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GH-8487: implement HGLM gaussian #16403

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GH-8487: implement HGLM gaussian #16403

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This PR fixes this issue: #8487

I have separated HGLM from GLM as its own toolbox. The only family that is supported now is Gaussian. I still need to do the following:

  1. client tests (java, python/R) to make sure model metrics are passed;
  2. client tests to make sure model summary, scoring history and coefficient tables are passed;
  3. check and make sure we use the correct formula to estimate the residual noise variance, refer to the doc.
  4. check and make sure we choose one of the likelihood methods. I implemented two. Refer to the doc.
    HGLM_H2O_Implementation.pdf

@wendycwong wendycwong force-pushed the wendy_gh_8487_HGLM_gaussian branch 2 times, most recently from 9ecc510 to 925042a Compare October 7, 2024 23:13
@wendycwong wendycwong force-pushed the wendy_gh_8487_HGLM_gaussian branch 3 times, most recently from 60ecdae to d7eeb43 Compare October 14, 2024 16:55
@wendycwong wendycwong force-pushed the wendy_gh_8487_HGLM_gaussian branch 4 times, most recently from f80efd6 to 283b66b Compare October 20, 2024 23:49
GH-8487: add HGLM as a separate toolbox.
ecf9a91 
GH-8487: crafting HGLM parameters.
GH-8487: implement EM algo.
GH-8487: forming the fixed matrices and vectors.
GH-8487: add test to make sure correct initialization of fixed, random coefficients, sigma values and T matrix.
GH-8487: Finished implementing EM to estimate fixed coefficients, random coefficients, tmat and tauEVar
GH-8487: finished implementing prediction but still need to figure out the model metrics calculation.
GH-8487: Adding support for models without random intercept.
GH-8487: adding normalization and denormalization of coefficients for fixed and random.
GH-8487: Completed prediction implementation and added tests to make sure prediction is correct when standardize=true/false, random_intercept = true/false.
GH-8487: fixing model metric classes.
GH-8487: add python and R tests.
GH-8487: adding hooks to generate synthetic data.
GH-8487: added scoring history, model summary, coefficient tables.
GH-8487: added modelmetrics for validation frame.
GH-8487: From experiment to find best tauEVar calculation process.  The one in equation 10 is best.
GH-8487: add capability in Python client to extract  scoring history, model summary, model metrics, model coefficients (fixed and random), icc, T matrix, residual variance.
GH-8487: done checking scoring history, model summary and model metrics.
GH-8487: added R client test for utility functions.
GH-8487: use lambda_ instead lf Lambda in pyunit_benign_glm.py
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@krasinski krasinski Awaiting requested review from krasinski

@valenad1 valenad1 Awaiting requested review from valenad1

@maurever maurever Awaiting requested review from maurever

@tomasfryda tomasfryda Awaiting requested review from tomasfryda

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