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1. What Is The Trade-Off Between Bias and Variance?
The trade-off between bias and variance is a crucial concept in machine learning. A model with high bias simplifies the problem too much, leading to underfitting. Conversely, a model with high variance is overly complex, fitting the noise in the data and leading to overfitting.
- High Bias: The model is too simple and cannot capture the underlying patterns in the data. It makes strong assumptions, leading to systematic errors.
- High Variance: The model is too complex and fits the training data very closely, including the noise. It is highly sensitive to small fluctuations in the training data.
- Finding the Balance: The goal is to find a model that strikes a balance between bias and variance, generalizing well to unseen data without overfitting or underfitting.
1.1. Strategies to Manage Bias and Variance
- For High Bias (Underfitting):
- Increase model complexity (e.g., add more layers to a neural network).
- Introduce more features or reduce regularization.
- Use a more sophisticated algorithm.
- For High Variance (Overfitting):
- Simplify the model (e.g., reduce the number of layers or parameters).
- Increase the amount of training data.
- Apply regularization techniques (L1, L2 regularization).
- Use cross-validation to evaluate model performance.
2. What Is Gradient Descent?
Gradient descent is an optimization algorithm used to minimize a function by iteratively moving in the direction of the steepest descent as defined by the negative of the gradient. It’s widely used in machine learning to find the optimal parameters of a model.
2.1. Types of Gradient Descent
- Batch Gradient Descent: Computes the gradient of the cost function using the entire training dataset in each iteration. It is accurate but can be slow for large datasets.
- Stochastic Gradient Descent (SGD): Computes the gradient using a single randomly selected data point in each iteration. It is faster than batch gradient descent but can be noisy.
- Mini-Batch Gradient Descent: Computes the gradient using a small batch of data points in each iteration. It balances the accuracy of batch gradient descent with the speed of SGD.
2.2. Gradient Descent Variants
- Momentum: Adds a fraction of the previous update vector to the current update vector, helping to accelerate convergence and dampen oscillations.
- Adam (Adaptive Moment Estimation): Combines the benefits of both momentum and RMSprop, adapting the learning rates for each parameter.
- RMSprop (Root Mean Square Propagation): Adapts the learning rates by dividing them by the exponentially decaying average of squared gradients.
3. Explain Over- and Under-Fitting and How to Combat Them?
Overfitting and underfitting are common issues in machine learning that affect a model’s ability to generalize to new data.
- Underfitting: Occurs when a model is too simple to capture the underlying patterns in the data. The model performs poorly on both the training and test datasets.
- Overfitting: Occurs when a model is too complex and fits the training data too closely, including the noise. The model performs well on the training data but poorly on the test data.
3.1. Techniques to Combat Over- and Under-Fitting
- Combating Underfitting:
- Increase model complexity.
- Add more features.
- Reduce regularization.
- Combating Overfitting:
- Simplify the model.
- Increase the amount of training data.
- Apply regularization techniques.
- Use cross-validation.
4. How Do You Combat The Curse of Dimensionality?
The curse of dimensionality refers to the challenges that arise when dealing with high-dimensional data. As the number of features increases, the amount of data needed to generalize accurately grows exponentially.
4.1. Techniques to Combat the Curse of Dimensionality
- Feature Selection: Choose the most relevant features and discard the irrelevant ones.
- Principal Component Analysis (PCA): Reduce the number of features by transforming them into a set of uncorrelated principal components.
- Multidimensional Scaling: Reduce the dimensionality of the data while preserving the distances between data points.
- Locally Linear Embedding: Reduce the dimensionality of the data while preserving local relationships.
5. What Is Regularization, Why Do We Use It, And Give Some Examples of Common Methods?
Regularization is a technique used to prevent overfitting by adding a penalty term to the cost function. This penalty term discourages the model from learning overly complex relationships in the data.
5.1. Types of Regularization
- L1 Regularization (Lasso): Adds the sum of the absolute values of the coefficients to the cost function. It can lead to sparse models with some coefficients being exactly zero.
- L2 Regularization (Ridge): Adds the sum of the squares of the coefficients to the cost function. It shrinks the coefficients towards zero without making them exactly zero.
- Elastic Net: Combines L1 and L2 regularization to provide a balance between feature selection and coefficient shrinkage.
5.2. Benefits of Regularization
- Reduces overfitting.
- Improves model generalization.
- Simplifies the model.
6. Explain Principal Component Analysis (PCA)?
Principal Component Analysis (PCA) is a dimensionality reduction technique used to transform a high-dimensional dataset into a lower-dimensional representation while retaining the most important information.
6.1. Steps in PCA
- Standardize the Data: Scale the data so that each feature has zero mean and unit variance.
- Compute the Covariance Matrix: Calculate the covariance matrix of the standardized data.
- Compute the Eigenvectors and Eigenvalues: Find the eigenvectors and eigenvalues of the covariance matrix.
- Select Principal Components: Sort the eigenvectors by their corresponding eigenvalues and choose the top k eigenvectors to form the principal components.
- Project the Data: Project the original data onto the new subspace spanned by the principal components.
6.2. Applications of PCA
- Dimensionality reduction.
- Feature extraction.
- Noise reduction.
7. Why Is ReLU Better And More Often Used Than Sigmoid In Neural Networks?
ReLU (Rectified Linear Unit) is a popular activation function in neural networks that outputs the input directly if it is positive, otherwise, it outputs zero. It is preferred over the sigmoid function for several reasons.
7.1. Advantages of ReLU over Sigmoid
- Computation Efficiency: ReLU is computationally more efficient than sigmoid because it involves simpler operations.
- Reduced Likelihood of Vanishing Gradient: ReLU’s gradient is either 0 or 1, which helps to alleviate the vanishing gradient problem that can occur with sigmoid.
- Sparsity: ReLU can introduce sparsity in the network by setting the activations of some neurons to zero, which can lead to more efficient computation and better generalization.
7.2. Disadvantages of ReLU
- Dying ReLU Problem: ReLU neurons can become inactive if they are always in the negative part of the input space, leading to a zero gradient and preventing them from learning.
8. Given Stride S And Kernel Sizes For Each Layer of A (1-Dimensional) CNN, Create A Function To Compute The Receptive Field of A Particular Node In The Network.
The receptive field of a neuron in a convolutional neural network (CNN) is the region of the input space that affects the neuron’s activation.
8.1. Calculating the Receptive Field
To compute the receptive field of a particular node in the network, you need to consider the kernel sizes and strides of each layer. The receptive field size can be calculated using the following formula:
$$
Ri = R{i-1} + (K_i – 1) times S_i
$$
Where:
- ( R_i ) is the receptive field size at layer ( i )
- ( K_i ) is the kernel size at layer ( i )
- ( S_i ) is the stride at layer ( i )
- ( R_0 = 1 ) (receptive field of the first layer is 1)
8.2. Example Function
def compute_receptive_field(kernel_sizes, strides):
receptive_field = 1
for k, s in zip(kernel_sizes, strides):
receptive_field = receptive_field + (k - 1) * s
return receptive_field
kernel_sizes = [3, 3, 3]
strides = [1, 2, 1]
receptive_field_size = compute_receptive_field(kernel_sizes, strides)
print(f"Receptive field size: {receptive_field_size}")
9. Implement Connected Components on An Image/Matrix.
Connected components labeling (CCL) is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled, based on a given heuristic.
9.1. Algorithm for Connected Components Labeling
- First Pass:
- Iterate through each pixel in the image.
- If the pixel is part of an object (foreground), check its neighbors.
- If no neighbors are labeled, assign a new label to the pixel.
- If one neighbor is labeled, assign that label to the pixel.
- If multiple neighbors are labeled, assign one of the labels and note the equivalence.
- Second Pass:
- Resolve the label equivalences by propagating the smallest equivalent label.
- Output:
- Assign the final labels to each pixel.
10. Implement A Sparse Matrix Class In C++.
A sparse matrix is a matrix in which most of the elements are zero. Representing a sparse matrix efficiently requires special data structures to store only the non-zero elements.
10.1. Data Structures for Sparse Matrices
- Coordinate List (COO): Stores each non-zero element as a tuple of (row, column, value).
- Compressed Sparse Row (CSR): Stores the non-zero elements row by row, along with row pointers and column indices.
- Compressed Sparse Column (CSC): Stores the non-zero elements column by column, along with column pointers and row indices.
10.2. C++ Implementation
#include <iostream>
#include <vector>
class SparseMatrix {
private:
int rows, cols;
std::vector<std::tuple<int, int, double>> data;
public:
SparseMatrix(int rows, int cols) : rows(rows), cols(cols) {}
void set(int row, int col, double value) {
if (value != 0) {
data.emplace_back(row, col, value);
}
}
double get(int row, int col) {
for (const auto& element : data) {
if (std::get<0>(element) == row && std::get<1>(element) == col) {
return std::get<2>(element);
}
}
return 0;
}
void print() {
for (int i = 0; i < rows; ++i) {
for (int j = 0; j < cols; ++j) {
std::cout << get(i, j) << " ";
}
std::cout << std::endl;
}
}
};
int main() {
SparseMatrix matrix(4, 4);
matrix.set(0, 0, 1.0);
matrix.set(1, 2, 2.5);
matrix.set(3, 3, 3.0);
matrix.print();
return 0;
}
11. Create A Function To Compute An Integral Image, And Create Another Function To Get Area Sums From The Integral Image.
An integral image (also known as a summed-area table) is a data structure that allows for the efficient calculation of the sum of pixel values within any rectangular region of an image.
11.1. Computing the Integral Image
The value at each location (x, y) in the integral image is the sum of all pixels above and to the left of (x, y), inclusive.
$$
I(x, y) = sum_{x’ leq x, y’ leq y} img(x’, y’)
$$
11.2. Calculating Area Sums
To calculate the sum of pixel values within a rectangular region defined by the top-left corner (x1, y1) and the bottom-right corner (x2, y2), use the following formula:
$$
sum = I(x2, y2) – I(x1 – 1, y2) – I(x2, y1 – 1) + I(x1 – 1, y1 – 1)
$$
11.3. Python Implementation
import numpy as np
def compute_integral_image(image):
integral_image = np.zeros(image.shape, dtype=np.int32)
for x in range(image.shape[0]):
for y in range(image.shape[1]):
integral_image[x, y] = image[x, y]
if x > 0:
integral_image[x, y] += integral_image[x-1, y]
if y > 0:
integral_image[x, y] += integral_image[x, y-1]
if x > 0 and y > 0:
integral_image[x, y] -= integral_image[x-1, y-1]
return integral_image
def get_area_sum(integral_image, x1, y1, x2, y2):
sum_value = integral_image[x2, y2]
if x1 > 0:
sum_value -= integral_image[x1-1, y2]
if y1 > 0:
sum_value -= integral_image[x2, y1-1]
if x1 > 0 and y1 > 0:
sum_value += integral_image[x1-1, y1-1]
return sum_value
image = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
integral_image = compute_integral_image(image)
area_sum = get_area_sum(integral_image, 0, 0, 1, 1)
print(f"Area sum: {area_sum}")
12. How Would You Remove Outliers When Trying To Estimate A Flat Plane From Noisy Samples?
Estimating a flat plane from noisy samples requires robust methods that are not easily influenced by outliers.
12.1. RANSAC Algorithm
RANSAC (Random Sample Consensus) is an iterative method to estimate parameters of a mathematical model from a set of observed data that contains outliers.
- Randomly Sample: Select a minimal set of data points to fit the model.
- Fit the Model: Estimate the model parameters using the selected data points.
- Find Inliers: Determine which data points are consistent with the estimated model within a given tolerance.
- Iterate: Repeat the process for a fixed number of iterations or until a good model is found.
12.2. Implementation
import numpy as np
from sklearn import linear_model
def ransac_plane_estimation(points, threshold, max_iterations):
best_model = None
best_inliers = []
for _ in range(max_iterations):
# Randomly sample 3 points
sample_indices = np.random.choice(len(points), 3, replace=False)
sample_points = points[sample_indices]
# Fit a plane to the sampled points
try:
plane_model = linear_model.LinearRegression()
X = sample_points[:, :2] # Use x and y coordinates
y = sample_points[:, 2] # Predict z coordinate
plane_model.fit(X, y)
# Find inliers
predictions = plane_model.predict(points[:, :2])
errors = np.abs(predictions - points[:, 2])
inliers = points[errors < threshold]
# Update best model if the current model has more inliers
if len(inliers) > len(best_inliers):
best_model = plane_model
best_inliers = inliers
except np.linalg.LinAlgError:
continue
return best_model, best_inliers
13. How Does CBIR Work?
Content-Based Image Retrieval (CBIR) is a technique for retrieving images from a database based on the visual content of the images, such as color, texture, and shape.
13.1. Steps in CBIR
- Feature Extraction: Extract visual features from the images in the database.
- Indexing: Create an index of the extracted features.
- Query Image: Extract visual features from the query image.
- Similarity Matching: Compare the features of the query image with the features in the index to find similar images.
- Ranking: Rank the similar images based on their similarity scores.
- Retrieval: Retrieve the top-ranked images.
13.2. Feature Extraction Methods
- Color Histograms: Represent the distribution of colors in an image.
- Texture Features: Capture the texture properties of an image using methods like Gabor filters or Local Binary Patterns (LBP).
- Shape Features: Describe the shape of objects in an image using methods like edge detection or shape contexts.
14. How Does Image Registration Work? Sparse vs. Dense Optical Flow and So On.
Image registration is the process of transforming different sets of data into one coordinate system. This is used to align images.
14.1. Types of Image Registration
- Feature-Based Registration: Detects and matches corresponding features in the images.
- Intensity-Based Registration: Directly compares the pixel intensities of the images.
14.2. Optical Flow
Optical flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and the scene.
- Sparse Optical Flow: Calculates the motion vectors for a sparse set of points in the image.
- Dense Optical Flow: Calculates the motion vectors for every pixel in the image.
15. Describe How Convolution Works. What About If Your Inputs Are Grayscale vs RGB Imagery? What Determines the Shape of the Next Layer?
Convolution is a fundamental operation in convolutional neural networks (CNNs) used to extract features from images.
15.1. Convolution Operation
The convolution operation involves sliding a kernel (filter) over the input image and performing element-wise multiplications between the kernel and the corresponding pixels in the image. The results are then summed up to produce a single value in the output feature map.
15.2. Grayscale vs RGB Imagery
- Grayscale Imagery: The input image has a single channel (intensity values). The kernel slides over the image in two dimensions.
- RGB Imagery: The input image has three channels (red, green, blue). The kernel is a 3D filter that slides over the image in two spatial dimensions and operates on all three color channels.
15.3. Shape of the Next Layer
The shape of the next layer (output feature map) in a CNN is determined by several factors:
- Input Size: The dimensions of the input image.
- Kernel Size: The dimensions of the convolutional kernel.
- Stride: The step size by which the kernel moves across the input image.
- Padding: The amount of padding added to the input image.
- Number of Filters: The number of different kernels applied to the input image.
The formula to calculate the output size is:
$$
OutputSize = frac{(InputSize – KernelSize + 2 times Padding)}{Stride} + 1
$$
16. Talk Me Through How You Would Create A 3D Model of An Object From Imagery And Depth Sensor Measurements Taken At All Angles Around The Object.
Creating a 3D model of an object from imagery and depth sensor measurements involves several steps:
16.1. Data Acquisition
- Imagery: Capture multiple images of the object from different viewpoints using a camera.
- Depth Sensor Measurements: Use a depth sensor to obtain depth information about the object from different angles.
16.2. Calibration
- Camera Calibration: Calibrate the camera to determine its intrinsic parameters (e.g., focal length, principal point) and distortion coefficients.
- Sensor Calibration: Calibrate the depth sensor to determine its intrinsic parameters and alignment with the camera.
16.3. Feature Extraction and Matching
- Feature Extraction: Extract distinctive features from the images (e.g., SIFT, SURF).
- Feature Matching: Match corresponding features between the images.
16.4. Structure from Motion (SfM) or Simultaneous Localization and Mapping (SLAM)
- SfM: Estimate the 3D structure of the object and the camera poses from the matched features.
- SLAM: Simultaneously estimate the 3D structure of the environment and the pose of the sensor.
16.5. Depth Map Fusion
- Depth Map Registration: Align the depth maps obtained from the depth sensor.
- Depth Map Fusion: Fuse the aligned depth maps to create a complete 3D model of the object.
16.6. Mesh Reconstruction
- Surface Reconstruction: Create a 3D mesh from the fused depth map using algorithms like Poisson reconstruction or marching cubes.
17. Implement SQRT(const double & x) Without Using Any Special Functions, Just Fundamental Arithmetic.
Implementing the square root function using fundamental arithmetic involves iterative methods like the Babylonian method (also known as Heron’s method).
17.1. Babylonian Method
- Initial Guess: Start with an initial guess for the square root (e.g., x/2).
- Iterative Refinement: Refine the guess using the formula:
$$
guess{new} = frac{guess{old} + frac{x}{guess_{old}}}{2}
$$
- Convergence: Repeat the iterative refinement until the guess converges to the true square root.
17.2. C++ Implementation
#include <iostream>
#include <cmath>
double sqrt_implementation(const double& x) {
if (x < 0) {
return NAN; // Not a number
}
if (x == 0) {
return 0;
}
double guess = x / 2.0;
double precision = 0.00001;
while (std::abs(guess * guess - x) > precision) {
guess = (guess + x / guess) / 2.0;
}
return guess;
}
int main() {
double num = 25.0;
double result = sqrt_implementation(num);
std::cout << "Square root of " << num << " is " << result << std::endl;
return 0;
}
18. Reverse A Bitstring.
Reversing a bitstring involves flipping the order of the bits in the string.
18.1. Python Implementation
def reverse_bitstring(bitstring):
return bitstring[::-1]
bitstring = "11001010"
reversed_bitstring = reverse_bitstring(bitstring)
print(f"Reversed bitstring: {reversed_bitstring}")
18.2. Efficient Bit Reversal
For efficient bit reversal, especially for larger bitstrings, bitwise operations can be used.
19. Implement Non Maximal Suppression As Efficiently As You Can.
Non-Maximum Suppression (NMS) is a technique used to eliminate redundant detections of the same object in an image.
19.1. Algorithm for NMS
- Sort Detections: Sort the bounding boxes based on their confidence scores.
- Iterate Through Detections:
- Select the bounding box with the highest score.
- Remove all other bounding boxes that have a high Intersection over Union (IoU) with the selected box.
- Repeat: Repeat the process until all bounding boxes have been processed.
19.2. Python Implementation
def non_max_suppression(boxes, scores, iou_threshold):
# Sort by score
sorted_indices = scores.argsort()[::-1]
keep_boxes = []
while sorted_indices.size > 0:
# Pick the box with the highest score
best_box_index = sorted_indices[0]
best_box = boxes[best_box_index]
keep_boxes.append(best_box_index)
# Compute IoU with the remaining boxes
ious = compute_iou(best_box, boxes[sorted_indices[1:]])
# Remove boxes with IoU greater than the threshold
remove_indices = np.where(ious > iou_threshold)[0]
sorted_indices = np.delete(sorted_indices, remove_indices + 1)
sorted_indices = np.delete(sorted_indices, 0)
return keep_boxes
20. Reverse A Linked List In Place.
Reversing a linked list in place involves modifying the pointers of the nodes such that the list is reversed without using additional memory.
20.1. Algorithm for Reversing a Linked List
- Initialize:
prev
=None
current
=head
next
=None
- Iterate:
- While
current
is notNone
:next
=current.next
current.next
=prev
prev
=current
current
=next
- While
- Update Head:
head
=prev
20.2. Python Implementation
class Node:
def __init__(self, data):
self.data = data
self.next = None
def reverse_linked_list(head):
prev = None
current = head
while(current is not None):
next_node = current.next
current.next = prev
prev = current
current = next_node
head = prev
return head
21. What Is Data Normalization And Why Do We Need It?
Data normalization is a preprocessing technique used to scale numerical features to a standard range of values.
21.1. Reasons for Data Normalization
- Improved Convergence: Normalization can speed up the convergence of optimization algorithms like gradient descent.
- Equal Weighting: Normalization ensures that all features are weighted equally by the model.
- Prevention of Numerical Instability: Normalization can prevent numerical instability caused by large feature values.
21.2. Common Normalization Techniques
- Min-Max Scaling: Scales the data to a range between 0 and 1.
$$
X{scaled} = frac{X – X{min}}{X{max} – X{min}}
$$
- Z-Score Standardization: Scales the data to have zero mean and unit variance.
$$
X_{standardized} = frac{X – mu}{sigma}
$$
22. Why Do We Use Convolutions For Images Rather Than Just FC Layers?
Convolutions are preferred over fully connected (FC) layers for image processing tasks due to several advantages:
22.1. Advantages of Convolutions
- Parameter Sharing: Convolutional layers use shared weights, which reduces the number of parameters compared to FC layers.
- Spatial Hierarchy: Convolutional layers learn hierarchical representations of the image, capturing local patterns and global structures.
- Translation Invariance: Convolutional layers are translation invariant, meaning they can detect the same pattern regardless of its location in the image.
23. What Makes CNNs Translation Invariant?
Convolutional Neural Networks (CNNs) achieve translation invariance through the use of shared weights and pooling layers.
23.1. Translation Invariance
- Shared Weights: Convolutional filters learn to detect specific patterns in the image. Since the same filter is applied across the entire image, the network can detect the pattern regardless of its location.
- Pooling Layers: Pooling layers reduce the spatial resolution of the feature maps, making the network more robust to small translations and distortions.
24. Why Do We Have Max-Pooling In Classification CNNs?
Max-pooling is a downsampling technique used in Convolutional Neural Networks (CNNs) to reduce the spatial dimensions of the feature maps.
24.1. Benefits of Max-Pooling
- Reduced Computation: Max-pooling reduces the number of parameters and computations in the network.
- Increased Receptive Field: Max-pooling increases the receptive field of the subsequent layers, allowing the network to capture more global context.
- Translation Invariance: Max-pooling makes the network more robust to small translations and distortions.
25. Why Do Segmentation CNNs Typically Have An Encoder-Decoder Style / Structure?
Segmentation CNNs typically have an encoder-decoder structure to capture both the context and the fine-grained details in the image.
25.1. Encoder-Decoder Structure
- Encoder: The encoder part of the network progressively reduces the spatial resolution of the input image, capturing the high-level context.
- Decoder: The decoder part of the network progressively increases the spatial resolution of the feature maps, recovering the fine-grained details and producing a segmentation map.
26. What Is The Significance Of Residual Networks?
Residual Networks (ResNets) are a type of deep neural network architecture that uses skip connections to allow information to flow directly from earlier layers to later layers.
26.1. Significance of Residual Networks
- Mitigating Vanishing Gradients: Skip connections help to mitigate the vanishing gradient problem, allowing for the training of very deep networks.
- Improved Information Flow: Skip connections allow for direct feature access from previous layers, making information propagation throughout the network much easier.
27. What Is Batch Normalization And Why Does It Work?
Batch normalization is a technique used to normalize the inputs of each layer in a neural network by scaling and shifting them to have zero mean and unit variance.
27.1. How Batch Normalization Works
- Compute Mean and Variance: Calculate the mean and variance of the activations for each mini-batch.
- Normalize: Normalize the activations using the computed mean and variance.
- Scale and Shift: Scale and shift the normalized activations using learnable parameters (gamma and beta).
27.2. Benefits of Batch Normalization
- Improved Convergence: Batch normalization can speed up the convergence of the network.
- Higher Learning Rates: Batch normalization allows for the use of higher learning rates.
- Regularization: Batch normalization acts as a regularizer, reducing overfitting.
28. Why Would You Use Many Small Convolutional Kernels Such As 3×3 Rather Than A Few Large Ones?
Using many small convolutional kernels, such as 3×3, is often preferred over a few large ones for several reasons:
28.1. Advantages of Small Kernels
- More Non-Linearities: Multiple layers with small kernels introduce more non-linear activation functions, allowing the network to learn more complex functions.
- Fewer Parameters: Multiple small kernels can achieve the same receptive field as a large kernel with fewer parameters.
29. Why Do We Need A Validation Set And Test Set? What Is The Difference Between Them?
Validation and test sets are essential for evaluating the performance of a machine learning model.
29.1. Differences Between Validation and Test Sets
- Validation Set: Used to tune the hyperparameters of the model and evaluate its performance during training.
- Test Set: Used to evaluate the final performance of the model after training and hyperparameter tuning.
29.2. Purpose of Validation and Test Sets
- Validation Set: Helps to prevent overfitting to the training data and to select the best model.
- Test Set: Provides an unbiased estimate of the model’s generalization performance on unseen data.
30. What Is Stratified Cross-Validation And When Should We Use It?
Stratified cross-validation is a cross-validation technique that preserves the proportion of target categories in each fold.
30.1. When to Use Stratified Cross-Validation
- Imbalanced Datasets: Stratified cross-validation is particularly useful when dealing with imbalanced datasets, where some categories have significantly fewer samples than others.
- Datasets with Multiple Categories: Stratified cross-validation ensures that each category is represented in both the training and validation sets.
31. Why Do Ensembles Typically Have Higher Scores Than Individual Models?
Ensembles combine the predictions of multiple models to create a single prediction. Ensembles typically have higher scores than individual models because they can reduce both bias and variance.
31.1. Benefits of Ensembles
- Reduced Bias: Ensembles can reduce bias by averaging the predictions of multiple models with different biases.
- Reduced Variance: Ensembles can reduce variance by averaging the predictions of multiple models with different variances.
- Improved Generalization: Ensembles can improve the generalization performance of the model by combining the strengths of multiple models.
32. What Is An Imbalanced Dataset? Can You List Some Ways To Deal With It?
An imbalanced dataset is one where the target categories have different proportions of samples.
32.1. Ways to Deal with Imbalanced Datasets
- Oversampling: Increase the number of samples in the minority category.
- Undersampling: Decrease the number of samples in the majority category.
- Data Augmentation: Create new samples in the minority category by modifying existing samples.
- Cost-Sensitive Learning: Assign different costs to misclassifications of different categories.
- Ensemble Methods: Use ensemble methods like bagging and boosting to combine the