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Introduction to Probability and Statistics

Instructor: Applied AI Course Duration: 17 mins

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Population and Sample
1.1
Introduction to IRIS dataset and 2D scatter plot

26 min
1.2
3D scatter plot

6 min
1.3
Pair plots

14 min
1.4
Limitations of pair plots

2 min
1.5
Histogram and Introduction to PDF(Probability Density Function)

17 min
1.6
Univariate Analysis using PDF

6 min
1.7
CDF(Cumulative Distribution Function)

1.8
Mean, Variance and Standard Deviation

17 min
1.9
Median

10 min
1.10
Percentiles and Quantiles

9 min
1.11
IQR(Inter Quartile Range) and MAD(Median Absolute Deviation)
30 min
1.12
Box-plot with Whiskers

9 min
1.13
Violin Plots

4 min
1.14
Summarizing Plots, Univariate, Bivariate and Multivariate analysis

6 min
1.15
Multivariate Probability Density, Contour Plot

9 min
1.16
Exercise: Perform EDA on Haberman dataset

4 min
2.1
Why learn it ?

4 min
2.2
Introduction to Vectors(2-D, 3-D, n-D) , Row Vector and Column Vector

14 min
2.3
Dot Product and Angle between 2 Vectors

14 min
2.4
Projection and Unit Vector

5 min
2.5
Equation of a line (2-D), Plane(3-D) and Hyperplane (n-D), Plane Passing through origin, Normal to a Plane

23 min
2.6
Distance of a point from a Plane/Hyperplane, Half-Spaces

10 min
2.7
Equation of a Circle (2-D), Sphere (3-D) and Hypersphere (n-D)

7 min
2.8
Equation of an Ellipse (2-D), Ellipsoid (3-D) and Hyperellipsoid (n-D)

6 min
2.9
Square ,Rectangle
6 min
2.10
Hyper Cube,Hyper Cuboid

3 min
2.11
Assignment[Optional]

30 min
2.12

3.1
Introduction to Probability and Statistics
17 min
3.2
Population and Sample
7 min
3.3
Gaussian/Normal Distribution and its PDF(Probability Density Function)
27 min
3.4
CDF(Cumulative Distribution function) of Gaussian/Normal distribution
11 min
3.5
Symmetric distribution, Skewness and Kurtosis
5 min
3.6
Standard normal variate (z) and standardization
15 min
3.7
Kernel density estimation
7 min
3.8
Sampling distribution & Central Limit theorem
19 min
3.9
Q-Q plot:How to test if a random variable is normally distributed or not?
23 min
3.10
Discrete and Continuous Uniform distributions
13 min
3.11
How to randomly sample data points (Uniform Distribution)
10 min
3.12
Log Normal Distribution
12 min
3.13
Power law distribution
12 min
3.14
Box cox transform
12 min
3.15
Co-variance
14 min
3.16
Pearson Correlation Coefficient
13 min
3.17
Spearman Rank Correlation Coefficient
7 min
3.18
Correlation vs Causation
3 min
3.19
Confidence interval (C.I) Introduction
8 min
3.20
Computing confidence-interval given distribution
11 min
3.21
C.I for mean of a normal random variable
14 min
3.22
Confidence interval using bootstrapping
17 min
3.23
Hypothesis testing methodology, Null-hypothesis, p-value
16 min
3.24
Resampling and permutation test
15 min
3.25
K-S Test
6 min
3.26
K-S Test for similarity of two distributions
15 min
3.27
Bernoulli and Binomial Distribution
11 min
3.28
Code Snippet K-S Test
6 min
3.29
Hypothesis Testing Intution with coin toss example
27 min
3.30
Hypothesis testing Mean differences Example
18 min
3.31
Resampling and Permutation test for Mean difference example
19 min
4.1
what is dimensionality reduction?
3 min
4.2
Row vector, Column vector: Iris dataset example
5 min
4.3
Represent a dataset: D= {x_i, y_i}
5 min
4.4
Represent a dataset as a Matrix
7 min
4.5
Data preprocessing: Column Normalization
20 min
4.6
Mean of a data matrix
6 min
4.7
Data preprocessing: Column Standardization
6 min
4.8
Co-variance of a Data Matrix
24 min
4.9
MNIST dataset (784 dimensional)
20 min
4.10
Code to load MNIST Dataset
12 min
5.1
Why learn it
4 min
5.2
Geometric intuition
14 min
5.3
Mathematical objective function
13 min
5.4
Alternative formulation of PCA: distance minimization
10 min
5.5
Eigenvalues and eigenvectors
23 min
5.6
PCA for dimensionality reduction and visualization
10 min
5.7
Visualize MNIST dataset
5 min
5.8
Limitations of PCA
5 min
5.9
Code example using visualization
19 min
5.10
PCA for dimensionality reduction (not-visualization)
15 min
6.1
What is t-SNE?
7 min
6.2
Neighborhood of a point, Embedding
7 min
6.3
Geometric intuition
9 min
6.4
Crowding Problem
8 min
6.5
How to apply t-SNE and interpret its output
38 min
6.6
t-SNE on MNIST
7 min
6.7
Code example
9 min