Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Everything is a linear model

danielroelfs.com

Post reply on HN
Print view View original

21–30 of 90 posts

Re: Everything is a linear model

#21

Post by sebastianavina »

t_mann wrote: post #13

Statistics is more than hypothesis testing, but you'll get surprisingly far without straying too far from linear models - I remember a Stats prof saying 'most of classical Statistics is GLM [0]' [0] https://en.wikipedia.org/wiki/Generalized_linear_model

"Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas. "

and everything turns around the same principles. For example dynamical models and PID controls.

yet solving a banana, is the only thing we really know how to do. So we end up fitting everything in our banana models.

Re: Everything is a linear model

#25

Post by Tommah »

sebastianavina wrote: post #21
t_mann wrote: post #13

Statistics is more than hypothesis testing, but you'll get surprisingly far without straying too far from linear models - I remember a Stats prof saying 'most of classical Statistics is GLM [0]' [0] https://en.wikipedia.org/wiki/Generalized_linear_model

"Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas. " and everything turns around the same principles. For example dynamical models and PID controls. yet solving a banana, is the only thing we really know how to do. So we end up fitting everything in our banana models.

Linear algebra was the first math class I took in undergrad. I thought the next one was going to be non-linear algebra! But it wasn't.

Re: Everything is a linear model

#26

Post by nyrikki »

tnecniv wrote: post #17
btdmaster wrote: post #4

I thought nonlinearity was very important to be able to make a larger model better than a smaller one? Like so important that tom7 made a half-joke demo with it: https://yewtu.be/watch?v=Ae9EKCyI1xU

Nonlinear things start looking like linear things again in very high dimensions

Only when you dimensions are truly independent and that is a stretch. Really what you are saying is that you are more likely to find a field for your problem, and fields don't exist in more than 2 dimensions.

Consider Predator Pray with fear and refuge, which is indeterminate, and not due to a lack of precision but a topological feature where ≥3 open sets share the same boundary set.

https://www.sciencedirect.com/science/article/abs/pii/S09600...

General relativity, with 3 spacial and one temporal dimension is another. One lens to consider this is that rotations are hyperbolic due to the lack of independence from the time dimension.

Quantum mechanics would have been much more difficult if it didn't have two exit basins. Which is similar to ANNs and linear regressions being binary output.

(Some exceptions will orthogonal dimensions like EM)

Re: Everything is a linear model

#27

Post by whatshisface »

sebastianavina wrote: post #21
t_mann wrote: post #13

Statistics is more than hypothesis testing, but you'll get surprisingly far without straying too far from linear models - I remember a Stats prof saying 'most of classical Statistics is GLM [0]' [0] https://en.wikipedia.org/wiki/Generalized_linear_model

"Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas. " and everything turns around the same principles. For example dynamical models and PID controls. yet solving a banana, is the only thing we really know how to do. So we end up fitting everything in our banana models.

I disagree with the implication that linearity is an unnatural concept, it appears whenever the changes being studied are small relative to the key parameters that determine the system. Every system is linear for small perturbations. Even logic gates; in negative feedback they can form passable inverting amplifiers. In a place as big as the universe it is rather common for two things to be very different in scale and yet interacting.

Re: Everything is a linear model

#28

Post by 3abiton »

t_mann wrote: post #13

Statistics is more than hypothesis testing, but you'll get surprisingly far without straying too far from linear models - I remember a Stats prof saying 'most of classical Statistics is GLM [0]' [0] https://en.wikipedia.org/wiki/Generalized_linear_model

It's true, until it's not. It's easy to make these claims, but would you bet your money on it?

Re: Everything is a linear model

#29

Post by notjoemama »

whatshisface wrote: post #27
sebastianavina wrote: post #21

Earlier quoted context omitted.

"Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas. " and everything turns around the same principles. For example dynamical models and PID controls. yet solving a banana, is the only thing we really know how to do. So we end up fitting everything in our banana models.

I disagree with the implication that linearity is an unnatural concept, it appears whenever the changes being studied are small relative to the key parameters that determine the system. Every system is linear for small perturbations. Even logic gates; in negative feedback they can form passable inverting amplifiers. In a place as big as the universe it is rather common for two things to be very different in scale and…

So, Lady Finger, not Cavendish. Got it.

Re: Everything is a linear model

#30

Post by szundi »

whatshisface wrote: post #27
sebastianavina wrote: post #21

Earlier quoted context omitted.

"Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas. " and everything turns around the same principles. For example dynamical models and PID controls. yet solving a banana, is the only thing we really know how to do. So we end up fitting everything in our banana models.

I disagree with the implication that linearity is an unnatural concept, it appears whenever the changes being studied are small relative to the key parameters that determine the system. Every system is linear for small perturbations. Even logic gates; in negative feedback they can form passable inverting amplifiers. In a place as big as the universe it is rather common for two things to be very different in scale and…

Interesting aspect to see the world from, thanks
Post reply on HN