Probability #
Random experiment - An act that has predefined number of outcomes.
Elementary Event - Each individual possiblity in a random experiment. All possible elementary events of an experiment together make the the sample space of the experiment.
Random event - Combination of set/subset of elementary events, such as tosssing a coin multiple times.
Marginal Probablity - Probablity of occurance of an event. This is probability in its most basic form. Probablity of an event A occuring is denoted as \(P(x = A)\) or simply \(P(A)\) .
Joint Probablity - Probablity of simultaneous occurance of two random events, represented as \(P(X = A, Y = B)\) or \(P(A, B)\) or \(P(A \cap B)\) .
Conditional Probability - Probability of an event occurring that another dependent event has occurend already. Represented as \(P(A \mid B)\)
Lagrange Multiplier Used to convert constrained problem into an unconstraint problem. Works only on equality constraints.
P-value #
- Probability that the random chance generated the data, or something else that is equal or rarer.
- Value ranges between 0 and 1
- Typical threshold is .05 or 5%
- Getting a small value in effect rejects the null hypothesis
- If the p-value is on the border line, then the data is inconclusive
Null Hypothesis #
- Hypothesis that states that there is no relation between the attributes and the outcome.
- If p-value is less then 5%, then the null hypothesis is rejected and the alternate hypothesis is accepted
Distance computations #
Points Euclidian, Manhattan, Minkowski, Chevskov Binary Jaccard Similarity Doc clustering Cosine
Euclidean - Not suitable for noisy data