Data Science Cheetsheet

1. Probability
2. Statistics
3. Machine Learning

1) Probability

1.1) Conditional Probability

1.2) Counting

1.2.1) Permutation

from itertools import permutations

a = [1,2,3]
perm = permutations(a)
print(list(perm))

# [(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]

1.2.1) Combination

from itertools import combinations

a = [1,2,3,4]
comb = combinations(a, 2)
print(list(comb))

# [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]

1.3) Probability Distributions

1.3.1) Discrete Probability Distributions

Num	Distribution	Definition	Usage
1	Binomial distribution	Probability of k number of successes in n independent trial	Coin flips (number of heads in n flips)
2	Poisson distribution	Number of events occurring within a particular fixed interval ( $\lambda$ )	Number of visits to a website in a certain period of time

1.3.2) Continuous Probability Distributions

Num	Distribution	Definition	Usage
1	Uniform distribution	Constant probability of X falling between a and b	In sampling and hypothesis testing cases
2	Exponential distribution	Poisson for continous data	The time until a credit defaul occurs
3	Normal distribution	Probability according to the bell curve over a range of Xs	The Central Limit Theorem

1.4) Markov Chains

2) Statistics

2.1) Random Variables

2.2) Central Limit Theorem

2.3) Hypothesis Testing

2.3.1) General Information

2.3.2) Type I and Type II Errors

2.3.3) p-values & Confidence Intervals

2.3.4) Test Statistics

2.4) MLE & MAP

Maximum Likelihood Estimation (MLE) and Maximum A Posteriori (MAP) estimation. The difference among them is the inclusion of the prior in MAP. Moreover, MLE can be seen as a special case of MAP with a uniform prior.

3) Machine Learning

3.1) Linear Algebra

3.1.1) Eigenvalues and Eigenvectors

3.2) Model Evaluation and Selection

3.2.1) Bias-Variance Trade-off

3.3) Model Training

3.3.1) Hyperparameter Tuning

3.4) Linear Regression

Linear regression assumptions

Num	Assumption	Description
1	Linearity	The relationship between the features and the target variable is linear
2	Homoscedasticity	The variance of the residuals is constant
3	Independence	All observations are independent of each other
4	Normality	The distribution of the target variable (Y) is assumed to be normal