Notation¶
Commonly used math symbols in machine learning texts.
Примечание
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Algebra¶
Symbol | Name | Description | Example |
\((f ∘ g)\) | composite function | a nested function | (f ∘ g)(x) = f(g(x)) |
\(∆\) | delta | change / difference | ∆x = x_1 - x_0 |
\(e\) | Euler’s number | e = 2.718281828 | s = frac{1}{1+e^{-z}} |
\(\sum\) | summation | sum of all values | ∑ x_i = x_1 + x_2 + x_3 |
\(\prod\) | capital pi | product of all values | ∏ x_i = x_1∙x_2∙x_3 |
\(\epsilon\) | epsilon | tiny number near 0 | lr = 1e-4 |
Calculus¶
Symbol | Name | Description | Example |
\(x'\) | derivative | first derivative | (x^2)“ = 2x |
\(x''\) | second derivative | second derivative | (x^2)““ = 2 |
\(\lim\) | limit | function value as x approaches 0 | |
\(∇\) | nabla | gradient | ∇f(a,b,c) |
Linear algebra¶
Symbol | Name | Description | Example |
\([ ]\) | brackets | matrix or vector | \(M = [1 3 5]\) |
\(\cdot\) | dot | dot product | \((Z = X \cdot W\) |
\(\odot\) | hadamard | hadamard product | \(A = B \odot C\) |
\(X^T\) | transpose | matrix transpose | \(W^T \cdot X\) |
\(\vec x\) | vector | vector | \(v = [1 2 3]\) |
\(X\) | matrix | capitalized variables are matrices | \(X, W, B\) |
\(\hat x\) | unit vector | vector of magnitude 1 | \(\hat x = [0.2 0.5 0.3]\) |
Probability¶
Symbol | Name | Description | Example |
\(P(A)\) | probability | probability of event A | P(x=1) = 0.5 |
Set theory¶
Symbol | Name | Description | Example |
\({ }\) | set | list of distinct elements | S = {1, 5, 7, 9} |
Statistics¶
Symbol | Name | Description | Example |
\(μ\) | population mean | mean of population values | |
\(\bar x\) | sample mean | mean of subset of population | |
\(σ^2\) | population variance | variance of population value | |
\(s^2\) | sample variance | variance of subset of population | |
\(σ_X\) | standard deviation | population standard deviation | |
\(s\) | sample std dev | standard deviation of sample | |
\(ρX\) | correlation | correlation of variables X and Y | |
\(\tilde x\) | median | median value of variable x |
References
[1] | http://www.tablesgenerator.com/text_tables |
[2] | http://www.rapidtables.com/math/symbols/Basic_Math_Symbols.htm |