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Q&A on Probability and Statistics

Instructor: Applied AI Course

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Code-Walkthrough: Probability and statistics-II
Code Walkthrough: Dimensionality Reduction for ML/AI
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)

15 min
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)

6 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
Assignment-1: Data Visualization with 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
Revision Questions
30 min
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
25 min
3.6
Standard normal variate (Z) and standardization
6 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
How distributions are used?
17 min
3.11
Chebyshev’s inequality
20 min
3.12
Discrete and Continuous Uniform distributions
13 min
3.13
How to randomly sample data points (Uniform Distribution)
10 min
3.14
Bernoulli and Binomial Distribution
11 min
3.15
Log Normal Distribution
12 min
3.16
Power law distribution
12 min
3.17
Box cox transform
12 min
3.18
Applications of non-gaussian distributions?
26 min
3.19
Co-variance
14 min
3.20
Pearson Correlation Coefficient
13 min
3.21
Spearman Rank Correlation Coefficient
7 min
3.22
Correlation vs Causation
5 min
3.23
How to use correlations?
13 min
3.24
Confidence interval (C.I) Introduction
8 min
3.25
Computing confidence interval given the underlying distribution
11 min
3.26
C.I for mean of a random variable
14 min
3.27
Confidence interval using bootstrapping
18 min
3.28
Hypothesis testing methodology, Null-hypothesis, p-value
16 min
3.29
Hypothesis Testing Intution with coin toss example
27 min
3.30
Resampling and permutation test
15 min
3.31
K-S Test for similarity of two distributions
15 min
3.32
Code Snippet K-S Test
6 min
3.33
Hypothesis testing: another example
18 min
3.34
Resampling and Permutation test: another example
19 min
3.35
How to use hypothesis testing?
23 min
3.36
Proportional Sampling
18 min
3.37
Revision Questions
30 min
4.1
Questions & Answers
30 min
5.1
What is Dimensionality reduction?

3 min
5.2
Row Vector and Column Vector

5 min
5.3
How to represent a data set?

4 min
5.4
How to represent a dataset as a Matrix.

7 min
5.5
Data Preprocessing: Feature Normalisation

20 min
5.6
Mean of a data matrix

6 min
5.7
Data Preprocessing: Column Standardization

16 min
5.8
Co-variance of a Data Matrix

24 min
5.9
MNIST dataset (784 dimensional)

20 min
5.10
Code to Load MNIST Data Set

12 min
6.1
Why learn PCA?

4 min
6.2
Geometric intuition of PCA

14 min
6.3
Mathematical objective function of PCA

13 min
6.4
Alternative formulation of PCA: Distance minimization

10 min
6.5
Eigen values and Eigen vectors (PCA): Dimensionality reduction

23 min
6.6
PCA for Dimensionality Reduction and Visualization

10 min
6.7
Visualize MNIST dataset

5 min
6.8
Limitations of PCA

5 min
6.9
PCA Code example

19 min
6.10
PCA for dimensionality reduction (not-visualization)

15 min
7.1
What is t-SNE?

7 min
7.2
Neighborhood of a point, Embedding

7 min
7.3
Geometric intuition of t-SNE

9 min
7.4
Crowding Problem

8 min
7.5
How to apply t-SNE and interpret its output

38 min
7.6
t-SNE on MNIST

7 min
7.7
Code example of t-SNE

9 min
7.8
Revision Questions
30 min
8.1
Questions & Answers
30 min
9.1
Introduction to A/B Tests

9.2
How do we randomly split users ?

9.3
Metrics to compare Control and Treatment

9.4
Permutation-Resampling test

9.5
Q&A: Why permute/shuffle?

9.6
Q&A: How would shuffle programatically?

9.7
Quick Recap [till now]

9.8
Q&A + Polls with participants

9.9
Hypothesis testing: p-values, significance level & errors

9.10
Estimating the power of Permutation Tests

9.11
Code Walkthrough: Permutation Test from scratch.

9.12
Simulations using Code

9.13
Q&A with participants

9.14
Poll + Recap [till now]

9.15
Pros and Cons of Permutation Testing

9.16
Variation: Measuring clicks

9.17
Mann-Whitney-U Test

9.18
Code for Mann-Whitney-U test

9.19
Q&A with participants

9.20
Multiple testing and solutions

9.21
Remdesivir for Covid-19: Research Paper

9.22
Q&A with participants

9.23
Quick Recap (till now)

9.24
Bootstrapping for Confidence Intervals

9.25
Introduction to Multi-Arm-Bandits

9.26
Q&A with participants