine learning as computer algorithms that improve with experience and data
- Describing examples like speech recognition, medical diagnosis, and game playing
- Outlining the components of designing a machine learning system like choosing the target function, representation, and learning algorithm
- Explaining concepts like version spaces, decision trees, and neural networks that are used in machine learning applications
The document discusses machine learning algorithms for learning first-order logic rules from examples. It introduces the FOIL algorithm, which extends propositional rule learning algorithms like sequential covering to learn more general first-order Horn clauses. FOIL uses an iterative specialization approach, starting with a general rule and greedily adding literals to better fit examples while avoiding negative examples. The document also discusses how combining inductive learning with analytical domain knowledge can improve learning, such as in the KBANN approach where a neural network is initialized based on the domain theory before training on examples.
This document discusses evaluating hypotheses and estimating hypothesis accuracy. It provides the following key points:
- The accuracy of a hypothesis estimated from a training set may be different from its true accuracy due to bias and variance. Testing the hypothesis on an independent test set provides an unbiased estimate.
- Given a hypothesis h that makes r errors on a test set of n examples, the sample error r/n provides an unbiased estimate of the true error. The variance of this estimate depends on r and n based on the binomial distribution.
- For large n, the binomial distribution can be approximated by the normal distribution. Confidence intervals for the true error can then be determined based on the sample error and standard deviation
The document discusses sequential covering algorithms for learning rule sets from data. It describes how sequential covering algorithms work by iteratively learning one rule at a time to cover examples, removing covered examples, and repeating until all examples are covered. It also discusses variations of this approach, including using a general-to-specific beam search to learn each rule and alternatives like the AQ algorithm that learn rules to cover specific target values. Finally, it describes how first-order logic can be used to learn more general rules than propositional logic by representing relationships between attributes.
This document discusses inductive bias in machine learning. It defines inductive bias as the assumptions that allow an inductive learning system to generalize beyond its training data. Without some biases, a learning system cannot rationally classify new examples. The document compares different learning algorithms based on the strength of their inductive biases, from weak biases like rote learning to stronger biases like preferring more specific hypotheses. It argues that all inductive learning systems require some inductive biases to generalize at all.
Advanced topics in artificial neural networksswapnac12
The document discusses various advanced topics in artificial neural networks including alternative error functions, error minimization procedures, recurrent networks, and dynamically modifying network structure. It describes adding penalty terms to the error function to reduce weights and overfitting, using line search and conjugate gradient methods for error minimization, how recurrent networks can capture dependencies over time, and algorithms for growing or pruning network complexity like cascade correlation.
Decision tree learning is a method for approximating discrete-valued functions that is widely used in machine learning. It represents learned functions as decision trees that classify instances described by attribute value pairs. The ID3 algorithm performs a top-down induction of decision trees by selecting the attribute that best splits the data at each step. This results in an expressive hypothesis space that is robust to noise while avoiding overfitting through techniques like reduced-error pruning.
1) The document discusses concept learning, which involves inferring a Boolean function from training examples. It focuses on a concept learning task where hypotheses are represented as vectors of constraints on attribute values.
2) It describes the FIND-S algorithm, which finds the most specific hypothesis consistent with positive examples by generalizing constraints. However, FIND-S has limitations like ignoring negative examples.
3) The Candidate-Elimination algorithm represents the version space of all hypotheses consistent with examples to address FIND-S limitations. It outputs the version space rather than a single hypothesis.
The document provides an overview of machine learning concepts including:
- Defining machine learning as computer algorithms that improve with experience and data
- Describing examples like speech recognition, medical diagnosis, and game playing
- Outlining the components of designing a machine learning system like choosing the target function, representation, and learning algorithm
- Explaining concepts like version spaces, decision trees, and neural networks that are used in machine learning applications
The document discusses machine learning algorithms for learning first-order logic rules from examples. It introduces the FOIL algorithm, which extends propositional rule learning algorithms like sequential covering to learn more general first-order Horn clauses. FOIL uses an iterative specialization approach, starting with a general rule and greedily adding literals to better fit examples while avoiding negative examples. The document also discusses how combining inductive learning with analytical domain knowledge can improve learning, such as in the KBANN approach where a neural network is initialized based on the domain theory before training on examples.
This document discusses evaluating hypotheses and estimating hypothesis accuracy. It provides the following key points:
- The accuracy of a hypothesis estimated from a training set may be different from its true accuracy due to bias and variance. Testing the hypothesis on an independent test set provides an unbiased estimate.
- Given a hypothesis h that makes r errors on a test set of n examples, the sample error r/n provides an unbiased estimate of the true error. The variance of this estimate depends on r and n based on the binomial distribution.
- For large n, the binomial distribution can be approximated by the normal distribution. Confidence intervals for the true error can then be determined based on the sample error and standard deviation
The document discusses sequential covering algorithms for learning rule sets from data. It describes how sequential covering algorithms work by iteratively learning one rule at a time to cover examples, removing covered examples, and repeating until all examples are covered. It also discusses variations of this approach, including using a general-to-specific beam search to learn each rule and alternatives like the AQ algorithm that learn rules to cover specific target values. Finally, it describes how first-order logic can be used to learn more general rules than propositional logic by representing relationships between attributes.
This document discusses inductive bias in machine learning. It defines inductive bias as the assumptions that allow an inductive learning system to generalize beyond its training data. Without some biases, a learning system cannot rationally classify new examples. The document compares different learning algorithms based on the strength of their inductive biases, from weak biases like rote learning to stronger biases like preferring more specific hypotheses. It argues that all inductive learning systems require some inductive biases to generalize at all.
Advanced topics in artificial neural networksswapnac12
The document discusses various advanced topics in artificial neural networks including alternative error functions, error minimization procedures, recurrent networks, and dynamically modifying network structure. It describes adding penalty terms to the error function to reduce weights and overfitting, using line search and conjugate gradient methods for error minimization, how recurrent networks can capture dependencies over time, and algorithms for growing or pruning network complexity like cascade correlation.
Decision tree learning is a method for approximating discrete-valued functions that is widely used in machine learning. It represents learned functions as decision trees that classify instances described by attribute value pairs. The ID3 algorithm performs a top-down induction of decision trees by selecting the attribute that best splits the data at each step. This results in an expressive hypothesis space that is robust to noise while avoiding overfitting through techniques like reduced-error pruning.
Bayesian Learning by Dr.C.R.Dhivyaa Kongu Engineering CollegeDhivyaa C.R
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, and maximum likelihood hypotheses. Bayes' theorem allows calculating the posterior probability of a hypothesis given observed data and prior probabilities. The maximum a posteriori hypothesis is the one with the highest posterior probability. Maximum likelihood hypotheses maximize the likelihood of the data. Bayesian learning faces challenges from requiring many initial probabilities and high computational costs but provides a useful perspective on machine learning algorithms.
This document provides an overview of artificial neural networks and the backpropagation algorithm. It discusses how neural networks are inspired by biological neural systems and how they represent problems as interconnected nodes. The backpropagation algorithm is introduced as a way to train multilayer neural networks by calculating error gradients to update weights. An example application of neural network for face recognition is also mentioned. Key aspects of neural network representations, perceptrons, the perceptron training rule, and gradient descent/delta rule for training are summarized.
Combining inductive and analytical learningswapnac12
The document discusses combining inductive and analytical learning methods. Inductive methods like decision trees and neural networks seek general hypotheses based solely on training data, while analytical methods like PROLOG-EBG seek hypotheses based on prior knowledge and training data. The document argues that combining these approaches could overcome their individual limitations by using prior knowledge to guide inductive learning methods. It examines using prior knowledge to initialize hypotheses, alter the search objective, and modify the search operators of inductive learners. As an example, it describes the KBANN algorithm, which initializes a neural network to perfectly fit a domain theory before refining it inductively to the training data.
The document discusses multilayer neural networks and the backpropagation algorithm. It begins by introducing sigmoid units as differentiable threshold functions that allow gradient descent to be used. It then describes the backpropagation algorithm, which employs gradient descent to minimize error by adjusting weights. Key aspects covered include defining error terms for multiple outputs, deriving the weight update rules, and generalizing to arbitrary acyclic networks. Issues like local minima and representational power are also addressed.
Bayesian Learning- part of machine learningkensaleste
This module provides an overview of Bayesian learning methods. It introduces Bayesian reasoning and Bayes' theorem as a probabilistic approach to inference. Key concepts covered include maximum likelihood hypotheses, naive Bayes classifiers, Bayesian belief networks, and the Expectation-Maximization (EM) algorithm. The EM algorithm is described as a method for estimating parameters of probability distributions when some variables are hidden or unobserved.
Bayesian learning uses prior knowledge and observed training data to determine the probability of hypotheses. Each training example can incrementally increase or decrease the estimated probability of a hypothesis. Prior knowledge is provided by assigning initial probabilities to hypotheses and probability distributions over possible observations for each hypothesis. New instances can be classified by combining the predictions of multiple hypotheses, weighted by their probabilities. Even when computationally intractable, Bayesian methods provide an optimal standard for decision making.
The document describes the backpropagation algorithm for training multilayer neural networks. It discusses how backpropagation uses gradient descent to minimize error between network outputs and targets by calculating error gradients with respect to weights. The algorithm iterates over examples, calculates error, computes gradients to update weights. Momentum can be added to help escape local minima. Backpropagation can learn representations in hidden layers and is prone to overfitting without validation data to select the best model.
Using prior knowledge to initialize the hypothesis,kbannswapnac12
1) The KBANN algorithm uses a domain theory represented as Horn clauses to initialize an artificial neural network before training it with examples. This helps the network generalize better than random initialization when training data is limited.
2) KBANN constructs a network matching the domain theory's predictions exactly, then refines it with backpropagation to fit examples. This balances theory and data when they disagree.
3) In experiments on promoter recognition, KBANN achieved a 4% error rate compared to 8% for backpropagation alone, showing the benefit of prior knowledge.
Inductive analytical approaches to learningswapnac12
This document discusses two inductive-analytical approaches to learning from data: 1) minimizing errors between a hypothesis and training examples as well as errors between the hypothesis and domain theory, with weights determining the importance of each, and 2) using Bayes' theorem to calculate the posterior probability of a hypothesis given the data and prior knowledge. It also describes three ways prior knowledge can alter a hypothesis space search: using prior knowledge to derive the initial hypothesis, alter the search objective to fit the data and theory, and alter the available search steps.
Mining single dimensional boolean association rules from transactionalramya marichamy
The document discusses mining frequent itemsets and generating association rules from transactional databases. It introduces the Apriori algorithm, which uses a candidate generation-and-test approach to iteratively find frequent itemsets. Several improvements to Apriori's efficiency are also presented, such as hashing techniques, transaction reduction, and approaches that avoid candidate generation like FP-trees. The document concludes by discussing how Apriori can be applied to answer iceberg queries, a common operation in market basket analysis.
The document discusses analytical learning methods like explanation-based learning. It explains that analytical learning uses prior knowledge and deductive reasoning to augment training examples, allowing it to generalize better than methods relying solely on data. Explanation-based learning analyzes examples according to prior knowledge to infer relevant features. The document provides examples of using explanation-based learning to learn chess concepts and safe stacking of objects. It also describes the PROLOG-EBG algorithm for explanation-based learning.
This document provides an introduction to machine learning and inductive inference. It discusses what machine learning is, common learning tasks like concept learning and function learning, different data representations, and example applications such as knowledge discovery and building adaptive systems. The course will cover generalizing from specific examples to broader concepts through inductive inference and different learning approaches.
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, maximum likelihood hypotheses, and how Bayesian learning relates to concept learning problems. Bayesian learning allows prior knowledge to be combined with observed data, hypotheses can make probabilistic predictions, and new examples are classified by weighting multiple hypotheses by their probabilities. While computationally intensive, Bayesian methods provide an optimal standard for decision making.
The document discusses the theoretical framework of computational learning theory and PAC (Probably Approximately Correct) learning. It defines what makes a learning problem PAC learnable and examines how the number of training examples needed for learning is affected by factors like the hypothesis space size, error tolerance, and confidence level. Key questions addressed include determining learnability of problem classes and bounding the sample complexity of learning algorithms.
Slide explaining the distinction between bagging and boosting while understanding the bias variance trade-off. Followed by some lesser known scope of supervised learning. understanding the effect of tree split metric in deciding feature importance. Then understanding the effect of threshold on classification accuracy. Additionally, how to adjust model threshold for classification in supervised learning.
Note: Limitation of Accuracy metric (baseline accuracy), alternative metrics, their use case and their advantage and limitations were briefly discussed.
Bayesian learning allows systems to classify new examples based on a model learned from prior examples using probabilities. It reasons by calculating the posterior probability of a hypothesis given new evidence using Bayes' rule. The maximum a posteriori (MAP) hypothesis that best explains the evidence is selected. Naive Bayes classifiers make a strong independence assumption between attributes. They classify new examples by calculating the posterior probability of each class and choosing the class with the highest value. Overfitting can occur if the learned model is too complex for the data. Model selection aims to avoid overfitting by evaluating models on separate training and test datasets.
Learning can occur through various methods like memorization, being taught directly, learning from examples, induction, and deduction. Rote learning involves simply memorizing information without understanding. Learning from advice involves translating advice from experts into operational rules. Learning from examples involves classifying things without explicit rules by being corrected when wrong. Various learning mechanisms exist, with rote learning being the simplest form of storing information, while learning from examples and analogies requires more complex inference.
The document discusses key concepts in machine learning theory such as sample complexity, computational complexity, and mistake bounds. It focuses on analyzing the performance of broad classes of learning algorithms characterized by their hypothesis space. Specific topics covered include probably approximately correct (PAC) learning, sample complexity for finite vs infinite hypothesis spaces, and mistake bounds for algorithms like HALVING and weighted majority. The goal is to understand how many training examples and computational steps are needed for a learner to converge to a successful hypothesis.
Decision tree learning involves growing a decision tree from training data to predict target variables. The ID3 algorithm uses a top-down greedy search to build decision trees by selecting the attribute at each node that best splits the data, measured by information gain. It calculates information gain for candidate attributes to determine the attribute that provides the greatest reduction in entropy when used to split the data. The attribute with the highest information gain becomes the decision node. The process then recurses on the sublists produced by each branch.
Decision tree learning involves creating a decision tree that classifies examples by sorting them from the root node to a leaf node. Each node tests an attribute and branches correspond to attribute values. Instances are classified by traversing the tree in this way. The ID3 algorithm uses information gain to select the attribute that best splits examples at each node, creating a greedy top-down search through possible trees. It calculates information gain, which measures the expected reduction in entropy (impurity), to determine which attribute best classifies examples at each step.
Bayesian Learning by Dr.C.R.Dhivyaa Kongu Engineering CollegeDhivyaa C.R
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, and maximum likelihood hypotheses. Bayes' theorem allows calculating the posterior probability of a hypothesis given observed data and prior probabilities. The maximum a posteriori hypothesis is the one with the highest posterior probability. Maximum likelihood hypotheses maximize the likelihood of the data. Bayesian learning faces challenges from requiring many initial probabilities and high computational costs but provides a useful perspective on machine learning algorithms.
This document provides an overview of artificial neural networks and the backpropagation algorithm. It discusses how neural networks are inspired by biological neural systems and how they represent problems as interconnected nodes. The backpropagation algorithm is introduced as a way to train multilayer neural networks by calculating error gradients to update weights. An example application of neural network for face recognition is also mentioned. Key aspects of neural network representations, perceptrons, the perceptron training rule, and gradient descent/delta rule for training are summarized.
Combining inductive and analytical learningswapnac12
The document discusses combining inductive and analytical learning methods. Inductive methods like decision trees and neural networks seek general hypotheses based solely on training data, while analytical methods like PROLOG-EBG seek hypotheses based on prior knowledge and training data. The document argues that combining these approaches could overcome their individual limitations by using prior knowledge to guide inductive learning methods. It examines using prior knowledge to initialize hypotheses, alter the search objective, and modify the search operators of inductive learners. As an example, it describes the KBANN algorithm, which initializes a neural network to perfectly fit a domain theory before refining it inductively to the training data.
The document discusses multilayer neural networks and the backpropagation algorithm. It begins by introducing sigmoid units as differentiable threshold functions that allow gradient descent to be used. It then describes the backpropagation algorithm, which employs gradient descent to minimize error by adjusting weights. Key aspects covered include defining error terms for multiple outputs, deriving the weight update rules, and generalizing to arbitrary acyclic networks. Issues like local minima and representational power are also addressed.
Bayesian Learning- part of machine learningkensaleste
This module provides an overview of Bayesian learning methods. It introduces Bayesian reasoning and Bayes' theorem as a probabilistic approach to inference. Key concepts covered include maximum likelihood hypotheses, naive Bayes classifiers, Bayesian belief networks, and the Expectation-Maximization (EM) algorithm. The EM algorithm is described as a method for estimating parameters of probability distributions when some variables are hidden or unobserved.
Bayesian learning uses prior knowledge and observed training data to determine the probability of hypotheses. Each training example can incrementally increase or decrease the estimated probability of a hypothesis. Prior knowledge is provided by assigning initial probabilities to hypotheses and probability distributions over possible observations for each hypothesis. New instances can be classified by combining the predictions of multiple hypotheses, weighted by their probabilities. Even when computationally intractable, Bayesian methods provide an optimal standard for decision making.
The document describes the backpropagation algorithm for training multilayer neural networks. It discusses how backpropagation uses gradient descent to minimize error between network outputs and targets by calculating error gradients with respect to weights. The algorithm iterates over examples, calculates error, computes gradients to update weights. Momentum can be added to help escape local minima. Backpropagation can learn representations in hidden layers and is prone to overfitting without validation data to select the best model.
Using prior knowledge to initialize the hypothesis,kbannswapnac12
1) The KBANN algorithm uses a domain theory represented as Horn clauses to initialize an artificial neural network before training it with examples. This helps the network generalize better than random initialization when training data is limited.
2) KBANN constructs a network matching the domain theory's predictions exactly, then refines it with backpropagation to fit examples. This balances theory and data when they disagree.
3) In experiments on promoter recognition, KBANN achieved a 4% error rate compared to 8% for backpropagation alone, showing the benefit of prior knowledge.
Inductive analytical approaches to learningswapnac12
This document discusses two inductive-analytical approaches to learning from data: 1) minimizing errors between a hypothesis and training examples as well as errors between the hypothesis and domain theory, with weights determining the importance of each, and 2) using Bayes' theorem to calculate the posterior probability of a hypothesis given the data and prior knowledge. It also describes three ways prior knowledge can alter a hypothesis space search: using prior knowledge to derive the initial hypothesis, alter the search objective to fit the data and theory, and alter the available search steps.
Mining single dimensional boolean association rules from transactionalramya marichamy
The document discusses mining frequent itemsets and generating association rules from transactional databases. It introduces the Apriori algorithm, which uses a candidate generation-and-test approach to iteratively find frequent itemsets. Several improvements to Apriori's efficiency are also presented, such as hashing techniques, transaction reduction, and approaches that avoid candidate generation like FP-trees. The document concludes by discussing how Apriori can be applied to answer iceberg queries, a common operation in market basket analysis.
The document discusses analytical learning methods like explanation-based learning. It explains that analytical learning uses prior knowledge and deductive reasoning to augment training examples, allowing it to generalize better than methods relying solely on data. Explanation-based learning analyzes examples according to prior knowledge to infer relevant features. The document provides examples of using explanation-based learning to learn chess concepts and safe stacking of objects. It also describes the PROLOG-EBG algorithm for explanation-based learning.
This document provides an introduction to machine learning and inductive inference. It discusses what machine learning is, common learning tasks like concept learning and function learning, different data representations, and example applications such as knowledge discovery and building adaptive systems. The course will cover generalizing from specific examples to broader concepts through inductive inference and different learning approaches.
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, maximum likelihood hypotheses, and how Bayesian learning relates to concept learning problems. Bayesian learning allows prior knowledge to be combined with observed data, hypotheses can make probabilistic predictions, and new examples are classified by weighting multiple hypotheses by their probabilities. While computationally intensive, Bayesian methods provide an optimal standard for decision making.
The document discusses the theoretical framework of computational learning theory and PAC (Probably Approximately Correct) learning. It defines what makes a learning problem PAC learnable and examines how the number of training examples needed for learning is affected by factors like the hypothesis space size, error tolerance, and confidence level. Key questions addressed include determining learnability of problem classes and bounding the sample complexity of learning algorithms.
Slide explaining the distinction between bagging and boosting while understanding the bias variance trade-off. Followed by some lesser known scope of supervised learning. understanding the effect of tree split metric in deciding feature importance. Then understanding the effect of threshold on classification accuracy. Additionally, how to adjust model threshold for classification in supervised learning.
Note: Limitation of Accuracy metric (baseline accuracy), alternative metrics, their use case and their advantage and limitations were briefly discussed.
Bayesian learning allows systems to classify new examples based on a model learned from prior examples using probabilities. It reasons by calculating the posterior probability of a hypothesis given new evidence using Bayes' rule. The maximum a posteriori (MAP) hypothesis that best explains the evidence is selected. Naive Bayes classifiers make a strong independence assumption between attributes. They classify new examples by calculating the posterior probability of each class and choosing the class with the highest value. Overfitting can occur if the learned model is too complex for the data. Model selection aims to avoid overfitting by evaluating models on separate training and test datasets.
Learning can occur through various methods like memorization, being taught directly, learning from examples, induction, and deduction. Rote learning involves simply memorizing information without understanding. Learning from advice involves translating advice from experts into operational rules. Learning from examples involves classifying things without explicit rules by being corrected when wrong. Various learning mechanisms exist, with rote learning being the simplest form of storing information, while learning from examples and analogies requires more complex inference.
The document discusses key concepts in machine learning theory such as sample complexity, computational complexity, and mistake bounds. It focuses on analyzing the performance of broad classes of learning algorithms characterized by their hypothesis space. Specific topics covered include probably approximately correct (PAC) learning, sample complexity for finite vs infinite hypothesis spaces, and mistake bounds for algorithms like HALVING and weighted majority. The goal is to understand how many training examples and computational steps are needed for a learner to converge to a successful hypothesis.
Decision tree learning involves growing a decision tree from training data to predict target variables. The ID3 algorithm uses a top-down greedy search to build decision trees by selecting the attribute at each node that best splits the data, measured by information gain. It calculates information gain for candidate attributes to determine the attribute that provides the greatest reduction in entropy when used to split the data. The attribute with the highest information gain becomes the decision node. The process then recurses on the sublists produced by each branch.
Decision tree learning involves creating a decision tree that classifies examples by sorting them from the root node to a leaf node. Each node tests an attribute and branches correspond to attribute values. Instances are classified by traversing the tree in this way. The ID3 algorithm uses information gain to select the attribute that best splits examples at each node, creating a greedy top-down search through possible trees. It calculates information gain, which measures the expected reduction in entropy (impurity), to determine which attribute best classifies examples at each step.
1. The document describes the C4.5 algorithm for building decision trees from a set of training data. It involves choosing attributes that best differentiate the training instances and creating tree nodes with child links for each attribute value.
2. It then discusses concepts like entropy, information gain, and using information gain to select the optimal attribute to test at each node.
3. The document provides a weather data example to illustrate how a decision tree is constructed recursively using these concepts.
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.
The document discusses decision tree learning and the ID3 algorithm. It covers topics like decision tree representation, entropy and information gain for selecting attributes, overfitting, and techniques to avoid overfitting like reduced error pruning. It also discusses handling continuous values, missing data, and attributes with many values or costs in decision tree learning.
Classifiers are algorithms that map input data to categories in order to build models for predicting unknown data. There are several types of classifiers that can be used including logistic regression, decision trees, random forests, support vector machines, Naive Bayes, and neural networks. Each uses different techniques such as splitting data, averaging predictions, or maximizing margins to classify data. The best classifier depends on the problem and achieving high accuracy, sensitivity, and specificity.
Decision trees are a supervised learning method that represents concepts as decision trees to classify data. The algorithm works by selecting the best attribute to test at each node using information gain, which measures the reduction in entropy from partitioning data by an attribute. It builds the tree in a top-down greedy manner, recursively selecting the attribute that best splits the data until the leaf nodes are pure or no further information gain is possible. The tree can then be converted to classification rules by tracing paths from the root to leaf nodes.
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.
Machine learning basics using trees algorithm (Random forest, Gradient Boosting)Parth Khare
This document provides an overview of machine learning classification and decision trees. It discusses key concepts like supervised vs. unsupervised learning, and how decision trees work by recursively partitioning data into nodes. Random forest and gradient boosted trees are introduced as ensemble methods that combine multiple decision trees. Random forest grows trees independently in parallel while gradient boosted trees grow sequentially by minimizing error from previous trees. While both benefit from ensembling, gradient boosted trees are more prone to overfitting and random forests are better at generalizing to new data.
EFFECTIVENESS PREDICTION OF MEMORY BASED CLASSIFIERS FOR THE CLASSIFICATION O...cscpconf
Classification is a step by step practice for allocating a given piece of input into any of the given
category. Classification is an essential Machine Learning technique. There are many
classification problem occurs in different application areas and need to be solved. Different
types are classification algorithms like memory-based, tree-based, rule-based, etc are widely
used. This work studies the performance of different memory based classifiers for classification
of Multivariate data set from UCI machine learning repository using the open source machine
learning tool. A comparison of different memory based classifiers used and a practical
guideline for selecting the most suited algorithm for a classification is presented. Apart fromthat some empirical criteria for describing and evaluating the best classifiers are discussed
The document discusses decision tree algorithms. It begins with an introduction and example, then covers the principles of entropy and information gain used to build decision trees. It provides explanations of key concepts like entropy, information gain, and how decision trees are constructed and evaluated. Examples are given to illustrate these concepts. The document concludes with strengths and weaknesses of decision tree algorithms.
The document discusses decision tree algorithms. It begins with an introduction and example, then covers the principles of entropy and information gain used to build decision trees. It provides explanations of key concepts like evaluating decision trees using training and testing accuracy. The document concludes with strengths and weaknesses of decision tree algorithms.
The document discusses machine learning decision trees and the ID3 algorithm for constructing decision trees from training data. ID3 is a top-down, greedy search algorithm that uses information gain to select the attribute that best splits the training examples at each node, without backtracking. It recursively builds the tree by creating child nodes for each value of the selected attribute, then applies the same process to partition the examples at each child node.
The document discusses machine learning and various related concepts. It provides an overview of machine learning, including well-posed learning problems, designing learning systems, supervised learning, and different machine learning approaches. It also discusses specific machine learning algorithms like naive Bayes classification and decision tree learning.
The document discusses concepts related to supervised machine learning and decision tree algorithms. It defines key terms like supervised vs unsupervised learning, concept learning, inductive bias, and information gain. It also describes the basic process for learning decision trees, including selecting the best attribute at each node using information gain to create a small tree that correctly classifies examples, and evaluating performance on test data. Extensions like handling real-valued, missing and noisy data, generating rules from trees, and pruning trees to avoid overfitting are also covered.
This is the most simplest and easy to understand ppt. Here you can define what is decision tree,information gain,gini impurity,steps for making decision tree there pros and cons etc which will helps you to easy understand and represent it.
The document discusses decision trees, which classify data by recursively splitting it based on attribute values. It describes how decision trees work, including building the tree by selecting the attribute that best splits the data at each node. The ID3 algorithm and information gain are discussed for selecting the splitting attributes. Pruning techniques like subtree replacement and raising are covered for reducing overfitting. Issues like error propagation in decision trees are also summarized.
Research scholars evaluation based on guides view using id3eSAT Journals
Abstract Research Scholars finds many problems in their Research and Development activities for the completion of their research work in universities. This paper gives a proficient way for analyzing the performance of Research Scholar based on guides and experts feedback. A dataset is formed using this information. The outcome class attribute will be in view of guides about the scholars. We apply decision tree algorithm ID3 on this dataset to construct the decision tree. Then the scholars can enter the testing data that has comprised with attribute values to get the view of guides for that testing dataset. Guidelines to the scholar can be provided by considering this constructed tree to improve their outcomes.
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.
The document provides an overview of machine learning concepts including training, rote learning, concept learning, hypotheses, general to specific ordering, version spaces, candidate elimination, inductive bias, decision tree induction, overfitting, the nearest neighbor algorithm, neural networks, supervised learning, unsupervised learning, and reinforcement learning. It discusses how machine learning systems are trained using classified data and how different algorithms like concept learning, decision trees, nearest neighbors and neural networks can be used to classify new unlabeled data.
Formal Languages and Automata Theory unit 5Srimatre K
This document summarizes key concepts from Unit 5, including types of Turing machines, undecidability, recursively enumerable languages, Post's correspondence problem, and counter machines. It defines undecidable problems as those with no algorithm to solve them. Examples of undecidable problems include the halting problem and determining if a Turing machine accepts a language that is not recursively enumerable. Post's correspondence problem and its modified version are presented with examples. Recursively enumerable languages are defined and properties like concatenation, Kleene closure, union, and intersection are described. Counter machines are defined as having states, input alphabet, start/final states, and transitions that allow incrementing, decrementing, and checking if a
Formal Languages and Automata Theory unit 4Srimatre K
The document discusses various topics related to context-free grammars including:
1. Normal forms like Chomsky normal form and Greibach normal form that put constraints on the structure of productions in a context-free grammar.
2. The pumping lemma for context-free languages and how it can be used to prove that a language is not context-free.
3. Closure properties of context-free languages like their closure under union, concatenation and Kleene star but not under intersection and complement.
4. Decision properties of context-free languages and how questions of emptiness, membership and finiteness can be solved.
5. An introduction to Turing machines as accepting devices for recursively enumerable
Formal Languages and Automata Theory unit 3Srimatre K
This document provides an overview of context-free grammars and pushdown automata. It begins with definitions and examples of context-free grammars, including their components, derivations, parse trees, ambiguity, and applications. It then covers pushdown automata, defining them as finite state machines with a stack. It discusses the two types of acceptability in PDAs - final state and empty stack acceptability. Examples of languages recognized by PDAs are provided. The document concludes with how to convert between context-free grammars and pushdown automata, including examples of converting a CFG to a PDA and vice versa. It also briefly discusses deterministic pushdown automata.
Formal Languages and Automata Theory unit 2Srimatre K
This document provides information about regular expressions and finite automata. It includes:
1. A syllabus covering regular expressions, applications of regular expressions, algebraic laws, conversion of automata to expressions, and the pumping lemma.
2. Details of regular expressions including operators, precedence, applications, and algebraic laws.
3. How to convert between finite automata and regular expressions using Arden's theorem and state elimination methods.
4. Properties of regular languages including closure properties and how regular languages satisfy the pumping lemma.
Formal Languages and Automata Theory Unit 1Srimatre K
The document describes the minimization of a deterministic finite automaton (DFA) using the equivalence theorem. It involves partitioning the states into sets where states in the same set are indistinguishable based on their transitions. The initial partition P0 separates final and non-final states. Subsequent partitions P1, P2, etc. further split sets if states within are distinguishable. The process stops when the partition no longer changes, resulting in the minimized DFA with states merged within each final set. An example application of the steps to a 6-state DFA is also provided.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
2. INTRODUCTION
Decision tree learning is a method for approximating
discrete-valued target functions, in which the learned
function is represented by a decision tree.
Learned trees can also be re-represented as sets of if-then
rules to improve human readability
3. DECISION TREE
REPRESENTATION
Decision trees classify instances by sorting them down the
tree from the root to some leaf node, which provides the
classification of the instance.
Each node in the tree specifies a test of some attribute of
the instance, and each branch descending from that node
corresponds to one of the possible values for this attribute.
4. Decision tree for the concept
PlayTennis.
Decision tree corresponds to the expression
(Outlook = Sunny Humidity = Normal)
V (Outlook = Overcast)
V (Outlook = Rain Wind = Weak)
5. For example, the instance
(Outlook = Sunny, Temperature = Hot, Humidity =
High, Wind = Strong)
The tree predicts that PlayTennis = no
6. APPROPRIATE PROBLEMS FOR DECISION
TREE LEARNING
Instances are represented by attribute-value pairs.
The target function has discrete output values.
Disjunctive descriptions may be required.
The training data may contain errors.
The training data may contain missing attribute values.
7. APPLICATIONS
Many practical problems have been found to fit these
characteristics.
Decision tree learning has therefore been applied to
problems such as learning to classify medical patients by
their disease, equipment malfunctions by their cause, and
loan applicants by their likelihood of defaulting on
payments.
Such problems, in which the task is to classify examples
into one of a discrete set of possible categories, are often
referred to as classification problems.
8. THE BASIC DECISION TREE
LEARNING ALGORITHM
Most algorithms that have been developed for learning
decision trees are variations on a core algorithm that
employs a top-down, greedy search through the space of
possible decision trees.
This approach is exemplified by the ID3(Iterative
Dichotomiser3) algorithm (Quinlan 1986) and its
successor C4.5 (Quinlan 1993).
9. Our basic algorithm, ID3(Iterative Dichotomiser3), learns
decision trees by constructing them topdown, beginning
with the question "which attribute should be tested at the
root of the tree?”
The best attribute is selected and used as the test at the
root node of the tree. A descendant of the root node is then
created for each possible value of this attribute, and the
training examples are sorted to the appropriate descendant
node.
10. The entire process is then repeated using
the training examples associated with
each descendant node to select the best
attribute to test at that point in the tree.
This forms a greedy search for an
acceptable decision tree, in which the
algorithm never backtracks to reconsider
earlier choices.
11. Which Attribute Is the Best
Classifier?
The statistical property, called information gain, that
measures how well a given attribute separates the training
examples according to their target classification.
ID3(Iterative Dichotomiser3) uses this information gain
measure to select among the candidate attributes at each
step while growing the tree.
12. ENTROPY MEASURES HOMOGENEITY OF
EXAMPLES
To define Information Gain, first need to know about the
information theory called entropy S.
It characterizes the impurity of an arbitrary collection of
examples.
13. In given collection ,containing positive and negative
examples of some target concept, the entropy of S relative
to this boolean classification is
where p is the proportion of positive examples in S and p
is the proportion of negative examples in S. In all
calculations involving entropy we define 0 log 0 to be 0.
14. For example, if all members are positive
(p+ve = I), then p-ve is 0, and
Entropy(S) =-1 . log2(1) - 0 . log2 0
= -1 . 0 - 0 . log2 0 = 0.
Note the entropy is 1 when the collection contains an
equal number of positive and negative examples. If the
collection contains unequal numbers of positive and
negative examples, the entropy is between 0 and 1.
15. suppose S is a collection of 14 examples of some Boolean
concept, including 9 positive and 5 negative examples (we
adopt the notation[9+, 5-] to summarize such a sample of
data). Then the entropy of S relative to
this Boolean classification is
16. The entropy function relative to a boolean
classification, as the proportion, p+ve, of
positive examples varies p-ve between 0 and 1.
17. More generally, if the target attribute can take on c
different values, then the entropy of S relative to this c-
wise classification is defined as
where pi is the proportion of S belonging to class i.
Note the logarithm is still base 2 because entropy is a
measure of the expected encoding length measured in bits.
Note also that if the target attribute can take on c possible
values, the entropy can be as large as log2 c.
18. INFORMATION GAIN MEASURES THE
EXPECTED REDUCTION IN ENTROPY
The entropy as a measure of the impurity in a collection of
training examples, we can now define a measure of the
effectiveness of an attribute in classifying the training data.
19. The Information gain, is simply the expected reduction in
entropy caused by partitioning the examples according to
this attribute. More precisely, the information gain,
Gain(S, A) of an attribute A, relative to a collection of
examples S, is defined as
where Values(A) is the set of all possible values for
attribute A, and S, is the subset of S for which attribute A
has value v
21. Gain(S, A) gives the expected reduction in entropy caused
by knowing the value of attribute.
For example, suppose S is a collection of training-example
days described by attributes including Wind, which can
have the values Weak or Strong. As before, assume S is a
collection containing 14 examples, [9+, 5-]. Of these 14
examples,
suppose 6 of the positive and 2 of the negative examples
have Wind = Weak, and the remainder have Wind =
Strong. The information gain due to sorting the original 14
examples by the attribute Wind may then be calculated as
25. ID3 determines the information gain for each
candidate attribute (i.e., Outlook, Temperature,
Humidity, and Wind).
The information gain values for all four attributes are
Gain(S, Outlook) = 0.246
Gain(S, Humidity) = 0.151
Gain(S, Wind) = 0.048
Gain(S, Temperature) = 0.029
26. According to the information gain measure, the Outlook
attribute provides the best prediction of the target
attribute, PlayTennis, over the training examples.
Therefore, Outlook is selected as the decision attribute
for the root node, and branches are created below the root
for each of its possible values (i.e.,Sunny, Overcast, and
Rain).
This process continues for each new leaf node until either
of two conditions is met: (1) every attribute has already
been included along this path through the tree, or (2) the
training examples associated with this leaf node all have
the same target attribute value (i.e., their entropy is zero).
30. HYPOTHESIS SPACE SEARCH IN
DECISION TREE LEARNING
ID3 can be characterized as searching a space of
hypotheses for one that fits the training examples.
The hypothesis space searched by ID3 is the set of
possible decision trees.
ID3 performs a simple-to complex, hill-climbing search
through this hypothesis space, beginning with the empty
tree, then considering progressively more elaborate
hypotheses in search of a decision tree that correctly
classifies the training data.
The evaluation function that guides this hill-climbing
search is the information gain measure.
31.
32. ID3 capabilities and limitations in search
space & search strategy
ID3 hypothesis space of all decision trees is a complete
space of finite discrete-valued functions, relative to the
available attributes.
ID3 maintains only a single current hypothesis as it
searches through the space of decision trees.
ID3 in its pure form performs no backtracking in its
search.
33. ID3 uses all training examples at each step in the
search to make statistically based decisions
regarding how to refine its current hypothesis.
Advantage of using statistical properties of all the
examples (e.g., information gain) is that the
resulting search is much less sensitive to errors in
individual training examples.
ID3 can be easily extended to handle noisy
training data by modifying its termination
criterion to accept hypotheses that imperfectly fit
the training data.
34. INDUCTIVE BIAS IN DECISION TREE
LEARNING
Inductive bias is the set of assumptions that,
together with the training data, deductively justify
the classifications assigned by the learner to future
instances.
Describing the inductive bias of ID3 therefore
consists of describing the basis by which it
chooses one of these consistent hypotheses over
the all possible decision trees.
35. Approximate inductive bias of ID3: Shorter trees
are preferred over larger trees it uses
BFS(Breadth First Search).
A closer approximation to the inductive bias of
ID3: Trees that place high information gain
attributes close to the root are preferred over those
that do not.
36. Restriction Biases and Preference Biases
ID3 searches a complete hypothesis space , from simple to
complex hypotheses, until its termination condition is met.
Its hypothesis space introduces no additional bias.
The version space CANDIDATE-ELIMINATION algorithm
searches an incomplete hypothesis.
It searches this space completely, finding every hypothesis
consistent with the training data. Its inductive bias is solely a
consequence of the expressive power of its hypothesis
representation.
Its search strategy introduces no additional bias
37. The inductive bias of ID3 follows from its search strategy,
whereas the inductive bias of the CANDIDATE-
ELIMINATION algorithm follows from the definition of its
search space.
The inductive bias of ID3 is thus a preference for certain
hypotheses over others (e.g., for shorter hypotheses). This form
of bias is typically called a preference bias (or, a search bias).
In contrast, the bias of the CANDIDAT-EELIMINATION
algorithm is in the form of a categorical restriction on the set
of hypotheses considered. This form of bias is typically called a
restriction bias (or, a language bias).
38. Why Prefer Short Hypotheses?
William of Occam was one of the first to discuss the
question, around the year 1320, so this bias often goes by
the name of Occam's razor.
Occam's razor: “Prefer the simplest hypothesis that fits
the data”.
It is the problem solving principle that the simplest
solution tends to be the right one.
When presented with competing hypothesis to solve a
problem, one should select a solution with the fewest
assumptions.
Shorter hypothesis fits the training data which are less
likely to be consist training data.
39. ISSUES IN DECISION TREE LEARNING
1.Avoiding Over fitting the Data
Reduced error pruning.
Rule post –pruning.
2. Incorporating Continuous-Valued Attributes.
3. Alternatively Measures for Selecting Attributes.
4. Handling Training Examples with Missing Attributes
Values.
5. Handling Attributes with Differing Costs.
40. ISSUES IN DECISION TREE LEARNING
Avoiding Overfitting the Data:
Definition: Given a hypothesis space H, a
hypothesis h H is said to overfit the training data
if there exists some alternative hypothesis h' H,
such that h has smaller error than h' over the
training examples, but h' has a smaller error than h
over the entire distribution of instances.
41. The impact of overfitting in a typical application of
decision tree learning. In this case, the ID3 algorithm is
applied to the task of learning which medical patients
have a form of diabetes.
42. There are several approaches to avoiding over fitting in
decision tree learning.
These can be grouped into two classes:
1.Approaches that stop growing the tree earlier, before it
reaches the point where it perfectly classifies the
training data.
2. Approaches that allow the tree to overfit the data, and
then post-prune the tree.
43. To determine the correct final tree size. Approaches include:
Use a separate set of examples, distinct from the training examples, to
evaluate the utility of post-pruning nodes from the tree.
Use all the available data for training, but apply a statistical test to estimate
whether expanding (or pruning) a particular node is likely to produce an
improvement beyond the training set. For example, Quinlan (1986) uses a
chi-square test to estimate whether further expanding a node is likely to
improve performance over the entire instance distribution, or only on the
current sample of training data.
Use an explicit measure of the complexity for encoding the training
examples and the decision tree, halting growth of the tree when this
encoding size is minimized. This approach, based on a heuristic called the
Minimum Description Length principle, as well as in Quinlan and Rivest
(1989) and Mehta et al. (199.5).
44. The available data are separated into 2 sets of examples: a
training set, which is used to form the learned hypothesis, and
a separate validation set, which is used to evaluate the accuracy
of this hypothesis over subsequent data and , in particular, to
evaluate the impact of pruning this hypothesis.
Withhold one-third of the available ex. for the validation set,
using the other two-thirds for training.
45. REDUCED ERROR PRUNING
One approach, called reduced-error pruning (Quinlan
1987), is to consider each of the decision
nodes in the tree to be candidates for pruning. Pruning a
decision node consists of removing the subtree rooted at
that node, making it a leaf node, and assigning it the most
common classification of the training examples affiliated
with that node.
Nodes are removed only if the resulting pruned tree
performs no worse than-the original over the validation
set.
46. As pruning proceeds, the number of nodes is reduced and accuracy over
the test set increases. Here, the available data has been split into three
subsets: the training examples, the validation examples used for pruning
the tree, and a set of test examples used to provide an unbiased estimate
of accuracy over future unseen examples.
47. The major drawback of this approach is that when
data is limited, withholding part of it for the
validation set reduces even further the number of
examples available for training.
48. RULE POST-PRUNING
One quite successful method for finding high accuracy
hypotheses is a technique we shall call rule post-
pruning.
1. Infer the decision tree from the training set, growing
the tree until the training data is fit as well as possible
and allowing over-fitting to occur.
2. Convert the learned tree into an equivalent set of
rules by creating one rule for each path from the root
node to a leaf node.
49. 3. Prune (generalize) each rule by removing any preconditions
that result in improving its estimated accuracy.
4. Sort the pruned rules by their estimated accuracy, and consider
them in this sequence when classifying subsequent instances.
In rule post pruning, one rule is generated for each leaf node in
the tree. Each attribute test along the path from the root to the
leaf becomes a rule antecedent (precondition) and the
classification at the leaf node becomes the rule consequent
(post condition).
50. Convert the decision tree to rules before
pruning has 3 main advantages.
Converting to rules allows distinguishing among the different
contexts in which a decision node is used. Because each
distinct path through the decision tree node produces a distinct
rule, the pruning decision regarding that attribute test can be
made differently for each path. In contrast, if the tree itself
were pruned, the only two choices would be to remove the
decision node completely, or to retain it in its original form.
Converting to rules removes the distinction between attribute
tests that occur near the root of the tree and those that occur
near the leaves. Thus, we avoid messy bookkeeping issues such
as how to reorganize the tree if the root node is pruned while
retaining part of the subtree below this test.
Converting to rules improves readability. Rules are often easier
for to understand.
51. 2.Incorporating Continuous-Valued Attributes
ID3 restrictions to attributes:
First, the target attribute whose value is predicted by the
learned tree must be discrete valued. Second, the attributes
tested in the decision nodes of the tree must also be discrete
valued.
Dynamically defining new discrete valued attributes that
partition the continuous attribute value into a discrete set of
intervals.
A that is continuous-valued, the algorithm can dynamically
create a new boolean attribute A, that is true if A < c and false
otherwise.
52. PlayTennis Ex. With possible temperatures.
These candidate thresholds can then be evaluated by computing the
information gain associated with each.
In the current example, there are two candidate thresholds,
corresponding to the values of Temperature at which the value of
PlayTennis changes: (48 + 60)/2 and (80 + 90)/2.
The information gain can then be computed for each of the candidate
attributes, (Temperature >54) and (Temperature > 85 )the best can
be selected (Temperature > 54). This dynamically created Boolean
attribute can then compete with the other discrete-valued candidate
attributes available for growing the decision tree.
53. 3. Alternative Measures for Selecting
Attributes
Selecting few attributes with information gain will give very
poor prediction over unseen instances. Ex. Date attribute to
construct decision tree give depth with 1 level classification.
One way to avoid this difficulty is to select decision attributes
based on some measure other than information gain. One
alternative measure that has been used successfully is the gain
ratio (Quinlan 1986). The gain ratio measure penalizes
attributes such as Date by incorporating a term, called split
information, that is sensitive to how broadly and uniformly the
attribute splits the data:
54. where S1 through S, are the c subsets of examples resulting
from partitioning S by the c-valued attribute A.
The Gain Ratio measure is defined in terms of the earlier Gain
measure, as well as this Splitlnformation, as follows
The Splitlnformation term discourages the selection of
attributes with many uniformly distributed values.
If attributes A and B produce the same information gain,
then clearly B will score higher according to the Gain Ratio
measure.
55. 4.Handling Training Examples with
Missing Attribute Values
Consider the situation in which Gain(S, A) is to be calculated at node n
in the decision tree to evaluate whether the attribute A is the best
attribute to test at this decision node. Suppose that (x, c(x)) is one of
the training examples in S and that the value A(x) is unknown.
One strategy for dealing with the missing attribute value is to assign it
the value that is most common among training examples at node n.
Alternatively, we might assign it the most common value among
examples at node n that have the classification c(x). The elaborated
training example using this estimated value for A(x) can then be used
directly by the existing decision tree learning algorithm. This strategy
is examined by Mingers (1989a).
56. A second, more complex procedure is to assign a
probability to each of the possible values of A
rather than simply assigning the most common
value to A(x).
These probabilities can be estimated again based
on the observed frequencies of the various values
for A among the examples at node n.
57. 5.Handling Attributes with Differing
Costs
Handling Attributes with Differing Costs.
ID3 can be modified to take into account attribute
costs by introducing a cost term into the attribute
selection measure.
For example, we might divide the Gain by the cost of
the attribute, so that lower-cost attributes would be
preferred. While such cost-sensitive measures do not
guarantee finding an optimal cost-sensitive decision
tree, they do bias the search in favor of low-cost
attributes.
58. Attribute cost is measured by the number of seconds
required to obtain the attribute value by positioning
and operating the sonar. They demonstrate that more
efficient recognition strategies are learned, without
sacrificing classification accuracy, by replacing the
information gain attribute selection measure by the
following measure
59. Nunez (1988) describes a related approach and its
application to learning medical diagnosis rules. Here the
attributes are different symptoms and laboratory tests with
differing costs. His system uses a somewhat different
attribute selection measure
where w [0, 1] is a constant that determines the relative
importance of cost versus information gain. Nunez (1991)
presents an empirical comparison of these two approaches
over a range of tasks.