COMP9517 Pattern Recognition Part 1
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Questions and Answers

What does the term 'entropy' refer to in the context of decision trees?

  • The evaluation of the tree's accuracy
  • The total number of nodes in a decision tree
  • The amount of information each event contains
  • The measure of uncertainty or disorder in a set of events (correct)

    • Information Gain is a criterion used to define the optimality of decision trees.

    True

    What is the primary purpose of using measures from information theory in decision tree construction?

    To evaluate the optimality of the tree's structure.

    In a decision tree, the criterion for optimality is often based on __________.

    <p>entropy</p> Signup and view all the answers

    Match the following tree structures with their descriptions:

    <p>Binary Tree = A tree where each node has at most two children Decision Tree = A flowchart-like structure used for decision making General Tree = A tree structure with no restrictions on the number of children per node Trie = A specialized tree used for storing associative data structures</p> Signup and view all the answers

    Which feature selection criterion is often preferred in decision tree algorithms?

    <p>Entropy</p> Signup and view all the answers

    The construction of decision trees is solely based on training data without any defined criteria.

    <p>False</p> Signup and view all the answers

    Name one advantage of using decision trees for classification.

    <p>They are easy to interpret and visualize.</p> Signup and view all the answers

    Which of the following is an advantage of decision trees?

    <p>Can handle both numerical and categorical data</p> Signup and view all the answers

    Random forests improve the predictive performance of individual decision trees by creating multiple models and averaging their outputs.

    <p>True</p> Signup and view all the answers

    What is the primary criterion used in decision tree splitting?

    <p>Information Gain</p> Signup and view all the answers

    The algorithm used in random forests to sample data with replacement is called __________.

    <p>bagging</p> Signup and view all the answers

    Match the following terms related to decision trees:

    <p>Overfitting = When a model learns noise from training data and performs poorly on unseen data Feature Bagging = Selecting a random subset of features at each split Greedy Algorithm = Makes a series of decisions to find a locally optimal solution Entropy = Measures the impurity of a set of data</p> Signup and view all the answers

    Which statement about decision trees is true?

    <p>They provide information on the importance of features.</p> Signup and view all the answers

    Decision trees only create vertical splits based on feature values.

    <p>True</p> Signup and view all the answers

    Which of the following is a characteristic of decision trees?

    <p>Leaf nodes contain the class labels.</p> Signup and view all the answers

    Decision trees classify a sample by following a sequence of questions.

    <p>True</p> Signup and view all the answers

    What is the main purpose of feature selection in decision tree construction?

    <p>To identify features that create the best classification tree.</p> Signup and view all the answers

    In a binary decision tree, each node selects a left or right branch based on whether the feature value is below or above a __________.

    <p>threshold</p> Signup and view all the answers

    Match the following terms related to decision trees with their definitions:

    <p>Node = Represents a decision point or a feature in the tree Leaf Node = Contains the class label or classification result Threshold = A value used to split the data Branch = Connects nodes and defines the relationship between decisions</p> Signup and view all the answers

    What is a disadvantage of using decision trees?

    <p>They are computationally expensive.</p> Signup and view all the answers

    The choice of priors in Bayesian decision theory is objective and based on empirical evidence.

    <p>False</p> Signup and view all the answers

    What happens to the correlation and strength of trees when the parameter 𝑚 is reduced?

    <p>Correlation decreases, strength decreases</p> Signup and view all the answers

    Increasing the strength of individual trees generally decreases the overall forest error rate.

    <p>True</p> Signup and view all the answers

    List one advantage of using random forests over traditional decision trees.

    <p>High accuracy or efficiently handles large datasets.</p> Signup and view all the answers

    In random forests, the majority vote of all trees determines the random forest __________.

    <p>prediction</p> Signup and view all the answers

    Match the type of error with its explanation regarding random forests.

    <p>Correlation error = Increased correlation between trees increases the forest error rate Strength error = Weak trees contribute to a higher forest error rate Overfitting error = Complex models fit training data too closely, harming performance on new data Interpretation error = Random forests are less interpretable than individual decision trees</p> Signup and view all the answers

    What is a common application of random forests mentioned?

    <p>Predicting Alzheimer’s disease</p> Signup and view all the answers

    Random forests require feature selection when dealing with thousands of input features.

    <p>False</p> Signup and view all the answers

    What is the effect of reducing the correlation between trees in a random forest?

    <p>It leads to better generalization.</p> Signup and view all the answers

    Random forests work effectively with missing values due to their __________ nature.

    <p>robust</p> Signup and view all the answers

    Study Notes

    Bayesian Decision Theory

    • Probabilities ( p(x|c_i) ) and ( p(c_i) ) can be estimated from samples.
    • For parametric models, parameters can be learned from samples.
    • A normal distribution may describe a class, with known covariance matrix ( \Sigma ) and unknown mean ( \mu ).
    • The mean can be estimated as the average of labeled training samples: ( \hat{\mu} = \bar{x} ).

    Bayesian Decision Rule Classifier

    • Pros:
      • Simple and intuitive approach.
      • Accounts for uncertainties in data.
      • Allows integration of new information with existing knowledge.
    • Cons:
      • Computationally intensive.
      • Selection of prior probabilities can be subjective.

    Decision Trees: Introduction

    • Effective for classification problems with real-valued features and some metric.
    • Handles nominal (categorical) data without natural ordering, e.g., {high, medium, low}.
    • Rules-based methods can classify both nominal and continuous data.

    Decision Trees: Example

    • Example of fish classification using length ( x_1 ) and width ( x_2 ).
    • Decision tree splits based on feature values, leading to classifications of salmon or sea bass.

    Decision Trees: Summary

    • Classification involves a sequence of questions based on feature values.
    • Directed decision tree structure with nodes representing features and leaf nodes containing class labels.
    • Each branching node has child nodes for possible values of the parent feature.

    Decision Trees Construction

    • Binary decision tree structure using a decision function at each node.
    • Each node uses a single feature and threshold for splitting.
    • Multiple valid decision trees may exist for given training samples based on feature selection.
    • Selecting features is aimed at achieving the "best" tree, often preferring smaller trees.

    Decision Trees Construction: Algorithm

    • Utilizes measures from information theory, such as entropy and information gain.

    Constructing Optimal Decision Tree

    • Optimal decision trees are defined based on minimizing entropy measured by: [ H(y) = -\sum_{i=1}^{P} p(y_i) \log p(y_i) ]
    • Decision trees are built iteratively by identifying features offering the highest information gain.

    Decision Trees: Classifier Pros and Cons

    • Pros:
      • Interpretable and easy to understand.
      • Handles both numerical and categorical data.
      • Robust against outliers and missing values.
      • Provides feature importance for selection.
    • Cons:
      • Prone to overfitting.
      • Only permits axis-aligned splits.
      • May not find the globally optimal tree due to greedy nature.

    Ensemble Learning

    • Combines multiple models to enhance predictive performance.
    • Models can vary by using different classifiers, parameters, training examples, or feature sets.

    Random Forests

    • A specific ensemble learning technique that builds multiple decision trees.
    • Classifications are determined by majority voting from all trees.
    • Reduces overfitting associated with single decision trees.

    Random Forests: Breiman’s Algorithm

    • Involves random sampling instances and features to build each decision tree.
    • Trees are constructed to maximum size without pruning.
    • Predictions from trees are aggregated through majority voting.

    Factors Influencing Random Forest Performance

    • Correlation between trees: High correlation may increase error rates.
    • Strength of individual trees: Strong trees have lower error rates.
    • Optimal feature selection parameter ( m ) balances correlation and strength.

    Random Forests: Pros and Cons

    • Pros:
      • High accuracy compared to traditional methods.
      • Efficient with large datasets and many input features.
      • Effectively manages missing values.
    • Cons:
      • Less interpretable than single decision trees.
      • More complex and time-intensive to develop.

    Random Forests: Application

    • Used in predicting Alzheimer’s disease based on features such as cortical thickness.

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    Description

    This quiz covers key concepts in Pattern Recognition, focusing on Bayesian Decision Theory and loss function definitions. Learn how to estimate probabilities and model parameters from empirical data. Get ready to apply these principles in practical scenarios!

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