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Questions and Answers

What is the main goal of Maximum Likelihood Estimation (MLE) in logistic regression?

  • To minimize the Cross-Entropy
  • To maximize the likelihood of making the observations given the parameters (correct)
  • To maximize the uncertainty associated with a random variable
  • To minimize the Mean Squared Error (MSE)

In logistic regression, what is the function that 'squeezes in' the weighted input into a probability space?

  • Exponential Decay Function
  • Linear Sigmoid Function
  • Quadratic Activation Function
  • Logistic Sigmoid Function (correct)

What is the measure of the uncertainty associated with a random variable in logistic regression?

  • Distribution Divergence
  • Mean Squared Error (MSE)
  • Cross-Entropy
  • Entropy (H) (correct)

What does the Logistic regression model specify in terms of binary output given input?

<p>Probability of binary output (B)</p> Signup and view all the answers

What is the method of estimating the parameters of a statistical model given observations in logistic regression?

<p>Maximum Likelihood Estimation (MLE) (A)</p> Signup and view all the answers

What is the purpose of minimizing the Kullback-Leibler Divergence in logistic regression?

<p>To measure the difference between two probability distributions (B)</p> Signup and view all the answers

In logistic regression, what is the role of the derivative of the logit function?

<p>To adjust the parameters in the gradient-descent based method (D)</p> Signup and view all the answers

Why is logistic regression considered insufficient for classification in the rings dataset?

<p>The dataset is not linearly separable (B)</p> Signup and view all the answers

What is the objective of a multi-layer perceptron (MLP) with regards to minimizing cross-entropy error?

<p>To create separation planes on the input space (A)</p> Signup and view all the answers

What influence can be observed in the simple MLP using the Neural Net Playground?

<p>Influence of activation functions and relation between absolute gradient value and learning rate (D)</p> Signup and view all the answers

What is the passing condition for the written final exam in the Neural Networks course?

<p>Scoring at least 30% in the written final exam (C)</p> Signup and view all the answers

What is the weightage of the project in the evaluation for exam entry?

<p>60% (A)</p> Signup and view all the answers

How many intermediary short presentations are required for the project evaluation?

<p>3 (A)</p> Signup and view all the answers

What is the weightage of the written final exam in the evaluation for exam entry?

<p>30% (B)</p> Signup and view all the answers

What is the main focus of Step 3 of the project?

<p>Final experiments and results (C)</p> Signup and view all the answers

Which optimization algorithm stores an exponentially decaying average of squared gradients and also an exponentially decaying average of past gradients?

<p>Adam (A)</p> Signup and view all the answers

What is the update rule for the Adadelta optimization algorithm?

<p>$\theta(t+1) = \theta(t) - \sqrt{\lambda E[g^2]_t + \epsilon} g_t$ (A)</p> Signup and view all the answers

In the context of optimization, what does the acronym CNN stand for?

<p>Convolutional Neural Network (A)</p> Signup and view all the answers

What is the main purpose of early stopping in the context of optimization?

<p>To prevent overfitting (D)</p> Signup and view all the answers

Which technique is used to make training more robust to poor initialization or highly irregular error functions?

<p>Gradient Noise (C)</p> Signup and view all the answers

What is the dimension of the output map when an input volume of 32 × 32 × 3 is convolved with a 5 × 5 × 3 filter?

<p>28 × 28 × 1 (D)</p> Signup and view all the answers

What does the size of the receptive field represent in a convolutional layer?

<p>Spatial extent of the local connectivity of each neuron (B)</p> Signup and view all the answers

What is the purpose of connecting each neuron to only a local region of the input volume in a convolutional layer?

<p>To reduce the number of parameters and computational complexity (A)</p> Signup and view all the answers

What is the disadvantage of using a large filter in a convolutional layer?

<p>Lose info about spatial arrangement of pixels (C)</p> Signup and view all the answers

In the context of convolutional layers, what does 'inductive bias' refer to?

<p>The assumptions made by the network to simplify learning (D)</p> Signup and view all the answers

In the context of optimization for linear regression, what is the gradient of the loss function f(θ) with respect to θ?

<p>−2XT y + 2XT Xθ (A)</p> Signup and view all the answers

What is the main issue with the second-order optimization algorithm in computing the direction of descent?

<p>Difficulty in inverting the Hessian matrix (A)</p> Signup and view all the answers

Which statement best describes the Stochastic Gradient Descent (SGD) algorithm?

<p>It uses a subset of the data to estimate the true gradient and updates the parameters based on this estimate. (B)</p> Signup and view all the answers

What is the main purpose of normalizing the input space in Stochastic Gradient Descent (SGD)?

<p>To improve numerical stability and convergence behavior (A)</p> Signup and view all the answers

Which feature distinguishes Adadelta from Adagrad in terms of updating individual parameter learning rates?

<p>Adadelta adapts learning rates based on parameter importance, while Adagrad uses a fixed learning rate for all parameters. (D)</p> Signup and view all the answers

What is the dimension of the output map when applying a filter of size 7 × 7 × 3 to an input volume of dimension 32 × 32 × 3?

<p>26 × 26 × 1 (B)</p> Signup and view all the answers

If the input volume has dimensions 50 × 50 × 3, a kernel size of 5 × 5 × 3, zero-padding of 1, and a stride of 2, what is the dimension of the output map?

<p>24 × 24 × 1 (D)</p> Signup and view all the answers

For an input volume of dimension 20 × 20 × 3 and a filter size of 5 × 5 × 3 with a stride of 3, what is the dimension of the output map?

<p>6 × 6 × 3 (A)</p> Signup and view all the answers

If the stride is set to 2, the input volume has dimensions of 30 × 30 × 3, and the filter size is 4 × 4 × 3, what padding can be used to ensure the output map has the same width and height as the input volume?

<p>2 (A)</p> Signup and view all the answers

What size of zero-padding should be applied to an input volume with dimensions of 40 × 40 × 3 and a filter size of 4 × 4 × 3 in order to obtain an output map of dimensions 40 × 40 × 1?

<p>1 (A)</p> Signup and view all the answers

When applying a convolution layer with a kernel size of 6 × 6 and a stride of 2 to an input volume with dimensions of H x W x D, what is the dimension of the output map?

<p>$(H - (6 - 1)) \times (W - (6 - 1)) \times D$ (B)</p> Signup and view all the answers

If parameter sharing is used in a CNN with an output volume of dimensions H x W x D and a filter size of K x K x D, how many parameters are shared within a depth slice?

<p>$K \times K \times D$ (B)</p> Signup and view all the answers

In a CNN with an output volume of dimensions H x W x D and a filter size of K x K x D, how many biases are needed when using parameter sharing?

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

For an input volume with dimensions H x W x D, if the kernel size is P x P x D and the stride is S, what is the constraint on P to ensure that the result of division when computing Hin has to be an integer?

<p>$P &lt; S$ (D)</p> Signup and view all the answers

If an input volume has dimensions H x W x D, a kernel size of K x K x D, zero-padding of P, and dilation factor of L, what is the formula for calculating Wout, the width of the output map?

<p>$W + (2P) - L(K - 1) - S + 1$ (A)</p> Signup and view all the answers

What is the loss function used in logistic regression?

<p>Cross-Entropy (B)</p> Signup and view all the answers

What is the derivative of the logit function used for in logistic regression?

<p>To compute the gradient of the loss function (B)</p> Signup and view all the answers

What is the main disadvantage of using logistic regression for classification in the rings dataset?

<p>It is not suitable for non-linearly separable datasets (B)</p> Signup and view all the answers

What is the objective of a multi-layer perceptron (MLP) in the context of minimizing cross-entropy error?

<p>To learn an optimal representation of the input data (A)</p> Signup and view all the answers

What influence can be observed in the simple MLP using the Neural Net Playground?

<p>Influence of activation functions on model performance (D)</p> Signup and view all the answers

In the context of optimization for linear regression, what is the update form of the steepest descent algorithm?

<p>θ (k+1) = θ (k) - λ(k) ∇f(θ (k) ) (A)</p> Signup and view all the answers

What is the algorithm derived from the second-order Taylor series approximation of J(θ) around θ (k) in the context of second-order optimization?

<p>Newton's algorithm (C)</p> Signup and view all the answers

What is the main limitation of using second-order optimization algorithms such as Newton's algorithm?

<p>Inversion of the Hessian matrix at each iteration (D)</p> Signup and view all the answers

What distinguishes Stochastic Gradient Descent (SGD) from Batch and Mini-batch Gradient Descent in terms of parameter updates?

<p>SGD updates parameters based on a subset or even instance of the data (A)</p> Signup and view all the answers

What is the intuition behind Nesterov Accelerated Gradient in optimization?

<p>To give momentum a sense of when to speed up before a slope increases (C)</p> Signup and view all the answers

Which optimization algorithm involves an update rule that includes a biased correction for the exponentially decaying average of squared gradients?

<p>Adam (A)</p> Signup and view all the answers

What is the equivalent of Adadelta without the exponential decay of squared parameter updates?

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

For big, redundant datasets, which optimization algorithm is specifically recommended?

<p>Adam (A)</p> Signup and view all the answers

Which method is used to make training more robust to poor initialization or highly irregular error functions?

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

What is the common practice to deal with the covariate shift in intermediary layer inputs during training in deep networks?

<p>Batch Normalization (B)</p> Signup and view all the answers

What is the primary focus of Step 2 in the project guidelines for the Neural Networks course?

<p>Evaluating the first results of the project (D)</p> Signup and view all the answers

In logistic regression, what is the main purpose of the derivative of the logit function?

<p>To adjust the model parameters during backpropagation (D)</p> Signup and view all the answers

What is the constraint on the kernel size (P) when applying a convolution layer with stride (S) to an input volume with dimensions H x W x D to ensure that the result of division when computing Hin has to be an integer?

<p>$P = \frac{H - 1}{S} + 1$ (B)</p> Signup and view all the answers

What is the passing condition for exam entry in the Neural Networks course?

<p>Earning at least 50% of semester activity, including project evaluations, and achieving 30% in the written final exam (D)</p> Signup and view all the answers

What is the main goal of Maximum Likelihood Estimation (MLE) in logistic regression?

<p>To maximize the log-likelihood function (B)</p> Signup and view all the answers

What is the main difference between linear regression and logistic regression?

<p>Linear regression uses a linear predictor, while logistic regression uses a logistic sigmoid function for classification. (D)</p> Signup and view all the answers

What is the purpose of the sigmoid function in logistic regression?

<p>To 'squeeze in' the weighted input into a probability space. (D)</p> Signup and view all the answers

What is the measure of the uncertainty associated with a random variable in logistic regression?

<p>Entropy (A)</p> Signup and view all the answers

What is the method of estimating the parameters of a statistical model given observations in logistic regression?

<p>Maximizing Likelihood Estimation (MLE) (C)</p> Signup and view all the answers

What is the main issue with the second-order optimization algorithm in computing the direction of descent?

<p>It involves computing and storing Hessian matrices. (B)</p> Signup and view all the answers

What is the dimension of the output map when applying a filter of size 5 × 5 × 3 to an input volume of dimension 32 × 32 × 3?

<p>28 × 28 × 1 (D)</p> Signup and view all the answers

What does the size of the receptive field represent in a convolutional layer?

<p>Spatial extent of the local connectivity of each neuron (B)</p> Signup and view all the answers

What is the disadvantage of using a large filter in a convolutional layer?

<p>Lose info about spatial arrangement of pixels (B)</p> Signup and view all the answers

What is the main purpose of connecting each neuron to only a local region of the input volume in a convolutional layer?

<p>Reduce the number of parameters and enforce translation invariance (D)</p> Signup and view all the answers

What influence can be observed in the simple MLP using the Neural Net Playground?

<p>Impact of different activation functions on model performance (A)</p> Signup and view all the answers

What is the dimension of the output map when applying a filter of size $5 \times 5 \times 3$ to an input volume of dimension $32 \times 32 \times 3$ with a stride of 1 and zero-padding of 0?

<p>$28 \times 28 \times 1$ (B)</p> Signup and view all the answers

If an input volume with dimensions $50 \times 50 \times 3$, a kernel size of $5 \times 5 \times 3$, zero-padding of 0, and a stride of 2, what is the dimension of the output map?

<p>$24 \times 24 \times 1$ (A)</p> Signup and view all the answers

For an input volume with dimensions $40 \times 40 \times 3$, a filter size of $4 \times 4 \times 3$, and zero-padding of 2, what is the dimension of the output map?

<p>$42 \times 42 \times 1$ (B)</p> Signup and view all the answers

If the stride is set to 2, the input volume has dimensions of $30 \times 30 \times 3$, and the filter size is $4 \times 4 \times 3$, what padding can be used to ensure the output map has the same width and height as the input volume?

<p>1 (A)</p> Signup and view all the answers

For an input volume with dimensions $20 \times 20 \times 3$ and a filter size of $5 \times 5 \times 3$ with a stride of 3, what is the dimension of the output map?

<p>$6 \times 6 \times 1$ (C)</p> Signup and view all the answers

What is the constraint on the kernel size ($P$) to ensure that the result of division when computing $H_{in}$ has to be an integer, given an input volume with dimensions $H\ times W\ times D$ and a stride of $S$?

<p>$P &lt;= H - S + W - S + D$ (D)</p> Signup and view all the answers

What is the formula for calculating $W_{out}$, the width of the output map, given an input volume with dimensions $H\ times W\ times D$, a kernel size of $P\ times P\ times D$, zero-padding of $Z$, and dilation factor of $L$?

<p>$W_{out} = W + Z - L*(P-1) - L-1 + S$ (D)</p> Signup and view all the answers

What does 'inductive bias' refer to in the context of convolutional layers?

<p>The assumption that features useful in one area are likely to be useful in another area (D)</p> Signup and view all the answers

What is the main issue with second-order optimization algorithms in computing the direction of descent?

<p>Computational complexity increases significantly with higher order derivatives (A)</p> Signup and view all the answers

What feature distinguishes Adadelta from Adagrad in terms of updating individual parameter learning rates?

<p>Adadelta uses an exponentially decaying average of past gradients in addition to squared gradients (A)</p> Signup and view all the answers

What are the passing conditions for the written final exam in the Neural Networks course?

<p>50% of semester activity required for exam entry (grades for HW + Intermediary presentations + Step 2 of project), 50% of final project, 30% of written exam</p> Signup and view all the answers

How many biases are needed when using parameter sharing in a CNN with an output volume of dimensions H x W x D and a filter size of K x K x D?

<p>1</p> Signup and view all the answers

What is the dimension of the output map when applying a filter of size 6 × 6 × D and a stride of 2 to an input volume with dimensions of H x W x D?

<p>((H - 6) / 2 + 1) × ((W - 6) / 2 + 1) × D</p> Signup and view all the answers

What is the weightage of the project in the evaluation for exam entry?

<p>50%</p> Signup and view all the answers

What is the update rule for the Adadelta optimization algorithm?

<p>w_t = w_{t-1} - (RMS[delta_w]_t / RMS[g]_t) * g_t</p> Signup and view all the answers

What is the main purpose of early stopping in the context of optimization?

<p>To prevent overfitting</p> Signup and view all the answers

What is the main difference between linear regression and logistic regression?

<p>Linear regression predicts continuous outcomes, while logistic regression predicts binary outcomes.</p> Signup and view all the answers

What is the main goal of Maximum Likelihood Estimation (MLE) in logistic regression?

<p>To estimate the parameters of a statistical model given observations</p> Signup and view all the answers

What is the primary focus of Step 2 in the project guidelines for the Neural Networks course?

<p>Intermediary project evaluation (e.g. first results)</p> Signup and view all the answers

What distinguishes Stochastic Gradient Descent (SGD) from Batch and Mini-batch Gradient Descent in terms of parameter updates?

<p>SGD updates parameters using a single training example at a time, while Batch and Mini-batch GD use multiple examples.</p> Signup and view all the answers

What is the weightage of the written final exam in the evaluation for exam entry?

<p>30%</p> Signup and view all the answers

What is the method of estimating the parameters of a statistical model given observations in logistic regression?

<p>Maximum Likelihood Estimation (MLE)</p> Signup and view all the answers

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Study Notes

  • The text outlines the course structure for a machine learning class, focusing on neural networks and their related topics.
  • The course consists of 14 lectures, programming and analysis homework assignments, and a project.
  • The project involves topic selection, presentation of state-of-the-art research, intermediary presentations, intermediate project evaluation, final project poster presentation, and final project paper.
  • The passing conditions for the course include completion of 50% of semester activities for exam entry and 50% of the final project, as well as 30% of the written exam.
  • The text covers the basics of linear regression, including the objective function, mean squared error loss, and the solution using gradient descent.
  • The text discusses the limitations of linear regression for classification tasks and introduces the logistic regression model.
  • Logistic regression models the probability of binary output given input, using a sigmoid activation function.
  • The text covers maximizing likelihood estimation and the minimization of cross-entropy using gradient descent for logistic regression.
  • The text also touches on Kullback-Leibler divergence and its relationship to minimizing cross-entropy.
  • The text briefly discusses the application of logistic regression as a neural network, introducing the softmax function for multiclass classification.
  • The text then covers backpropagation, a method used to train multi-layered neural networks.
  • The text outlines the forward and backward passes in a neural network and discusses the calculation of delta values for each layer during backpropagation.
  • The text concludes by mentioning the insufficiency of logistic regression for the given rings dataset and the need for a multi-layered perceptron to address the classification problem.

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