Machine learning terms; cheat sheet

docs/Public/Math/LaTeX cheat sheet.md

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 `\begin{figure}[h]`: Starts a figure 
 
 `\circ`: $\circ$
-
 `\Sigma`: $\Sigma$
 
 `\overline{ab}`: $\overline{ab}$
 
 `\infty`: $\infty$
+
+`\sqrt{}`: $\sqrt{}$

docs/Public/Math/Statistics/correlation.md

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+*See: [[covariance]]*
+
+*Correlation* measures the linear relationship between two variables ([[variable]]) $X$ and $Y$ using the Pearson correlation coefficient, the most commonly used measure of correlation for [[continuous]] variables. 
+
+$$
+\rho_{X,Y} = \frac{cov(X,Y)}{\sigma_{X}\sigma_{Y}}
+$$
+$$
+\sigma_X=\sqrt{\frac{\sum_{i=1}^n\left(X_i-\bar{X}\right)^2}{n}}
+$$
+$$
+\sigma_Y=\sqrt{\frac{\sum_{i=1}^n\left(Y_i-\bar{Y}\right)^2}{n}}
+$$
+
+*Correlation* measures the direction and magnitude of the linear relationship ([[linear regression]]). 

docs/Public/Math/Statistics/covariance.md

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+*See: [[correlation]]*
+
+*Covariance* is a normalized ([[normalmeasure of how two variables ([[variable]]) $X$ and $Y$ change together linearly. 
+
+Given a population of size $n$, it is calculated as follows:
+
+$$
+COV[X, Y] = E[(X - E[X])(Y - E[Y])] = \frac{\Sigma^n_{i=1} (X_i-\overline{X})(Y_i-\overline{Y})}{n}
+$$
+The sign of the *covariance* indicates the direction of the relationship between variables:
+- when $COV[X, Y] > 0$, $X$ and $Y$ increase and decrease together.
+- when $COV[X, Y] < 0$, $X$ tends to decrease while $Y$ tends to increase and vice versa.
+- when $COV[X, Y] = 0$, $X$ and $Y$ do not display any of the above two tendencies. No linear relationship between $X$ and $Y$. 
+
+Note: *Covariance can only measure the directional relationship, not the magnitude. *

docs/Public/Software/AI/bias.md

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+*Bias* is the error between average model prediction (i.e. $E[g(x)]$) and the ground truth $f(x)$. 
+
+*Bias* indicates the training error. 
+
+$$
+Bias^2 = E[(E[(g(x)-f(x))^2])]
+$$

docs/Public/Software/AI/coefficient of determination.md

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+The *coefficient of determination*, or $R^2$, measures the strength of the relationship between [[independent variable]] (inputs and the [[dependent variable]] (outputs).
+
+It indicates the goodness of the fit of a [[linear regression]].
+$$
+0.0 \le R^2 \le 1.0
+$$
+Note: $R^2$ can increase as more predictors are added to a model, which can give an illusion of improvement. 

docs/Public/Software/AI/cross validation.md

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+*Cross validation* is used to compare models and prevent overfitting. 
+
+It is a resampling procedure to help he model to generalize well 

docs/Public/Software/AI/curve fitting.md

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+*Curve fitting* refers to the process of determining a [[function]] that best approximates the relationship between some [[independent variable]] and some [[dependent variable]]. 
+
+We want to minimize the overall error. 
+
+*Under-fitting* is when a model fails to capture the complex underlying patterns in the data
+- Bias-Variance Trade off: if a model has high bias and low variance, the model under-fits the data

docs/Public/Software/AI/dependent variable.md

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+A *dependent variable* is a [[variable]] which depends on changes in the [[independent variable]]. [^1]In other words, it is the effect of the change. 
+
+[^1]: https://www.scribbr.com/methodology/independent-and-dependent-variables/

docs/Public/Software/AI/error.md

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+In [[machine learning]], the *error* of a model is:
+
+$$
+Bias^2 + Variance + Ireeducible Error
+$$
+where $Bias^2$ is
+
+![bias](bias)
+
+and $Variance$ is
+
+![variance](variance)

docs/Public/Software/AI/independent variable.md

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+An *independent variable* is a [[variable]] that stands alone and isn't changed by the other variables you're trying to measure. [^1] In other words, it causes change. 
+
+[^1]: https://nces.ed.gov/nceskids/help/user_guide/graph/variables.asp

docs/Public/Software/AI/mean squared error.md

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+The *mean squared error*, or $MSE$, is a way to measure the fit of the model on training data. 
+
+It can also be used to measure the fit of the model on the test data. 
+
+Note: $MSE$ doesn't inherently increase with more predictors, making it a more "honest" metric when tweaking model complexity. 

docs/Public/Software/AI/variable.md

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+A *variable* is any characteristic that can take on multiple values, such as height, age, temperature, and score. [^1]
+
+[^1]: https://www.scribbr.com/methodology/independent-and-dependent-variables/

docs/Public/Software/Networks/IP address.md

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+An *IP address* (Internet Protocol address) is an [[address]] primarily used to identify a device connected on a [[network]] using the Internet Protocol. 

docs/Public/Software/Networks/MAC address.md

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+A *MAC address* (Media Access Control address) is an [[address]] primarily used as a unique identifier assigned to a piece of [[hardware]]. 
+
+It is a 12-digit hexadecimal number assigned to each device connected to the [[network]]. 

docs/Public/Software/Networks/address.md

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+An *address* is a way to identify where some [[hardware]] or [[software]] is located. 

docs/Public/Software/Networks/network.md

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+A *network* is a [[set]] of computers ([[hardware]]) sharing resources (like printers) and exchanging [[data]] with each other. [^1]
+
+[^1]: https://fcit.usf.edu/network/chap1/chap1.htm