1. Related concepts commonly used in the mathematical part of machine learning:
(1). Advanced Mathematics
1) Function
2) Limit
3) Derivative
4) Extreme value and maximum value
5) Taylor series
6) Gradient
7) Gradient descent
(2). Linear algebra
1) Basic concepts
2) Determinant
3) Matrix
4) Least square method
5) Linear correlation of vectors
(3). Probability Theory
1) Event
2) Permutation and combination
3) Probability
4) Bayes' theorem
5) Probability distribution
6) Expectation and variance
7) Parameter estimation
2. Video learning content: https://www.bilibili.com/video/BV1Tb411H7uC?p=2
1) P2 probability theory and Bayesian prior
2) P3 matrix and linear algebra
Machine learning is a multi-disciplinary interdisciplinary subject that involves more mathematical knowledge. The knowledge in this lesson has been learned before. This time it will be reorganized according to the key points. We must pay more attention to it. By watching the video, everyone deepened their impression of the basic mathematics of the course.
It is recommended that you take notes while watching, record the main points and the time point, so that you can look back when necessary. Study notes are also part of the assignment.
3. Requirements:
(1) Paste the video study notes, which require authenticity, do not copy, you can take pictures by handwriting.
1) P2 probability theory and Bayesian prior
Record notes (formula) learned in the video
2) P3 matrix and linear algebra
The main contents of matrix and linear algebra are as follows:
The knowledge of linear algebra used is:
1. Operations between determinants of square matrix
2. Algebraic cofactor
3. Vandermonde determinant Vandermonde
4. Matrix multiplication
5. The rank of the matrix
6. The relationship between rank and the solution of linear equations
7. Orthogonal array
8. Eigenvalues and eigenvectors
9. Positive Definite Array
(2) Summarize "gradient", "gradient descent" and "Bayes' theorem" in your own words. Word editing, mind mapping, handwriting and photographing are required, and conciseness and neat layout are required.
The original meaning of the gradient is a vector (vector), which means that the directional derivative of a function at that point takes the maximum value along the direction, that is, the function changes at the point along the direction (the direction of the gradient) the fastest The rate is the largest (the modulus of the gradient). Simply put, in the case of univariate real-valued functions, the gradient is only a derivative, or, for a linear algebra, that is, the slope of the line.
Gradient descent is an iterative method that can be used to solve least squares problems (both linear and nonlinear). When solving the model parameters of machine learning algorithms, that is, unconstrained optimization problems, gradient descent is one of the most commonly used methods. Simply put, it is to find the fastest and steepest route down the mountain from the top of the mountain .
Bayes' Theorem: The Bayesian formula is based on the conditional probability to find the cause of the event (that is, under the condition that the large event A has occurred, the small event in the segmentation
Probability), suppose
Is a division of the sample space Ω, then for any event A (P (A)> 0), there is Bayes' theorem:
For the feature set x, we want to know which category the sample belongs to under this feature set x, that is, find the class label with the largest posterior probability P (c | x). Based on the Bayes formula, we can get:
Bayes' theorem is a theorem used to describe the relationship between two conditional probabilities, such as P (A | B) and P (B | A). Generally, the probability of event A under the condition that event B occurs {P (A | B)} The probability {P (B | A)} of event B under the condition of event A is different, but there is a definite relationship between the two, and Bayes' rule is a statement of this relationship.