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Types of Regression Analysis

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Re: Types of Regression Analysis

#21
post #4

Earlier quoted context omitted.

Why wouldn't you just run weka or something locally?

I just want to provide the data and let a service decide the best algorithm. Weka and various ML tools require you select the algorithm and do the A/B testing on your own. There's an opportunity for an Optimizely of ML.

[deleted]

Re: Types of Regression Analysis

#22

Earlier quoted context omitted.

It is actually wrong. The assumption is that y is a linear combination of the covariates in X. You can run regressions like y = x + x^2 (i.e. you permit a quadratic relationship) just fine.

It's not wrong, it's just a way of looking at things that speaks to the underlying math rather than the full extent of what you can do with it if you extend it with things like kernel methods. When you use linear regression to fit a model like y ~ ax + b(x^2) what you're technically doing is fitting a linear function with two parameters on two variables. One variable happens to always be equal to the square of the ot…

Fair enough. Mechanically, all you're ever doing when estimating a parameter vector using OLS is projecting Y onto the span of X, and that requires linearity in the sense that Y = XB. But far too often I've met people who've come away thinking OLS is useless because they mistake the linearity in parameters with 'y must be a linear function of x', which is they think is too simplistic, and so they go do more complicated methods when OLS would have been just fine as long as they used polynomials and/or interaction terms.

Re: Types of Regression Analysis

#23

Despite what the article claims, normality is not actually an assumption of linear regression. It is "required" for doing F-tests (the F-distribution being related to the normal distribution), but it is not required for proving that the regression coefficients are consistent.

It's actually not even required for that! See http://davegiles.blogspot.com/2011/08/being-normal-is-option... which cites King (1980): > If the error vector in our regression model follows any distribution in the family of Elliptically Symmetric distributions, then any test statistic that is scale-invariant has the same null and alternative distributions as they have when the errors are normally distributed.

Note also that any distributional assumptions are really only necessary for inference (i.e., tests and confidence intervals) in finite samples (read: small samples); the central limit theorem guarantees the tests work asymptotically, so you're usually going to be fine.

Most of the attention paid to distributional assumptions in regression is wasted, and would be better spent on really thinking through the assumed moment conditions underlying the estimator.

Re: Types of Regression Analysis

#24
Now this is a topic I desperately need. Can anyone here by any chance explain why would one choose predictors in multilinear regression that are NOT correlated to the target? I am having trouble understanding paper [1] where authors avoid using predictors that are correlated to target. Target is ozone concentration shown by referent instrument and predictors are low cost sensor outputs.

[1] https://www.sciencedirect.com/science/article/pii/S092540051... Section 4.1 about ozone predictors

Re: Types of Regression Analysis

#25

Are there any ML APIs or web services that accept a vector and run various regression scenarios to identify optimal fit? I suppose vectors for both training and testing would be required. Would gladly pay $1-$5 per batch for a service to do this.

I'm working on an MLaaS service now and I'd love to add that feature. That said, I'd like to learn a little more about exactly how you envision the use case working. To that end, if you can spare some time to chat sometime, would you drop me a line (prhodes@fogbeam.com)?

Re: Types of Regression Analysis

#26
post #7

Are there any ML APIs or web services that accept a vector and run various regression scenarios to identify optimal fit? I suppose vectors for both training and testing would be required. Would gladly pay $1-$5 per batch for a service to do this.

I think that's DataRobot's business model, although I think they run more sophisticated models as well. It was 5+ years ago that I spoke to them but IIRC they were able to compete pretty well in Kaggle competitions with a fairly hands-off algorithm.

Could you perhaps point me to a Kaggle competition where they perform well with a hands-off approach?

Re: Types of Regression Analysis

#27
This article is obviously a jumping off point kind of article. Most people using linear regression have never even heard of things like ridge regression. So I like the article.

However, there are at least two types of regression I'd add to the list, and a suggestion.:

1 Multivariate Distance Matrix Regression (MDMR; Anderson, 2001; McArdle & Anderson, 2001).

2. Regression with splines

3. On polynomial regression, add mention of orthogonal polynomials.

Re: Types of Regression Analysis

#28

Now this is a topic I desperately need. Can anyone here by any chance explain why would one choose predictors in multilinear regression that are NOT correlated to the target? I am having trouble understanding paper [1] where authors avoid using predictors that are correlated to target. Target is ozone concentration shown by referent instrument and predictors are low cost sensor outputs. [1] https://www.sciencedirect.…

The issue is intra-predictor correlation. In the extreme case that a predictor is duplicated, the correct beta might be {betaa, beta(1-a)} for a in [0, 1], which an algorithm may not estimate in a stable manner. A significant degree of correlation introduces this general problem.

Re: Types of Regression Analysis

#29

Now this is a topic I desperately need. Can anyone here by any chance explain why would one choose predictors in multilinear regression that are NOT correlated to the target? I am having trouble understanding paper [1] where authors avoid using predictors that are correlated to target. Target is ozone concentration shown by referent instrument and predictors are low cost sensor outputs. [1] https://www.sciencedirect.…

When predictors are correlated with each other you get multicollinearity potentially leading to incorrect statistical inferences.

Re: Types of Regression Analysis

#30
post #26
post #7

Earlier quoted context omitted.

I think that's DataRobot's business model, although I think they run more sophisticated models as well. It was 5+ years ago that I spoke to them but IIRC they were able to compete pretty well in Kaggle competitions with a fairly hands-off algorithm.

Could you perhaps point me to a Kaggle competition where they perform well with a hands-off approach?

I'm afraid I can't. Take it with a grain of salt, I only mention it because it was the anecdote that stood out in my memory for 5+ years :)
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