Questions and Answers
What does qualitative refer to?
Variables without numeric value (e.g. eye color)
What is classification in data analysis?
Predicting qualitative responses
What is a classifier?
Generic name for a classification technique
What is logistic regression used for?
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What does Linear Discriminant Analysis (LDA) assume about predictors?
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What is a binary response?
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What is k-Nearest Neighbors?
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What is the logistic function represented by?
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What is maximum likelihood fitting?
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What does odds represent?
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What are log-odds / logits?
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What does confounding refer to?
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What is the prior in probability?
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What does a density function do?
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What does Bayes' Theorem express?
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What is the posterior probability?
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What is the normal Gaussian distribution formula?
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What is a discriminant function?
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What defines a multivariate Gaussian?
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What is overfitting in modeling?
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What is a null classifier?
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What is a confusion matrix?
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What does sensitivity measure in classification?
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What does specificity measure in classification?
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What is the Receiver Operating Characteristic (ROC) curve?
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What is quadratic discriminant analysis?
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Study Notes
Qualitative Variables
- Defined as variables without numeric value; examples include eye color and gender.
Classification
- Refers to predicting qualitative responses based on input data.
Classifier
- A generic term encompassing various classification techniques used to categorize data.
Logistic Regression
- A classification technique modeling the probability of a response belonging to a specific class using a sigmoid function.
Linear Discriminant Analysis (LDA)
- A classifier that assumes predictors follow a Gaussian distribution; it uses Bayes' Theorem to determine the most probable class for a given observation.
Binary Response
- A type of response variable with only two possible outcomes.
k-Nearest Neighbors (k-NN)
- A non-parametric classification method that classifies observations based on majority class membership of nearby data points.
Logistic Function
- Mathematically expressed as $\frac{e^{\beta X}}{1 + e^{\beta X}}$, representing the sigmoid curve used in logistic regression.
Maximum Likelihood
- A parameter estimation method where the likelihood function is maximized to fit a statistical model.
Odds
- Defined as $\frac{P(X)}{1 - P(X)}$, a measure of the likelihood of an event occurring relative to it not occurring.
Log-Odds / Logit
- Expressed as $\ln{\frac{P(X)}{1 - P(X)}}$, representing the logarithm of the odds.
Confounding
- Occurs when correlations among predictors skew the perceived relationships between them and the response variable.
Prior Probability
- Refers to the likelihood that a randomly selected observation belongs to a specific class before considering any evidence.
Density Function
- A continuous function, denoted as f(x), describing the probability of a variable x occurring.
Bayes' Theorem
- A foundational concept in probability, expressed as $p(A and B) = P(B | A)P(A)$, relating conditional probabilities.
Posterior Probability
- Represents the probability of a class given observed evidence, denoted as $f(a) = p(A = a | B)$.
Normal Gaussian Distribution
- Mathematically defined as $\frac{1}{\sqrt{2\pi}\sigma} \exp{( -\frac{1}{2\sigma^{2}} (x-\mu_{k})^{2} )}$, characterizing the bell-shaped curve of typical distribution.
Discriminant Function
- Utilizes auxiliary functions to estimate the class most likely associated with a test observation.
Multivariate Gaussian
- Extends Gaussian distribution to multiple dimensions, encompassing p > 1 variables.
Overfitting
- Occurs when a model captures noise from the training data rather than the underlying relationship, potentially leading to poor performance on new data.
Null Classifier
- A baseline classifier assigning observations to the most frequent class in the training set without additional information.
Confusion Matrix
- A comprehensive representation of classifier performance, summarizing true positive/negative and false positive/negative counts.
Sensitivity
- A crucial classifier metric measuring the proportion of true positives identified correctly.
Specificity
- A metric that represents the proportion of true negatives accurately identified by the classifier.
Receiver Operating Characteristic (ROC) Curve
- A graphical representation plotting true positive rate against false positive rate across various threshold settings to evaluate classifier performance.
Quadratic Discriminant Analysis
- A model that assumes observations from each class originate from Gaussian distributions with distinct covariance matrices for each class.
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Test your knowledge of key terms from Chapter 4 of ISLR. This set of flashcards covers essential concepts such as qualitative variables, classification techniques, and logistic regression. Perfect for anyone studying data science and statistics.