5 - Birds of a Feather Flashcards
What was the Cholera Inquiry Committee’s report primarily about?
A severe cholera outbreak in a London parish in 1854
The report highlighted the impact of the outbreak, particularly in the Soho area.
Who was a notable member of the Cholera Inquiry Committee?
John Snow
Snow was a physician known for his contributions to anesthesiology and epidemiology.
What hypothesis did John Snow propose regarding cholera?
Cholera was a waterborne disease
This hypothesis was supported by the clustering of the outbreak around a specific water pump.
What did John Snow’s map of Soho illustrate?
The locations of cholera deaths and water pumps
The map included a dotted line indicating the area affected by cholera.
What is a Voronoi cell?
A region defined such that any point inside is closer to a specific seed than to any other seed
In Snow’s context, the seed was a water pump.
What did Snow’s inner dotted line represent?
Equidistant points from the Broad Street pump and surrounding pumps
It helped demonstrate the relationship between deaths and proximity to water sources.
What modern concept is illustrated by Snow’s analysis of the cholera outbreak?
Nearest neighbor search algorithms
This concept is fundamental in various fields, including machine learning.
What is Manhattan distance?
A measure of distance based on grid-like paths, summing the absolute differences of coordinates
It contrasts with Euclidean distance, which measures straight-line distance.
What historical figure is known for significant contributions to optics and vision?
Abu Ali al-Hasan Ibn al-Haytham (Alhazen)
Alhazen’s work transformed the understanding of vision during the Islamic Golden Age.
What is the ‘faculty of discrimination’ according to Alhazen?
The cognitive process that compares what is seen to stored memories
This process aids in recognizing objects.
What algorithm is associated with the concept of nearest neighbors?
Nearest Neighbor (NN) rule
This algorithm was formally analyzed in the 1950s and is crucial for pattern recognition.
True or False: Alhazen’s theories on vision were widely accepted in his time.
False
His ideas were revolutionary compared to the prevailing theories at the time.
Fill in the blank: John Snow’s analysis of the cholera outbreak led to the inspection of the _______.
Broad Street pump
This inspection revealed the contamination source related to the cholera outbreak.
What did the Cholera Inquiry Committee find regarding death rates in the ‘Cholera area’?
Deaths were over 10 percent, about 1,000 to every 10,000 persons living
This statistic highlights the severity of the outbreak.
What was a key innovation in Snow’s mapping technique?
Annotated map showing the correlation between cholera deaths and water pump locations
This visualization was groundbreaking for epidemiology.
How did Snow demonstrate that distance affected cholera infection rates?
He showed that deaths decreased as proximity to the Broad Street pump increased
This finding was crucial in establishing the waterborne theory.
What does the nearest neighbor rule help classify?
Data as belonging to one category or another
Who is associated with the initial concept of the nearest neighbor rule?
Alhazen
What mathematical concept is used to represent points in a 2D or 3D coordinate system?
Vectors
How can a 7×9 image be represented mathematically?
As a 63-dimensional vector
What do the pixels in a 7×9 image represent in terms of values?
0 for white and 1 for black
What happens when you draw a numeral on a touch screen?
The pattern is stored as a 63-bit long number
What is the significance of clustering in the context of the nearest neighbor rule?
Vectors representing similar patterns cluster near each other in 63D space
What is the main task of a machine learning algorithm when given a new unlabeled pattern?
To determine whether it belongs to category 2 or 8
What is the nearest neighbor rule based on?
Finding the point nearest to a new unlabeled vector in hyperdimensional space
When was the nearest neighbor rule first mathematically mentioned?
In a 1951 technical report by Fix and Hodges
What is a key feature of the nearest neighbor algorithm regarding data distribution?
It does not make any assumptions about the underlying data distribution
What is a potential issue with using only one nearest neighbor?
Overfitting
What is the recommended number of nearest neighbors to avoid ties in classification?
An odd number
What happens when the nearest neighbor algorithm is applied with three neighbors?
It uses majority voting to classify the new data point
What is the effect of increasing the number of nearest neighbors?
The boundary becomes smoother and more generalized
What does overfitting refer to in machine learning?
The algorithm fitting too closely to the training data, including noise
What is the trade-off when avoiding overfitting in a classifier?
Some misclassifications may occur in the training dataset
What is the primary goal of the nearest neighbor algorithm?
To classify new data points based on proximity to labeled data
Fill in the blank: Each point in a 3D coordinate system is represented by a _______.
[x, y, z]
True or False: The nearest neighbor algorithm can only classify linearly separable data.
False
What is overfitting in the context of classifiers?
Overfitting occurs when a classifier misclassifies some data points in the training dataset to achieve better performance on unseen data.
Why is it desirable for a classifier to not overfit the training data?
A classifier that does not overfit is likely to make fewer errors when tested with unseen data.
What is the Bayes optimal classifier?
The Bayes optimal classifier is the best a machine algorithm can do, assuming access to the underlying probability distributions of the data.
How does the nearest neighbor algorithm differ from the Bayes optimal classifier?
The nearest neighbor algorithm makes fewer assumptions about the underlying distributions and relies solely on the available data.
What is the significance of Jensen’s inequality and the dominated convergence theorem in the context of the nearest neighbor algorithm?
These mathematical results were significant in developing the intuition and proofs needed for the nearest neighbor algorithm’s efficacy.
What is the 1-nearest neighbor (1-NN) rule?
The 1-NN rule classifies a new data point based on the closest point in the training dataset.
What happens when the 1-NN algorithm is applied to a new penguin with a given bill depth?
The algorithm will classify the new penguin based on the majority class of its nearest neighbors.
What is the relationship between the number of samples and the performance of the k-NN algorithm?
As the number of samples increases, the k-NN algorithm’s performance approaches that of the Bayes optimal classifier.
What is the curse of dimensionality?
The curse of dimensionality refers to the challenges and inefficiencies that arise when analyzing data in high-dimensional spaces.
How does the dimensionality of data affect the number of samples in a specific region?
As dimensionality increases, the probability of finding samples in a defined region decreases significantly.
What is a nonparametric model?
A nonparametric model has no fixed number of parameters and uses all instances of training data for inference.
What are the steps involved in the k-NN algorithm?
- Store all instances of sample data. 2. Calculate distances to new data points. 3. Sort distances and rearrange labels. 4. Classify based on majority label among nearest neighbors.
True or False: The k-NN algorithm requires a fixed number of parameters.
False
What is the mathematical relationship between the k-NN algorithm and the Bayes optimal classifier as the sample size increases?
The performance of the k-NN algorithm approaches that of the Bayes optimal classifier as the sample size increases.
What is the primary disadvantage of the k-NN algorithm?
It requires increasing amounts of computational power and memory as the size of datasets grows.
Fill in the blank: The k-NN algorithm classifies a new data point as ______ if the majority of its nearest neighbors are labeled as that class.
the same class
What happens to the chance of finding a data point as the number of features increases to 1,000 or more?
The chance of finding a data point within a unit hypercube rapidly diminishes.
What is a unit hypercube?
A unit hypercube is a geometric figure where the length of each side is equal to 1.
What does Julie Delon mean by ‘In high dimensional spaces, nobody can hear you scream’?
It refers to the difficulty of finding data points in high-dimensional spaces.
How can the problem of the curse of dimensionality be mitigated?
By increasing the number of data samples, but this must grow exponentially with the number of dimensions.
What is the k-NN algorithm?
A machine learning algorithm that calculates distances between a new data point and each sample in the training dataset.
What is the assumption behind the k-NN algorithm regarding data points?
Similar points have smaller distances between them than dissimilar points.
What happens to distances between data points in high-dimensional space?
The behavior of distances becomes counterintuitive, affected by the volumes of hyperspheres and hypercubes.
What is the volume of a unit sphere in higher dimensions?
The volume tends to zero as the number of dimensions increases.
What is the volume of a unit hypercube regardless of dimensionality?
The volume is always 1.
How does the number of vertices in a hypercube change with dimensions?
The number of vertices is 2 raised to the power of the number of dimensions (2^d).
In a 3D unit cube, how far are the vertices from the origin?
The vertices are farther away than the surfaces of the cube which are 1 unit away from the origin.
What happens to the volume of the unit hypersphere as dimensions increase?
Most of the volume of the hypercube ends up near the vertices, and the internal volume occupied by the hypersphere vanishes.
What is the consequence of data points populating the corners of the hypercube?
Most corners are devoid of data points, leading to points being almost equidistant from each other.
What is principal component analysis (PCA)?
A technique used to reduce high-dimensional data to a lower-dimensional space while preserving variation.
What does Bellman suggest about the curse of dimensionality?
Significant results can still be obtained despite the curse.
Fill in the blank: The k-NN algorithm works best for ______ data.
[low-dimensional]
True or False: The volume of a unit hypersphere increases as the dimensionality increases.
False
