#Help !! Which statistical tool do I use? [for research, beginner]

107 messages · Page 1 of 1 (latest)

split blade
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How can I use data about past occupied horizontal land mass/area in creating an equation that predicts the value after 20 years megathonk ? And which statistical tool is most appropriate? Thankss!! :3

naive marshBOT
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teal kindle
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For starters

split blade
teal kindle
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You have data points X and you want to predict Y, in the form <w, X> + b

split blade
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what if the points are too scattered tho? that means i cant rely on the regression model to write an equation for prediction ryt??

teal kindle
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Where w is a vector and < . , . > is the dot product

teal kindle
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To fit the best plane to fit your data

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If you feel that a linear model is not appropriate, there must be something else that can be used

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I'm just saying linear regression because it is fairly simple and beginner friendly

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Otherwise in general you look for a feature map f so that you compute predictions Y ~ <w, f(X)> + b

split blade
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we just had to state which tool we're gonna use

teal kindle
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Two decades ago i think they used SVMs and whatnot

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Decision trees too

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It may sound a bit daunting but machine learning offers many other methods of regression

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That are mostly more flexible than linear regression

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That being said, usually the simpler the model the better

split blade
split blade
split blade
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i rlly dont know stuff so im sorry xDD but likeee

split blade
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or nahh ?

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our research topic rlly got us

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making equations and allat

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lol

split blade
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inevitably we have to write one

teal kindle
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For a svm?

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This is the complicated version

split blade
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i'm def gonna consider ittt

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in what ways is it better than just plain linear ?

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i trust u thooo that it's more flexible n stuff : D

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i just gootta know how to justify it to my group and my adviser too

teal kindle
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So essentially, the idea is as follows

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You have two random variables $X \in \mathbb{R}^p$ and $Y \in \mathbb{R}$, you want to find out how they are related

junior remnantBOT
teal kindle
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So what you usually do is an estimation: $\hat{Y} = f(X)$, and you want your estimation not to be too far from $Y$

junior remnantBOT
teal kindle
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So the entire question is, how do you build $f$ ?

junior remnantBOT
teal kindle
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Here, what we call a model, you can think of it as a set of assumptions over the distribution of $X$ and the distribution of $Y$

junior remnantBOT
teal kindle
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For instance, the linear regression model assumes that $Y = \langle w, X \rangle + b + \epsilon$, where $\epsilon \sim \mathcal{N}(0, \sigma^2)$

junior remnantBOT
teal kindle
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In other words, a linear relationship with X, plus a small error

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So you obviously want to find the w and b that fit best

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So, here, your estimation of $Y$ is $\hat{Y} = \langle w, X \rangle + b$

junior remnantBOT
teal kindle
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And this is a fairly simple model

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because it's just linear

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$\hat{Y} = f_{w,b}(X) = \langle w, X \rangle + b$

junior remnantBOT
teal kindle
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But in general, there are models that come up with more complicated estimations of Y

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In which case, without losing generality, you can denote them:
$\hat{Y} = f_{\theta}(X)$

junior remnantBOT
teal kindle
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Where $\theta$ is the parameter of your model, which you want to fit

junior remnantBOT
teal kindle
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Just like the line slope and intercept

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Do you understand up to this point?

split blade
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yahhh ey

teal kindle
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Ok, that's very good

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Because if you understand up to now

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you basically understood machine learning

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We make a model for the data, and we optimize the parameter $\theta$ to fit data the best

junior remnantBOT
teal kindle
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And here, support vector machine is one such model

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with its own specific set of parameters $\theta$

junior remnantBOT
teal kindle
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And there are many other models, with their own sets of assumptions and their $f_\theta$

junior remnantBOT
teal kindle
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It just turns out that in linear regression, $\theta = (w, b)$ and that the estimation $f_\theta$ is fairly simple

junior remnantBOT
teal kindle
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That's why, if linear regression does not suffice, perhaps you need a better model

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that isn't so simple, but may accurately model the variety of your data

split blade
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yeahhh : D

teal kindle
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And a couple of decades ago, before neural networks were popular, people liked SVMs a lot

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But since nowadays you have more modern techniques to do regression, nowadays SVM is just a good math textbook exercise

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by no means it is bad, just to be clear

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definitely an affordable method to see if you just want to look around

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but of course there are other things than SVM too

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gaussian mixture

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linear discriminant analysis (though mainly for classification)

split blade
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ooooo~ i'll look into themm i can understand if i rlly tried xDD

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nice knowing regressions r rlly the ones for thiss

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i thought mayb i was geeking T__T

teal kindle
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If my 10 minutes crash course got to you, then you understood basically what regression using ML is like

split blade
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ooooo~ realll !

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i get ittt

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i think i got what i needed to know flush ech

teal kindle
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I do advise you to talk with your teacher or professor about this too

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Maybe they will have better insights to provide

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I'm very biased because I do research in AI so there's that

split blade
split blade
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thanksss brahh

teal kindle
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You're welcome

split blade
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stuff was fun gwahahahaha

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i'll be sleeping now it's almost 4am in here xD

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THANKS AGAINNN RAHHHHH