14. Linear vs Nonlinear models

[@richardaversa7128]

Thank you for explicitly addressing linear vs. nonlinear, I have seen this be a point of confusion for many. To help clarify, is it correct that in the data science/ML context we are talking about linear/nonlinear *with respect to the parameters* (and not the independent variables)? In my understanding, the kinematic equation with t² is certainly not a linear model with respect to the independent variable, time. Tell a physicist that equation shows position varies linearly with time and they will laugh. But in data science, at least in the context of regression, it doesn't matter so much the linearity w.r.t the independent variable(s), what matters is the linearity w.r.t. the parameters. This is because the parameters are what need to be calculated, by the regression algorithm. The independent variables are already fixed in a way, by the known data, so t, t², sin(t) are all just constant values for each data point t, when the regression algorithm is run to vary the parameters. So, beyond just the polynomial shown at 2:16, these would also be considered linear models: Y = a·log(X₁²) + b·(X₁·sin(X₂)) Y = a·e^X and these would be considered nonlinear models: Y = a·e^bX Y = a·X₁ + b·X₂ + (a·b)·(X₁+X₂) ...in the context of data science / statistics / ML, where we consider with respect to the parameter(s) - to be distinguished from the rest of the quantitative sciences and engineering, where we consider with respect to independent variable(s). My understanding, please let me know if there are other perspectives. Hopes this helps some folks.

[@TaylorSparks]

I share your understanding

[@0001-exe]

this is such a great video!! i finally understood the difference between linear and nonlinear models :'D

[@TaylorSparks]

Woohooooo. Glad to help

[@Kaushh06]

didn't quite understood at 2:11 , you saying the second equation to be linear ? HOW if we have t^2

[@justeuphoria2]

Here's what our professor wrote us about linear and nonlinear models (we're studying environmental management and modelling, what do u think does the text below make a sense??? Linear vs. nonlinear: If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. A model is considered to be nonlinear otherwise. The definition of linearity and nonlinearity is dependent on context. Nonlinearity, even in fairly simple systems, is often associated with phenomena such as chaos and irreversibility (aspects such as irreversibility are strongly tied to nonlinearity). Although there are exceptions, nonlinear systems and models tend to be more difficult to study than linear ones.

[@TaylorSparks]

Lol. Not to me! 🤔🤔🤔

[@Kaushh06]

How is that equation with t^2 in it linear?

[@uclteam21bhf76]

Great video!