Add loss function equations for each distribution to Docs

[exalate-issue-sync]

Users have been confused on which loss functions are used within H2O 3. Providing equations to docs will reduce confusion.

Request:
Add loss function equations (below) to [https://docs.h2o.ai/h2o/latest-stable/h2o-docs/data-science/algo-params/distribution.html|https://docs.h2o.ai/h2o/latest-stable/h2o-docs/data-science/algo-params/distribution.html] .

bernoulli
−2w(y∗log⁡(f)+(1−y)∗log⁡(1−f))

quasibinomial
y==f:
0

f>1:
−2w∗y∗log⁡(f)
f<0:
−2w∗(1−y)∗log⁡(1−f)
else:
−2w∗(y∗log⁡(f)+(1−y)∗log⁡(1−f))

gaussian
Equivalent to wMSE (weighted mean squared error):
w∗(y−f)^2

poisson
with f = link(f)
−2w∗(y∗f−exp( f ))

gamma
with f = link(f)
2w∗(y∗exp⁡(−f)+f)

laplace
w∗|y−f|

quantile
y > f:
wQuantileAlpha(y-f)
y≤f:
w∗(1−QuantileAlpha)∗(f−y)

huber

|y-f| ≤Huber_Delta :

  w*(y-f)^2   (Equivalent to wMSE)

y≤f:

  2w∗(|y−f|  −Huber_Delta)∗Huber_Delta (Equivalent to wMAE)

modified_huber
with yf = (2y-1)f
yf <−1:
-4w(yf)
yf>1:
0
else:
w*(yf)^2

tweedie
with f = link(f), requires 1> _tweediePower > 2 :
2wy^(2-Tweedie_Power)/((1-Tweedie_Power)(2-Tweedie_Power)) - yexp(f(1-Tweedie_Power))/(1-Tweedie_Power)+exp(f*(2-Tweedie_Power))/(2-Tweedie_Power)

[~accountid:5bd237b8dd3cc64b77e71676], please verify the definitions are correct. The equations were created based on code: [https://github.com/h2oai/h2o-3/blob/master/h2o-core/src/main/java/hex/DistributionFactory.java|https://github.com/h2oai/h2o-3/blob/master/h2o-core/src/main/java/hex/DistributionFactory.java]

[h2o-ops]

JIRA Issue Details

Jira Issue: PUBDEV-8261
Assignee: hannah.tillman
Reporter: Neema Mashayekhi
State: Resolved
Fix Version: 3.34.0.1
Attachments: N/A
Development PRs: Available

[h2o-ops]

Linked PRs from JIRA

#5623