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Questions and Answers
What does qualitative refer to?
What does qualitative refer to?
Variables without numeric value (e.g. eye color)
What is classification in data analysis?
What is classification in data analysis?
Predicting qualitative responses
What is a classifier?
What is a classifier?
Generic name for a classification technique
What is logistic regression used for?
What is logistic regression used for?
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What does Linear Discriminant Analysis (LDA) assume about predictors?
What does Linear Discriminant Analysis (LDA) assume about predictors?
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What is a binary response?
What is a binary response?
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What is k-Nearest Neighbors?
What is k-Nearest Neighbors?
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What is the logistic function represented by?
What is the logistic function represented by?
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What is maximum likelihood fitting?
What is maximum likelihood fitting?
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What does odds represent?
What does odds represent?
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What are log-odds / logits?
What are log-odds / logits?
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What does confounding refer to?
What does confounding refer to?
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What is the prior in probability?
What is the prior in probability?
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What does a density function do?
What does a density function do?
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What does Bayes' Theorem express?
What does Bayes' Theorem express?
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What is the posterior probability?
What is the posterior probability?
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What is the normal Gaussian distribution formula?
What is the normal Gaussian distribution formula?
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What is a discriminant function?
What is a discriminant function?
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What defines a multivariate Gaussian?
What defines a multivariate Gaussian?
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What is overfitting in modeling?
What is overfitting in modeling?
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What is a null classifier?
What is a null classifier?
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What is a confusion matrix?
What is a confusion matrix?
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What does sensitivity measure in classification?
What does sensitivity measure in classification?
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What does specificity measure in classification?
What does specificity measure in classification?
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What is the Receiver Operating Characteristic (ROC) curve?
What is the Receiver Operating Characteristic (ROC) curve?
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What is quadratic discriminant analysis?
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.