Unit 5: Dimensionality Reduction and Neural Networks - Practice Quiz

1 What is the main purpose of dimensionality reduction?

2 Which problem can dimensionality reduction help address?

3 A dataset has 50 features, and dimensionality reduction changes it to 10 features. What has happened?

4 Which is a common benefit of using dimensionality reduction?

5 What type of information should a good dimensionality reduction method try to preserve?

6 What does PCA stand for?

7 In PCA, what are principal components?

8 Which principal component usually captures the greatest amount of variance?

9 What does PCA typically produce from the original features?

10 Before applying PCA, why are features often standardized?

11 What measure is commonly used to decide how many PCA components to keep?

12 Are principal components usually correlated with one another?

13 How does information generally move through a feedforward neural network?

14 Which layer receives the original features in a neural network?

15 What is the main role of the output layer?

16 What is the purpose of an activation function in a neural network?

17 What does a neural network weight represent?

18 What is an MLP?

19 Which type of layer is found between the input and output layers of an MLP?

20 What is one common use of an MLP?

21 A dataset contains 200 variables, but many variables are highly correlated. What is the main benefit of applying dimensionality reduction before training a predictive model?

22 A model performs very well on training data but poorly on unseen data when trained with 500 features and only 100 observations. Which issue is dimensionality reduction most likely to help address?

23 Why should feature scaling often be performed before a distance-based dimensionality reduction method?

24 A two-dimensional dataset is reduced to one dimension, and the retained dimension explains 82% of the original variance. How should this result be interpreted?

25 In PCA, the first principal component is the direction that:

26 Before applying PCA to variables measured in dollars, kilograms, and centimeters, what is usually the most appropriate preprocessing step?

27 Suppose the eigenvalues from a PCA are , , , and . What proportion of total variance is explained by the first two components?

28 A PCA model is fitted on a training set and then used to transform a test set. Which procedure avoids information leakage?

29 A principal component is written as . What does the coefficient indicate, assuming the input variables are standardized?

30 Why can PCA components sometimes be difficult to interpret in a business application?

31 In a feedforward neural network, information flows from the input layer to the output layer without:

32 A neuron receives inputs and , with weights , , and bias . What is its pre-activation value?

33 Which activation function is commonly used in the output layer of a binary classification network with one output neuron?

34 A neural network is used to predict house prices. Which output-layer activation and loss pairing is generally appropriate?

35 During training, the loss decreases on the training set but increases on the validation set after several epochs. What is the most likely explanation?

36 What is the main advantage of using hidden layers with nonlinear activation functions in an MLP?

37 An MLP has 4 input features, one hidden layer with 6 neurons, and 2 output neurons. Including biases, how many trainable parameters does it have?

38 For a three-class classification problem, an MLP has three output neurons. Which output configuration is most appropriate?

39 Why is backpropagation important when training an MLP?

40 An MLP performs poorly on both the training and validation sets. Which change is most likely to address underfitting?

41 A dataset contains 500 features and 2,000 observations. The first 50 features are nearly exact linear combinations of the remaining features, while the target depends on a low-variance direction. Which strategy best reduces dimensionality while limiting the risk of discarding predictive information?

42 A dimensionality-reduction pipeline is evaluated with five-fold cross-validation. Standardization and projection are fitted once on the complete dataset before the folds are created. What is the principal statistical problem?

43 A high-dimensional dataset has 10,000 features but only 80 observations. Which issue most directly makes an unconstrained nonlinear embedding unreliable for downstream prediction?

44 A compressed representation is used for a fraud classifier. The reconstruction error is very low, but validation AUC falls substantially compared with the original features. Which conclusion is most defensible?

45 Two reduced representations have the same number of dimensions. Representation A preserves pairwise distances globally, while Representation B preserves local neighborhoods but distorts large-scale distances. Which task most favors Representation B?

46 For centered data, the covariance matrix has eigenvalues , , and . How much total variance is explained by the first two principal components?

47 Two features measure the same physical quantity in meters and centimeters. PCA is applied to the raw covariance matrix rather than the correlation matrix. What is the main consequence?

48 A standardized dataset has two nearly identical features. The first principal component has approximately equal loadings, while the second has opposite loadings and a tiny eigenvalue. What does the second component primarily represent?

49 A PCA model is fitted to training data, and a new observation is projected using without subtracting the training mean. What error is introduced?

50 A PCA component has loading vector . Which statement remains true if the algorithm returns instead of ?

51 A feedforward network uses ReLU activations and no biases. For any input , it satisfies . Which architectural property explains this behavior?

52 A binary classifier outputs a sigmoid probability, but the positive class occurs in only 1% of cases. Which evaluation practice is most appropriate for assessing ranking quality under severe imbalance?

53 A neural network has a linear output layer and is trained with mean squared error. If every hidden activation is also linear, what is the maximum function class the network can represent?

54 During training, a hidden ReLU unit receives strongly negative pre-activations for every example in a minibatch and has zero gradient for its incoming weights. Which intervention most directly addresses this state?

55 A network produces logits . Which statement correctly describes softmax probabilities and their behavior if the same constant is added to every logit?

56 An MLP has one hidden layer with two ReLU units and a linear output. Why can it represent a piecewise-linear function with more than two linear regions?

57 An MLP for multiclass classification uses two output neurons with independent sigmoid activations for three mutually exclusive classes. What is the fundamental modeling defect?

58 An MLP fits training data almost perfectly but performs poorly on a temporally later test set. The input includes a feature computed using records collected after each prediction time. What is the most likely cause?

59 Consider an MLP with input dimension , one hidden layer of units, and one scalar output. Every neuron has a bias. How many trainable parameters does it contain?

60 An MLP uses batch normalization before a ReLU layer. At inference time, which statistics should batch normalization use?