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About these flashcards

This flashcard set covers advanced topics in computer science, focusing on pattern recognition, machine learning, and statistical methods at a university level. It delves into key concepts like principal components, data distributions, classifiers, and probability functions, with a strong emphasis on practical applications such as support vector machines (SVM), logistic regression, and Gaussian mixture models (GMM). The flashcards are particularly useful for students and researchers aiming to deepen their understanding of data analysis, model optimization, and algorithmic techniques, providing both theoretical insights and practical problem-solving strategies.

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Which of these formulas are correct?

You are using a binary classifier on i.i.d. data. A point p is classified in class c1 if the L2 distance to the mean c1 is smaller than to the mean of c2. The two classes have equal prior probabilies. What assumptions must be made such that a Bayes Classifier is equivalent?

The covariance matrices of the two classes are isotropic but not identical

The covariance matrices of the two classes are identical but not isotropic

The covariance matrices of the two classes are both isotropic and identical

If the covariance matrix of two normal distribuions of your two classes are isotropic and identical which of the following two methods can you than use to classify a new point x?

pdf

mahalanobis distance

euclidean distance

all of them

If two events A and B are independent, then:

their joint probability P(A,B) is equal to the product of their probabilities P(A) and P(B)

The conditional probabilities P(A|B) and P(B|A) are equal

The conditional probabilities P(A|B) is equal to P(A)

Given three statistically dependent random variables a,b,c. You want to factorize the joint density p(a,b,c) into the marginal densities of the individual variables a,b,c using the product rule of probability. How many different factorizations are there?

infinite

Why is the log-likelihood instead of the likelihood itself often computed (MC)?

It is used in the case of estimating Normal-Distributions to cancel out the exponential function.

For fast growing functions, the log-likelihood is more informative

To avoid the derivative of the product of probabilities

It is a convention, only used to make the values more comparable

How does the introduced skin and non-skin priors influence the classification results on the test images and why does this happen?

Always improves the classification accuracy

Improves the classification if the training and the test images are similarly distributed

Lowers the number of false positives

Might improve the result if the target image is similar to the information contained in the prior

You are estimating the density function of a random variable x. You decide to model x with a Gaussian Mixture Model (GMM) consisting of M components, because a single Gaussian distribution captures your data of size N poorly. Each component has a mixing coefficient c_i and parameters theta_i. Select the correct statements.

You can use the expectation maximization (EM) algorithm to find the globally optimal solution for you GMM.

Cluster labels are missing for the data points, which are iteratively estimated with the EM algorithm

The probability density function in equation 1 for the mixture model is correct

The EM algorithm is used to solve the GMM problem. What are the hidden variables in this application?

Mean and covariance matrix

Cluster labels for all data points

Hyperparameter K

What is the hyperparameter that you had to initialize the algorithm with, and how does its value influence the fitting results?

Mean and covariance matrix

Cluster labels for each datapoint

K-number of clusters

The ML maximization method is used to compute (MC):

the maximum likelihood of the parameter of a distribution

the maximal parameters of a distribution

the parameters of a distribution that maximize the likelihood of the data

the probability density function that best describes the data

What is the difference between Maximum Likelihood (ML) and Maximum A Posteriori (MAP) parameter estimation?

ML estimation find the parameters which maximizes the data likelihood function of the given distribution. The likelihood of observing the data is maximized. MAP maximizes the posterior (introduces prior, not just likelihood).

We compute the class posterior P(w_i | x) using Bayes' rule, with x as random variable and w_i as the label for class i. Which of the following are true (MC)?

The evidence term is computed as the sum over every p(w_i, x).

The likelihood term is computed as the sum over every p(w_i, x).

The prior is a probability of a discrete variable.

The prior is a probability density function.

The Naive Bayes and Logistic Regression classifiers are both:

examples of generative models

provide the class posterior distribution as output

can be used to generate novel instances from the classes

The Naive Bayes classifier takes the following assumptions:

Conditionally independent features

Bag-of-words representation

Gaussian-distributed feature likelihoods

Equal class priors

In logistic regression on data X with the label vector Y,

the likelihood distribution is modeled by applying the logistic function to a linear classifier

the posterior distributions is modeled by applying the logistic function to a linear classifier

the loglikelihood function provided in Equation 3 is correct

Regularization in logistic regression. Choose the correct answers.

is better in the non-separable case

decreases the influence of the training data on the classifier

encourages smaller values for the discriminative function weights

The SVM cost functions aims to

maximize the distance between support vectors in a class

maximize the margin

maximize the discriminative function weights

You are trying to find the optimal parameters w of a linear SVM in the separable case. The size of the dataset is N, the dimensionality of the feature space is d. Which of the following is/are true?

The number of unknowns in the primal and dual problems are equal

In the primal formulation, the number of unknowns depends on the number of data points.

In the primal formulation, the number of unknowns depends on the dimensionality of the feature space

What is the role of the C parameter in a linear SVM classifier applied to inseparable data?

The C paraemeter influences the number of support vectors.

The larger the C parameter, the stricter the linear classifier

The larger the C parameter, the lower the generalization ability

You are training a nonlinear SVM classifier with an RBF kernel. As you increase the value of sigma in the kernel,

the decision surface will become smoother

the decision surface will have more small islands around single data inputs

the number of support vectors will increase

You want to train a classifier representing an XOR logic gat for two binary inputs. Which of the following will be able to classify the outputs correctly after training?

A single layer perceptron

A classifier that maps the input space to a higher dimensional space

A multi layer perceptron that does not map the input to a higher dimensional space

Which of the following techniques can be used for regularization in neural networks?

Data augmentation

Early stopping

Dropout

Stochastic gradient descent

You are building a convolutional neural network. Given a color (RGB) image of size 32 by 32, what is the dimension after the first hidden layer (kernel-size = 3x3, stride=1, padding=0, number of output filters=100)?

32 x 32 x 1000

30 x 30 x 100

32 x 32 x 3

30 x 30 x 3

How to compute PCA from SVD? Given X = DB and X = U Sigma V^T

In PCA, how to zero mean the data?

What is the ovariance of a mean-zero data matrix?

Which statements are true for principal components?

They are orthogonal

They form a basis in the feature space

They form a basis in the data space

The number of principal components is less than min (M, N)

Each principal component has the dimension of N

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