Github user sethah commented on a diff in the pull request:
https://github.com/apache/spark/pull/13139#discussion_r64803173
--- Diff: docs/ml-classification-regression.md ---
@@ -374,6 +374,137 @@ regression model and extracting model summary
statistics.
</div>
+## Generalized linear regression
+
+Contrasted with linear regression where the output is assumed to follow a
Gaussian
+distribution, [generalized linear
models](https://en.wikipedia.org/wiki/Generalized_linear_model) (GLMs) are
specifications of linear models where the response variable $Y_i$ may take on
_any_
+distribution from the [exponential family of
distributions](https://en.wikipedia.org/wiki/Exponential_family).
+Spark's `GeneralizedLinearRegression` interface
+allows for flexible specification of GLMs which can be used for various
types of
+prediction problems including linear regression, Poisson regression,
logistic regression, and others.
+Currently in `spark.ml`, only a subset of the exponential family
distributions are supported and they are listed
+[below](#available-families).
+
+**NOTE**: Spark currently only supports up to 4096 features through its
`GeneralizedLinearRegression`
+interface, and will throw an exception if this constraint is exceeded. See
the [advanced section](ml-advanced) for more details.
+ Still, for linear and logistic regression, models with an increased
number of features can be trained
+ using the `LinearRegression` and `LogisticRegression` estimators.
+
+The canonical form of an exponential family distribution is given as:
+
+$$
+f_Y(y|\theta, \tau) = h(y, \tau)\exp{\left( \frac{\theta \cdot T(y) -
A(\theta)}{d(\tau)} \right)}
--- End diff --
So, it seems as though every source on the internet, academic and
otherwise, explains GLMs/exponential families differently with different
notation and different terminology. My understanding is that GLMs usually work
with an exponential family in its "natural" form, which is a transformed
version of an even more generic specification of exponential families. Most
_every_ resource I find **besides** wikipedia assumes this "natural" form and
does not even mention it. So the `T(y)` appears sometimes, but mostly not. I
think the updated explanation is correct, but please let me know if you think
it could be clearer.
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