Questions and Answers
What does the term 'entropy' refer to in the context of decision trees?
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 __________.
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Match the following tree structures with their descriptions:
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Which feature selection criterion is often preferred in decision tree algorithms?
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The construction of decision trees is solely based on training data without any defined criteria.
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Name one advantage of using decision trees for classification.
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Which of the following is an advantage of decision trees?
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Random forests improve the predictive performance of individual decision trees by creating multiple models and averaging their outputs.
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What is the primary criterion used in decision tree splitting?
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The algorithm used in random forests to sample data with replacement is called __________.
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Match the following terms related to decision trees:
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Which statement about decision trees is true?
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Decision trees only create vertical splits based on feature values.
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Which of the following is a characteristic of decision trees?
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Decision trees classify a sample by following a sequence of questions.
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What is the main purpose of feature selection in decision tree construction?
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In a binary decision tree, each node selects a left or right branch based on whether the feature value is below or above a __________.
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Match the following terms related to decision trees with their definitions:
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What is a disadvantage of using decision trees?
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The choice of priors in Bayesian decision theory is objective and based on empirical evidence.
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What happens to the correlation and strength of trees when the parameter 𝑚 is reduced?
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Increasing the strength of individual trees generally decreases the overall forest error rate.
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List one advantage of using random forests over traditional decision trees.
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In random forests, the majority vote of all trees determines the random forest __________.
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Match the type of error with its explanation regarding random forests.
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What is a common application of random forests mentioned?
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Random forests require feature selection when dealing with thousands of input features.
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What is the effect of reducing the correlation between trees in a random forest?
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Random forests work effectively with missing values due to their __________ nature.
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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
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Pros:
- Simple and intuitive approach.
- Accounts for uncertainties in data.
- Allows integration of new information with existing knowledge.
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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
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Pros:
- Interpretable and easy to understand.
- Handles both numerical and categorical data.
- Robust against outliers and missing values.
- Provides feature importance for selection.
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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
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Pros:
- High accuracy compared to traditional methods.
- Efficient with large datasets and many input features.
- Effectively manages missing values.
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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!