k-NN Classification Quiz

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Questions and Answers

What is the primary reason for selecting an odd value of k in the k-NN algorithm?

  • To create a balanced classification outcome
  • To increase the number of neighbors considered
  • To ensure computational efficiency
  • To avoid ties between classes during classification (correct)

In a k-NN classification scenario, what happens when a test data-point has an equal number of neighbors from two different classes?

  • The point is assigned a label based on distance to the neighbors
  • A tie-breaker algorithm automatically selects a class
  • The data-point cannot be classified without uncertainty (correct)
  • The test data-point is classified based on arbitrary choice

When applying the k-NN algorithm, what should be the focus for classifying a data-point effectively?

  • Only the nearest training data-points need to be analyzed (correct)
  • Consideration of all training data-points equally
  • Weights should be assigned based on distance to neighbors
  • Only the furthest training data-points should influence classification

What can lead to classification uncertainty in the k-NN algorithm?

<p>Selecting an even k value (C)</p> Signup and view all the answers

What characterizes the predicted label for a test data point when using the k-NN algorithm?

<p>It is the most common label among the nearest neighbors (D)</p> Signup and view all the answers

What is the main purpose of the Gaussian Naive Bayes algorithm?

<p>To classify data points based on probability distributions. (B)</p> Signup and view all the answers

In the context of a linear classifier, what does the sign of the dot-product with the weight vector indicate?

<p>The relative angle between the data point and the weight vector. (A)</p> Signup and view all the answers

When using the K-NN algorithm to classify a new data point, how many distance calculations are required for a dataset of n data points?

<p>All n distances need to be computed. (A)</p> Signup and view all the answers

In a binary classification problem, if the weight vector indicates a negative dot-product for a data point, what label will it likely be assigned?

<p>Negative class label. (C)</p> Signup and view all the answers

What is a key assumption made by Gaussian Naive Bayes regarding the features?

<p>Features are independent given the class label. (D)</p> Signup and view all the answers

What defines the decision boundary in a linear classifier?

<p>The hyperplane formed by the weight vector. (D)</p> Signup and view all the answers

Which of the following is NOT typically a characteristic of Gaussian distribution in classification?

<p>All features must have the same variance. (A)</p> Signup and view all the answers

What is the primary output of applying parameter estimation in Naive Bayes?

<p>Probability estimates for each class. (C)</p> Signup and view all the answers

What is the primary purpose of using parameter estimation in a Naive Bayes algorithm?

<p>To estimate probabilities for classification (C)</p> Signup and view all the answers

Given a binary classification scenario with estimated values of 0.3 for one label, what is the probable threshold for predicting the opposite label?

<p>0.6 (D)</p> Signup and view all the answers

In a k-NN algorithm, what does the 'k' represent?

<p>The number of neighbors to consider for voting (C)</p> Signup and view all the answers

What conclusion can be drawn about the storage requirements of the k-NN algorithm?

<p>It must save the entire dataset for accurate predictions (D)</p> Signup and view all the answers

If a test point is classified without uncertainty as 'red' by a k-NN classifier, what can be concluded about the nearest neighbors?

<p>The nearest neighbors are overwhelmingly of the 'red' class (B)</p> Signup and view all the answers

What is a common misconception regarding the Gaussian distribution in the context of Naive Bayes?

<p>It cannot handle categorical data effectively (B)</p> Signup and view all the answers

When estimating parameters for a feature with three possible values, how many distinct parameters are typically necessary in a Naive Bayes model?

<p>Two parameters (C)</p> Signup and view all the answers

In a binary classification task with 1000 data points, what role does the probability estimate of 0.3 play in deciding the predicted label?

<p>It indicates the likelihood of the label being '0' (B)</p> Signup and view all the answers

Flashcards

K-Nearest Neighbors (k-NN) Algorithm

A classification algorithm that predicts the label of a new data point based on the labels of its k-nearest neighbors in the training data.

Euclidean Distance

A method to measure the distance between two points in a multi-dimensional space. It's calculated by taking the square root of the sum of the squared differences between their coordinates.

k-value for k-NN

The number of nearest neighbors used in the k-NN algorithm to make predictions.

Nearest Neighbors Classification

A classification method that uses the class labels of the neighbors to determine the prediction for unclassified data.

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Predicting a New Point with k-NN

To predict the label of a new data point, find its k-nearest neighbors within the training set using a distance metric (e.g., Euclidean), and use the majority class among those k neighbors as the predicted label.

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Gaussian Naive Bayes

A probabilistic classification algorithm based on Bayes' Theorem, assuming features are independent given the class label and have Gaussian distributions.

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Decision Boundary

The line (or hyperplane in higher dimensions) that separates data points belonging to different classes in a classification model.

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What is ?

The conditional probability of observing a particular feature value given a specific class in Gaussian Naive Bayes.

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What is ?

The mean of a feature distribution for a specific class in Gaussian Naive Bayes.

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What is ?

The standard deviation of a feature distribution for a specific class in Gaussian Naive Bayes.

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Distance Computation in k-NN

Calculating the Euclidean distance between every training data point and a new test point to find its k-nearest neighbors.

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Linear Classifier

A classification model that uses a linear function to separate data points into different classes.

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Dot Product in Linear Classifiers

The inner product of a data point's feature vector and the weight vector of a linear classifier, used to determine its class.

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K-NN Parameter Count

The total number of parameters needed for the k-NN algorithm depends on the number of features and possible values each feature can take. For example, if a feature has 'n' possible values, we need 'n-1' parameters to model it.

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K-NN Memory Requirement

K-NN algorithms require storing the entire training dataset in memory. This is because it needs to calculate distances for each training data point to predict a new data point's label.

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K-NN Algorithm

The k-NN algorithm predicts the label of a new data point by considering the labels of its k-nearest neighbors in the training dataset. This is done by calculating distances from the new point to existing points and picking the k-nearest neighbors.

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K-NN: How to Predict a Label

To predict the label of a test point using k-NN, calculate the distance from the test point to each training point, then find the k nearest neighbors based on those distances. The class that appears most frequently among those k neighbors is the predicted label for the test point.

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Naive Bayes: Feature Dependence

Naive Bayes assumes that all features are independent, meaning that the value of one feature doesn't affect the value of any other feature.

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Naive Bayes: Estimated Probability

The estimated probability of a class label given a feature value is calculated based on the observed frequency of that feature value in the training data for that class.

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Naive Bayes Algorithm

The Naive Bayes algorithm is a probabilistic classification technique that utilizes the independence assumption to calculate the probability of a given class label for a new data point.

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Naive Bayes: Prediction

A new data point is assigned to the class with the highest probability calculated using the Naive Bayes algorithm.

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Study Notes

Graded Assignment Study Notes

  • Question 1: Consider two generative model-based algorithms (Model 1 and Model 2). Model 1's feature occurrences aren't independent of each other, while Model 2 assumes conditional independence of features from the label. Model 1 requires estimating more independent parameters.

  • Question 2: The correct statement(s) about the Naive Bayes algorithm for binary classification with all binary features is (are) that if the probability p is 0 for a label, then p is also 0 for the other label within the same parameter and there are no labeled instances in the training set with a j-th feature value as 1 for a specific label Y.

  • Question 3: For a Naive Bayes model trained on a dataset containing d features with labels 0 and 1, the expression P(y = 1|x) > P(y = 0|x) is sufficient for predicting the label as 1.

  • Question 4: Consider a binary classification dataset that contains only one feature. The data points for label 0 follow a normal distribution with mean 0 and a variance of 4 and for label 1 follow a normal distribution with mean 2. The variance is σ². If the decision boundary learned using a Gaussian Naive Bayes algorithm is linear, the value of σ² is 2

  • Question 5: Consider a binary classification dataset with two binary features (f1 and f2). If f2 is always 0 for label 0 examples and can be 1 or 0 for label 1 examples, insufficient information is present to predict for [1,1] using a Naive Bayes algorithm.

  • Question 6 and 7: Consider binary classification with two features f₁ and f₂ that follow a Gaussian distribution. The values of p (estimate for P(y=1)) in question 6 is 0.5. In question 7, p is not stated, but the model involves estimating parameters for the distributions of f given the label y.

  • Question 8: Consider a binary classification dataset (f1 and f2). f₁ is categorical, taking three values, and f₂ is numerical with Gaussian distribution. Using Naive Bayes, 9 independent parameters are needed to be estimated.

  • Question 9: A naive Bayes algorithm was run on a binary classification. The probability of label y=1 is 0.3. The probabilities concerning features f1 = 1 | y = 0 is 0.2, f2= 1 | y = 0 is 0.3, f1 = 1 | y = 1 is 0.1 and f2= 1 | y = 1 is 0.2. The probability of feature value f2 = 0 | y=1 is 0.8.

  • Question 10 and 11: Consider a binary classification dataset (f1 and f2) with all binary features. Question 10 asks for the value of P(f2 = 0 | y = 1), given certain data. Question 11 is about classifying a data point [0,1].

  • Question 1: Consider a classification problem using a K-NN algorithm with a dataset of 1000 points. Statement S1 (k=10, it's enough to store 10 points) and S3 (more data points need to be stored with a higher k value) are correct. Statement S2 (need the entire dataset when k=10) and S4 are correct, where S4 has no dependency on k

  • Question 2: Consider a binary classification dataset and a k-NN classifier with k = 4. The black train point should be colored red; if it were blue, there is uncertainty.

  • Question 3: Consider a k-NN algorithm with k = 3. The predicted label for the test point given by the provided data is 1.

  • Question 4: A decision tree is terminated at the given level. The labels for L1 and L2 are 0 and 1 respectively.

  • Question 5: If Entropy is used to measure impurity and p is the proportion belonging to class-1, then the impurity of L1 is 0.954

  • Question 6: Information Gain is 0.030

  • Question 7: A test point passes through a minimum of 1 and a maximum of 4 questions before being assigned a label.

  • Question 8: The impurity of a node p increases from 0 to 0.5. It decreases afterwards. The value p = 0.5 corresponds to the case of maximum impurity.

  • Question 9: The weight vector for the given dataset is [1 1 -1 -1]

  • Question 10: The valid decision regions for a decision tree are horizontal lines and vertical lines.

  • Question 11: What is the value of P(y = 1)?

  • Question 12: The predicted label for a test point [0, 1]T is 0.

  • Question 1: Model 1 has more independent parameters.

  • Question 2: The correct answer is "Insufficient information to predict".

  • Question 1: The correct answer is (c) because S1 and S3 are true statements.

  • Question 2: The correct answer is (b).

  • Question 3: The correct answer is (c).

  • Question 4: The correct answer is (d).

  • Question 5: The correct answer is 0.98.

  • Question 6: The correct answer is 0.030.

  • Question 7: The correct answer is max = 4.

  • Question 8: The correct answer is (d).

  • Question 9: The correct answer is (b).

  • Question 10: The correct answer is (a).

  • Question 1-10, Practice: A variety of questions addressing different aspects of machine learning, including classification, regression, cross-validation, and model selection. Several require identifying correct statements or selecting the best model among different choices based on given data, characteristics, or performance metrics.

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