Free Stanford Machine Learning practice test

A. ✓ Correct: According to the probability rules, the intersection of two events A and B has a probability that cannot exceed the minimum probability of either event.

B. × Incorrect: The maximum probability does not apply to intersections; it would be relevant for unions or other scenarios but not here.

C. × Incorrect: The sum of probabilities for individual events can never be less than their intersection, which could even be zero if they are disjoint.

D. × Incorrect: This formula incorrectly combines complements and does not reflect a valid probability rule.

A. × Incorrect: Predicting ratings based on similar users' preferences describes collaborative filtering, not content-based filtering.

B. ✓ Correct: Recommending items that match the user's feature profile accurately reflects the goal of content-based filtering in aligning item features with user preferences.

C. × Incorrect: Maximizing variance explained by each component relates to Principal Component Analysis (PCA), which is unrelated to content-based recommendation systems.

D. × Incorrect: Separating mixed signals into statistically independent components pertains to Independent Component Analysis (ICA) and does not apply to recommender systems.

A. ✓ Correct: It accurately describes a key step in parameter optimization involving hidden variables in the EM algorithm.

B. × Incorrect: Minimizing distance between data points and centroids is relevant to K-means clustering, not EM algorithm.

C. × Incorrect: Ensuring predicted probabilities sum to one pertains to softmax regression, unrelated to EM algorithm's steps.

D. × Incorrect: Defining similarity using a covariance function relates to Gaussian processes, not the EM algorithm.

A. ✓ Correct: Setting the gradient to zero identifies critical points, which can include local minima if additional conditions like positive definiteness of the Hessian are met.

B. × Incorrect: A positive definite Hessian alone does not guarantee optimality without checking other conditions such as convexity.

C. × Incorrect: F(x*) equaling 0 would only be relevant for specific scenarios and not generally for identifying optimal points.

D. × Incorrect: Lying on the boundary of the feasible region can indicate constraint-activated minima but does not address the gradient condition necessary for an interior point.

A. ✓ Correct: Regularization helps prevent overfitting by adding a penalty term to the loss function that discourages overly complex models with large parameter values.

B. × Incorrect: Increasing model complexity can lead to overfitting, which regularization aims to avoid.

C. × Incorrect: While SVMs aim to maximize margins, regularization does not directly control margin size but rather penalizes model complexity.

D. × Incorrect: Dimensionality reduction is a different technique from regularization and is not the primary goal of adding a penalty term.

A. ✓ Correct: Features are assumed to be conditionally independent given the class label in Naive Bayes classifiers, allowing for simplified probability calculations.

B. × Incorrect: Naive Bayes assumes conditional independence rather than mutual dependence among features within a specific class.

C. × Incorrect: This option contradicts the assumption that feature distributions can vary between different classes in Naive Bayes classifiers.

D. × Incorrect: Gaussian distribution assumptions are not required for Naive Bayes classifiers, although they may be used in other models like Gaussian discriminant analysis.

A. ✓ Correct: Gradient descent aims to minimize a cost function through iterative updates using derivatives, which helps find optimal parameter values for linear regression models.

B. × Incorrect: While accuracy is important, gradient descent specifically focuses on minimizing error rather than maximizing prediction accuracy directly.

C. × Incorrect: Selecting features is part of the model design phase and not directly related to the process of updating parameters via gradient descent.

D. × Incorrect: D is incorrect as non-negative coefficients are a constraint that might be applied in certain contexts but are unrelated to the core purpose of minimizing cost through iterative updates.

A. × Incorrect: Vector because multiplying a matrix with its inverse results in an identity matrix, not a vector.

B. × Incorrect: Another matrix because the product of a matrix and its inverse specifically yields the identity matrix, which has ones on the diagonal and zeros elsewhere.

C. ✓ Correct: The identity matrix is correct as it represents the result when multiplying any square matrix by its inverse.

D. × Incorrect: A scalar because the multiplication results in an entire matrix (the identity matrix), not just a single number.

A. × Incorrect: Dimensionality reduction because it helps in predicting user preferences by simplifying the feature space.

B. × Incorrect: Clustering because it groups similar data points but does not directly predict user preferences based on ratings.

C. × Incorrect: Anomaly detection because it identifies unusual patterns and does not focus on predicting user preferences from historical ratings.

D. ✓ Correct: Collaborative filtering is incorrect although related, as it uses past user behavior to recommend items but does not specifically address dimensionality reduction.

A. ✓ Correct: To maximize the variance explained by each component accurately reflects the primary goal of PCA in identifying directions (principal components) that capture maximum variability in the data set, aligning with the concept's purpose as described in the source.

B. × Incorrect: Minimizing reconstruction error during dimensionality reduction is a related but distinct objective often associated with other techniques like autoencoders rather than being the primary goal of PCA.

C. × Incorrect: Ensuring equal distribution of variance across all dimensions contradicts the fundamental principle of PCA, which aims to concentrate variability along fewer principal components.

D. × Incorrect: Maintaining original data variance without transformation does not align with the purpose of PCA, which seeks to transform and reduce the dimensionality of data while retaining as much information (variance) as possible.