Index of Machine Learning

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Integration

1. What happens when we reverse the limits of a definite integral?
2. Can you give the example of an odd integrand and prove that it is odd?
3. What is the differentiation and integration of f(x)=1 wrt dx
4. Show step by step integration of exp(-x by a)
5. Change in limits of integration when changing from cartesian to polar coordinates
6. Gaussian Integral: Integrate exp(-x^2) from -infinite to +infinite

Vector Calculus

1. y = w.x Where w and x are vectors. What is the derivative of y wrt w?
2. x is a vector and y = euclidean_norm(x). What is the derivative of y wrt x?
3. y = (norm(x))^2. What is the derivative of y wrt x?
4. Can you show the derivative X-transpose.X wrt x?
5. What is Jacobian of change of variables?
6. Derive Jacobian when we are changing from 2D cartesian coordinates to polar coordinates.
7. Derive generalized Gaussian Integral from the Special Case of Gaussian Integral for Mu = 0 and Sigma = 1-by-sqrt(2)
8. Solving 2D Gaussian Integral w.r.t x and y and also w.r.t polar coordinates

Exercises from the book "Pattern Recognition and Machine Learning" by Christopher Bishop

1. Exercise 1.1 On Linear Equations for Regression - From Pattern Recognition and ML - By Christopher Bishop
2. Exercise 1.2 On Regularization in Linear Regression - Pattern Recognition and ML - By Christopher Bishop
3. Exercise 1.3 on 'sum rule and product rule of probability' (From the book Pattern Recognition and ML by Christopher Bishop)
4. Exercise 1.4 On Probability Densities - Pattern Recognition and ML - By Christopher Bishop
5. Exercise 1.5 On Concept of Variance From Statistics - Pattern Recognition and ML - By Christopher Bishop
6. Exercise 1.6 On Covariance - Pattern Recognition and ML - By Christopher Bishop
7. Exercise 1.7 - Identifying normalization constant for Gaussian Distribution and Proving that it's integral equals 1 - From Pattern Recognition and ML - By Christopher Bishop
8. Ex 1.8 - Show that the mean value of Gaussian distribution is µ. (Pattern Recognition and ML by Christopher Bishop)
9. Ex 1.9 - Show that the mode of the multivariate Gaussian is given by µ. (Pattern Recognition and ML by Christopher Bishop)
10. Ex 1.10 - On mean and variance of two variables (Pattern Recognition and ML by Christopher Bishop)
11. • Question 1.11 - On Gaussian Distribution and it's Log Likelihood (Pattern Recognition and ML by Christopher Bishop)
    • Solution 1.11
12. Ex 1.12 - Pattern Recognition and ML by Christopher Bishop

Statistics

1. If x and y are two random variables, what is E[xy]?
2. From Simple Mean to Exponential Weighting: Unveiling the EMA (Exponential Moving Average)
3. Unit Test 5 - Exploring bivariate numerical data (From Khan Academy)
4. Unit 11 - Confidence intervals (Statistics)
5. Significance tests (hypothesis testing)
   • Lesson 12.1: The idea of significance tests (Statistics)
   • Lesson 12.2: Error probabilities and power

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