Podcast
Questions and Answers
What is the goal of optimization in the context of machine learning?
What is the goal of optimization in the context of machine learning?
- To reduce a cost function $J(W)$ to optimize some performance measure $P$. (correct)
- To increase the training error on the data.
- To maximize a cost function to improve performance.
- To minimize the performance measure $P$ while ignoring the cost function.
In machine learning, what is the significance of minimizing $J(W)$ with respect to parameter $W$ on training data?
In machine learning, what is the significance of minimizing $J(W)$ with respect to parameter $W$ on training data?
- It directly optimizes the performance on unseen data.
- It only focuses on minimizing training error without considering test data.
- It aims to achieve low error on both training and unseen data. (correct)
- It ensures the test error is high.
Which of the following is not an assumption typically made in machine learning optimization?
Which of the following is not an assumption typically made in machine learning optimization?
- The training set and test set are identically distributed.
- Data samples in each dataset are independent.
- Data samples are dependent on each other. (correct)
- Test and Training data are generated by the same probability distribution.
How does altering the capacity of a learning algorithm relate to overfitting and underfitting?
How does altering the capacity of a learning algorithm relate to overfitting and underfitting?
What does 'Underfitting' refer to in the context of machine learning models?
What does 'Underfitting' refer to in the context of machine learning models?
What characterizes 'Overfitting' in machine learning models?
What characterizes 'Overfitting' in machine learning models?
In the context of binary classification, which of the following equations represents Logistic Regression?
In the context of binary classification, which of the following equations represents Logistic Regression?
What is the primary role of the Softmax classifier?
What is the primary role of the Softmax classifier?
What is the purpose of introducing nonlinearity in neural networks?
What is the purpose of introducing nonlinearity in neural networks?
Which of the following activation functions introduces nonlinearity into a neural network?
Which of the following activation functions introduces nonlinearity into a neural network?
What does the ReLU (Rectified Linear Unit) activation function do?
What does the ReLU (Rectified Linear Unit) activation function do?
Match the component to its function in a neuron:
Match the component to its function in a neuron:
In the context of neural networks, what is a key function of the 'Axon'?
In the context of neural networks, what is a key function of the 'Axon'?
A perceptron is used to implement a two-input AND function. Given the inputs X1 and X2, which of the following conditions must be met to produce an output of 1?
A perceptron is used to implement a two-input AND function. Given the inputs X1 and X2, which of the following conditions must be met to produce an output of 1?
In the context of neural networks, what does the expression $f^{(K)}(f^{(K-1)}...(f^{(i)}...(f^{(2)}(f^{(1)}(X)))))$ represent
In the context of neural networks, what does the expression $f^{(K)}(f^{(K-1)}...(f^{(i)}...(f^{(2)}(f^{(1)}(X)))))$ represent
What is the output of an OR function, given inputs $X_1 = 0$ and $X_2 = 0$?
What is the output of an OR function, given inputs $X_1 = 0$ and $X_2 = 0$?
Considering a threshold function where the output is 1 if $x \geq 0$ and 0 if $x < 0$, what will be the output (y) if the input (x) is -2?
Considering a threshold function where the output is 1 if $x \geq 0$ and 0 if $x < 0$, what will be the output (y) if the input (x) is -2?
Consider the function $y = max(0, x)$. What is the value of $y$ when $x = -5$?
Consider the function $y = max(0, x)$. What is the value of $y$ when $x = -5$?
What is a notable downside of using Stochastic Gradient Descent in optimizing a model?
What is a notable downside of using Stochastic Gradient Descent in optimizing a model?
Why can frequent updates in Stochastic Gradient Descent be considered both an advantage and a disadvantage?
Why can frequent updates in Stochastic Gradient Descent be considered both an advantage and a disadvantage?
What is a primary benefit of using Batch Gradient Descent over Stochastic Gradient Descent?
What is a primary benefit of using Batch Gradient Descent over Stochastic Gradient Descent?
What is a significant drawback of Batch Gradient Descent?
What is a significant drawback of Batch Gradient Descent?
How does Mini-Batch Gradient Descent balance the trade-offs between Stochastic and Batch Gradient Descent?
How does Mini-Batch Gradient Descent balance the trade-offs between Stochastic and Batch Gradient Descent?
What is a key disadvantage of using Mini-Batch Gradient Descent?
What is a key disadvantage of using Mini-Batch Gradient Descent?
Given the function for AND logic:
$X_1$ | $X_2$ | y
---|---|
0 | 0 | 0
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1
Which inequality describes the decision boundary implemented by the perceptron?
Given the function for AND logic: $X_1$ | $X_2$ | y ---|---| 0 | 0 | 0 0 | 1 | 0 1 | 0 | 0 1 | 1 | 1
Which inequality describes the decision boundary implemented by the perceptron?
The XOR function satisfies what expression?
The XOR function satisfies what expression?
The XOR function satisfies what table?
$X_1$
$X_2$
$h_1$=$X_1$+$X_2$
$h_2$=$\overline{X_1}$ + $\overline{X_2}$
$h_1$ . $h_2$=X1$\bigoplus$X2
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
The XOR function satisfies what table?
| $X_1$ | $X_2$ | $h_1$=$X_1$+$X_2$ | $h_2$=$\overline{X_1}$ + $\overline{X_2}$ | $h_1$ . $h_2$=X1$\bigoplus$X2 |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 |
The XOR problem requires what type of network?
The XOR problem requires what type of network?
Considering you have to classify images of cats, dogs, and birds. Which of the below is most appropriate?
Considering you have to classify images of cats, dogs, and birds. Which of the below is most appropriate?
What is true about nonlinearity?
What is true about nonlinearity?
Which is the best way to prevent underfitting?
Which is the best way to prevent underfitting?
What will be the value of 'y' if $x=5$ in the following function? $y = max(0, x)$
What will be the value of 'y' if $x=5$ in the following function? $y = max(0, x)$
Flashcards
Optimization in ML
Optimization in ML
Adjusting parameters to minimize a cost function and optimize a performance metric.
Cost Function Minimization
Cost Function Minimization
A cost function, denoted as J(W), is minimized with respect to the parameter W using training data.
Data assumptions for ML
Data assumptions for ML
Generated by a probability distribution and these samples are also independent.
Underfitting
Underfitting
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Overfitting
Overfitting
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Controlling Over/Underfitting
Controlling Over/Underfitting
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Linear/Logistic Regression
Linear/Logistic Regression
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Linear Regression Formula
Linear Regression Formula
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Logistic Regression Formula
Logistic Regression Formula
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Softmax Classifier
Softmax Classifier
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Nonlinearity in ML
Nonlinearity in ML
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Linear separability
Linear separability
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Threshold Activation
Threshold Activation
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ReLU (Rectified Linear Unit)
ReLU (Rectified Linear Unit)
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Dendrite
Dendrite
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Synapse
Synapse
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Soma
Soma
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Axon
Axon
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Neuron Function
Neuron Function
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Neural Network
Neural Network
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AND Logic NN
AND Logic NN
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OR Logic NN
OR Logic NN
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XOR Function NN
XOR Function NN
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Multi-Layer Model
Multi-Layer Model
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Study Notes
Optimization Lecture 16:
- Multiclass SVM Loss Function, Optimization, Stochastic Gradient Descent, Batch Optimization, and Mini-Batch Optimization will be covered.
- The goal is to optimize the Loss Function via: L = 1/N * ∑∑[max(0,W'Xⱼ -W'X(yi) + ∇] + λ∑∑W²
- Gradient descent is characterized by: W(yi)(k+1) ← (1-η)W(yi)(k) + 1/N ∑∑[Xi|(W'X-W'X(yi) + ∇ > 0)]
- Global Minima: The absolute lowest point on a loss function.
- Local Minima: A point on a loss function that is lower than its surrounding points but not the absolute lowest.
- Stochastic Gradient Descent: Frequent updates occur, giving insight into model performance and improvement rate and it is the simplest to understand and implement.
- Batch Gradient Descent: Efficient computation makes convergence stable and prediction errors support parallel processing implementations
- Mini-Batch Gradient Descent: Update frequency is higher than batch-gradient descent which allows for robust convergence with good batching efficiency
Optimization in Machine Learning Lecture 17:
- Covered topics include optimization, stochastic gradient descent, batch optimization, mini-batch optimization, optimization in ML, linear and logistic regression, softmax classifier, and nonlinearity.
- The goal of optimization is to reduce a cost function J(W)
- The performance of ML is its ability to make the training error small and reduce the gap between training and test error.
- Underfitting refers to a model that cannot obtain sufficiently low training error
- Overfitting refers to a model where the gap between training and test error is too large.
- Overfitting/Underfitting can be controlled by altering a model's capacity, giving algorithms selection ability
- Linear Regression: f : X ∈ Rᵈ → y ∈ R, ŷ = WᵗX
- Logistic Regression: p( y | X ;W ) = σ(WᵗX )
- σ(W ᵗX ) = 1 / 1 + e⁻ᵂ'X
- Generalization of Binary Logistic Classifier to Multiple Classes: s(yi) = f(Xi, W)(yi) = (W *Xi)(yi)= W(yi)ᵗX(i)
- Softmax Classifier: p(yi|Xi;W) = e^(Syi) / ∑e^(Sj)
Neural Network Lecture 19
- Covered topics include nonlinearity, neural networks, AND logic, OR logic, XOR logic, feed-forward NN, and back-propagation learning.
- Neuron: Dendrites receive signals, synapses are points of connection, the soma processes info, and the axon transmits the neuron's output.
- Threshold: Used to distinguish when x >= 0 or x < 0
- ReLU: Rectified Linear Unit; y = max(0, x)
- AND Function: Can be modeled with X1 + X2 −1.5 = 0
- OR Function: Can be modeled with X1 + X2 − 0.5 = 0
Neural Network II Lecture 20
- Covered topics include neural networks, AND logic, OR logic, XOR logic, feed-forward NN, and back-propagation learning.
- XOR Function: Can be expressed as: (X1 ⊕ X2 = (X1 + X2).(X̅1 + X̅2)
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