https://issues.apache.org/jira/browse/SPARK-16445

## What changes were proposed in this pull request?

Create Multilayer Perceptron Classifier wrapper in SparkR

## How was this patch tested?

Tested manually on local machine

Author: Xin Ren <iamshrek@126.com>

Closes #14447 from keypointt/SPARK-16445.

[SPARK-17086][ML] Fix InvalidArgumentException issue in QuantileDiscretizer when some quantiles are duplicated

## What changes were proposed in this pull request?

In cases when QuantileDiscretizerSuite is called upon a numeric array with duplicated elements,  we will  take the unique elements generated from approxQuantiles as input for Bucketizer.

## How was this patch tested?

An unit test is added in QuantileDiscretizerSuite

QuantileDiscretizer.fit will throw an illegal exception when calling setSplits on a list of splits
with duplicated elements. Bucketizer.setSplits should only accept either a numeric vector of two
or more unique cut points, although that may produce less number of buckets than requested.

Signed-off-by: VinceShieh <vincent.xieintel.com>

Author: VinceShieh <vincent.xie@intel.com>

Closes #14747 from VinceShieh/SPARK-17086.

## What changes were proposed in this pull request?
Fix a typo

## How was this patch tested?
no tests

Author: Zheng RuiFeng <ruifengz@foxmail.com>

Closes #14772 from zhengruifeng/minor_numClasses.

## What changes were proposed in this pull request?

In Latex, it is common to find "}}}" when closing several expressions at once. [SPARK-16822](https://issues.apache.org/jira/browse/SPARK-16822) added Mathjax to render Latex equations in scaladoc. However, when scala doc sees "}}}" or "{{{" it treats it as a special character for code block. This results in some very strange output.

Author: Jagadeesan <as2@us.ibm.com>

Closes #14688 from jagadeesanas2/SPARK-17095.

## What changes were proposed in this pull request?

Add expert param support to SharedParamsCodeGen where aggregationDepth a expert param is added.

Author: hqzizania <hqzizania@gmail.com>

Closes #14738 from hqzizania/SPARK-17090-minor.

## What changes were proposed in this pull request?

Add missing `numFeatures` and `numClasses` to the wrapped Java models in PySpark ML pipelines. Also tag `DecisionTreeClassificationModel` as Expiremental to match Scala doc.

## How was this patch tested?

Extended doctests

Author: Holden Karau <holden@us.ibm.com>

Closes #12889 from holdenk/SPARK-15113-add-missing-numFeatures-numClasses.

## What changes were proposed in this pull request?

Spark SQL doesn't have its own meta store yet, and use hive's currently. However, hive's meta store has some limitations(e.g. columns can't be too many, not case-preserving, bad decimal type support, etc.), so we have some hacks to successfully store data source table metadata into hive meta store, i.e. put all the information in table properties.

This PR moves these hacks to `HiveExternalCatalog`, tries to isolate hive specific logic in one place.

changes overview:

1.  **before this PR**: we need to put metadata(schema, partition columns, etc.) of data source tables to table properties before saving it to external catalog, even the external catalog doesn't use hive metastore(e.g. `InMemoryCatalog`)
**after this PR**: the table properties tricks are only in `HiveExternalCatalog`, the caller side doesn't need to take care of it anymore.

2. **before this PR**: because the table properties tricks are done outside of external catalog, so we also need to revert these tricks when we read the table metadata from external catalog and use it. e.g. in `DescribeTableCommand` we will read schema and partition columns from table properties.
**after this PR**: The table metadata read from external catalog is exactly the same with what we saved to it.

bonus: now we can create data source table using `SessionCatalog`, if schema is specified.
breaks: `schemaStringLengthThreshold` is not configurable anymore. `hive.default.rcfile.serde` is not configurable anymore.

## How was this patch tested?

existing tests.

Author: Wenchen Fan <wenchen@databricks.com>

Closes #14155 from cloud-fan/catalog-table.

## What changes were proposed in this pull request?

Linear/logistic regression use treeAggregate with default depth (always = 2) for collecting coefficient gradient updates to the driver. For high dimensional problems, this can cause OOM error on the driver. This patch makes it configurable to avoid this problem if users' input data has many features. It adds a HasTreeDepth API in `sharedParams.scala`, and extends it to both Linear regression and logistic regression in .ml

Author: hqzizania <hqzizania@gmail.com>

Closes #14717 from hqzizania/SPARK-17090.

## What changes were proposed in this pull request?

Add Alternating Least Squares wrapper in SparkR. Unit tests have been updated.

## How was this patch tested?

SparkR unit tests.

(If this patch involves UI changes, please attach a screenshot; otherwise, remove this)

![screen shot 2016-07-27 at 3 50 31 pm](https://cloud.githubusercontent.com/assets/15318264/17195347/f7a6352a-5411-11e6-8e21-61a48070192a.png)
![screen shot 2016-07-27 at 3 50 46 pm](https://cloud.githubusercontent.com/assets/15318264/17195348/f7a7d452-5411-11e6-845f-6d292283bc28.png)

Author: Junyang Qian <junyangq@databricks.com>

Closes #14384 from junyangq/SPARK-16443.

## What changes were proposed in this pull request?
In the existing code, ```MinMaxScaler``` handle ```NaN``` value indeterminately.
* If a column has identity value, that is ```max == min```, ```MinMaxScalerModel``` transformation will output ```0.5``` for all rows even the original value is ```NaN```.
* Otherwise, it will remain ```NaN``` after transformation.

I think we should unify the behavior by remaining ```NaN``` value at any condition, since we don't know how to transform a ```NaN``` value. In Python sklearn, it will throw exception when there is ```NaN``` in the dataset.

## How was this patch tested?
Unit tests.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14716 from yanboliang/spark-17141.

## What changes were proposed in this pull request?

This patch adds a new estimator/transformer `MultinomialLogisticRegression` to spark ML.

JIRA: [SPARK-7159](https://issues.apache.org/jira/browse/SPARK-7159)

## How was this patch tested?

Added new test suite `MultinomialLogisticRegressionSuite`.

## Approach

### Do not use a "pivot" class in the algorithm formulation

Many implementations of multinomial logistic regression treat the problem as K - 1 independent binary logistic regression models where K is the number of possible outcomes in the output variable. In this case, one outcome is chosen as a "pivot" and the other K - 1 outcomes are regressed against the pivot. This is somewhat undesirable since the coefficients returned will be different for different choices of pivot variables. An alternative approach to the problem models class conditional probabilites using the softmax function and will return uniquely identifiable coefficients (assuming regularization is applied). This second approach is used in R's glmnet and was also recommended by dbtsai.

### Separate multinomial logistic regression and binary logistic regression

The initial design makes multinomial logistic regression a separate estimator/transformer than the existing LogisticRegression estimator/transformer. An alternative design would be to merge them into one.

**Arguments for:**

* The multinomial case without pivot is distinctly different than the current binary case since the binary case uses a pivot class.
* The current logistic regression model in ML uses a vector of coefficients and a scalar intercept. In the multinomial case, we require a matrix of coefficients and a vector of intercepts. There are potential workarounds for this issue if we were to merge the two estimators, but none are particularly elegant.

**Arguments against:**

* It may be inconvenient for users to have to switch the estimator class when transitioning between binary and multiclass (although the new multinomial estimator can be used for two class outcomes).
* Some portions of the code are repeated.

This is a major design point and warrants more discussion.

### Mean centering

When no regularization is applied, the coefficients will not be uniquely identifiable. This is not hard to show and is discussed in further detail [here](https://core.ac.uk/download/files/153/6287975.pdf). R's glmnet deals with this by choosing the minimum l2 regularized solution (i.e. mean centering). Additionally, the intercepts are never regularized so they are always mean centered. This is the approach taken in this PR as well.

### Feature scaling

In current ML logistic regression, the features are always standardized when running the optimization algorithm. They are always returned to the user in the original feature space, however. This same approach is maintained in this patch as well, but the implementation details are different. In ML logistic regression, the unregularized feature values are divided by the column standard deviation in every gradient update iteration. In contrast, MLlib transforms the entire input dataset to the scaled space _before_ optimizaton. In ML, this means that `numFeatures * numClasses` extra scalar divisions are required in every iteration. Performance testing shows that this has significant (4x in some cases) slow downs in each iteration. This can be avoided by transforming the input to the scaled space ala MLlib once, before iteration begins. This does add some overhead initially, but can make significant time savings in some cases.

One issue with this approach is that if the input data is already cached, there may not be enough memory to cache the transformed data, which would make the algorithm _much_ slower. The tradeoffs here merit more discussion.

### Specifying and inferring the number of outcome classes

The estimator checks the dataframe label column for metadata which specifies the number of values. If they are not specified, the length of the `histogram` variable is used, which is essentially the maximum value found in the column. The assumption then, is that the labels are zero-indexed when they are provided to the algorithm.

## Performance

Below are some performance tests I have run so far. I am happy to add more cases or trials if we deem them necessary.

Test cluster: 4 bare metal nodes, 128 GB RAM each, 48 cores each

Notes:

* Time in units of seconds
* Metric is classification accuracy

| algo   |   elasticNetParam | fitIntercept   |   metric |   maxIter |   numPoints |   numClasses |   numFeatures |    time | standardization   |   regParam |
|--------|-------------------|----------------|----------|-----------|-------------|--------------|---------------|---------|-------------------|------------|
| ml     |                 0 | true           | 0.746415 |        30 |      100000 |            3 |        100000 | 327.923 | true              |          0 |
| mllib  |                 0 | true           | 0.743785 |        30 |      100000 |            3 |        100000 | 390.217 | true              |          0 |

| algo   |   elasticNetParam | fitIntercept   |   metric |   maxIter |   numPoints |   numClasses |   numFeatures |    time | standardization   |   regParam |
|--------|-------------------|----------------|----------|-----------|-------------|--------------|---------------|---------|-------------------|------------|
| ml     |                 0 | true           | 0.973238 |        30 |     2000000 |            3 |         10000 | 385.476 | true              |          0 |
| mllib  |                 0 | true           | 0.949828 |        30 |     2000000 |            3 |         10000 | 550.403 | true              |          0 |

| algo   |   elasticNetParam | fitIntercept   |   metric |   maxIter |   numPoints |   numClasses |   numFeatures |    time | standardization   |   regParam |
|--------|-------------------|----------------|----------|-----------|-------------|--------------|---------------|---------|-------------------|------------|
| mllib  |                 0 | true           | 0.864358 |        30 |     2000000 |            3 |         10000 | 543.359 | true              |        0.1 |
| ml     |                 0 | true           | 0.867418 |        30 |     2000000 |            3 |         10000 | 401.955 | true              |        0.1 |

| algo   |   elasticNetParam | fitIntercept   |   metric |   maxIter |   numPoints |   numClasses |   numFeatures |    time | standardization   |   regParam |
|--------|-------------------|----------------|----------|-----------|-------------|--------------|---------------|---------|-------------------|------------|
| ml     |                 1 | true           | 0.807449 |        30 |     2000000 |            3 |         10000 | 334.892 | true              |       0.05 |

| algo   |   elasticNetParam | fitIntercept   |   metric |   maxIter |   numPoints |   numClasses |   numFeatures |    time | standardization   |   regParam |
|--------|-------------------|----------------|----------|-----------|-------------|--------------|---------------|---------|-------------------|------------|
| ml     |                 0 | true           | 0.602006 |        30 |     2000000 |          500 |           100 | 112.319 | true              |          0 |
| mllib  |                 0 | true           | 0.567226 |        30 |     2000000 |          500 |           100 | 263.768 | true              |          0 |e           | 0.567226 |        30 |     2000000 |          500 |           100 | 263.768 | true              |          0 |

## References

Friedman, et al. ["Regularization Paths for Generalized Linear Models via Coordinate Descent"](https://core.ac.uk/download/files/153/6287975.pdf)
[http://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html](http://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html)

## Follow up items
* Consider using level 2 BLAS routines in the gradient computations - [SPARK-17134](https://issues.apache.org/jira/browse/SPARK-17134)
* Add model summary for MLOR - [SPARK-17139](https://issues.apache.org/jira/browse/SPARK-17139)
* Add initial model to MLOR and add test for intercept priors - [SPARK-17140](https://issues.apache.org/jira/browse/SPARK-17140)
* Python API - [SPARK-17138](https://issues.apache.org/jira/browse/SPARK-17138)
* Consider changing the tree aggregation level for MLOR/BLOR or making it user configurable to avoid memory problems with high dimensional data - [SPARK-17090](https://issues.apache.org/jira/browse/SPARK-17090)
* Refactor helper classes out of `LogisticRegression.scala` - [SPARK-17135](https://issues.apache.org/jira/browse/SPARK-17135)
* Design optimizer interface for added flexibility in ML algos - [SPARK-17136](https://issues.apache.org/jira/browse/SPARK-17136)
* Support compressing the coefficients and intercepts for MLOR models - [SPARK-17137](https://issues.apache.org/jira/browse/SPARK-17137)

Author: sethah <seth.hendrickson16@gmail.com>

Closes #13796 from sethah/SPARK-7159_M.

## What changes were proposed in this pull request?

Add LDA Wrapper in SparkR with the following interfaces:

- spark.lda(data, ...)

- spark.posterior(object, newData, ...)

- spark.perplexity(object, ...)

- summary(object)

- write.ml(object)

- read.ml(path)

## How was this patch tested?

Test with SparkR unit test.

Author: Xusen Yin <yinxusen@gmail.com>

Closes #14229 from yinxusen/SPARK-16447.

## What changes were proposed in this pull request?
Gaussian Mixture Model wrapper in SparkR, similarly to R's ```mvnormalmixEM```.

## How was this patch tested?
Unit test.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14392 from yanboliang/spark-16446.

## What changes were proposed in this pull request?

(Please fill in changes proposed in this fix)

Add Isotonic Regression wrapper in SparkR

Wrappers in R and Scala are added.
Unit tests
Documentation

## How was this patch tested?
Manually tested with sudo ./R/run-tests.sh

(Please explain how this patch was tested. E.g. unit tests, integration tests, manual tests)

Author: wm624@hotmail.com <wm624@hotmail.com>

Closes #14182 from wangmiao1981/isoR.

[SPARK-16934][ML][MLLIB] Update LogisticCostAggregator serialization code to make it consistent with LinearRegression

## What changes were proposed in this pull request?

Update LogisticCostAggregator serialization code to make it consistent with #14109

## How was this patch tested?
MLlib 2.0:
![image](https://cloud.githubusercontent.com/assets/19235986/17649601/5e2a79ac-61ee-11e6-833c-3bd8b5250470.png)

After this PR:
![image](https://cloud.githubusercontent.com/assets/19235986/17649599/52b002ae-61ee-11e6-9402-9feb3439880f.png)

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #14520 from WeichenXu123/improve_logistic_regression_costfun.

## What changes were proposed in this pull request?
Fix ```LogisticRegression``` typo in error message.

## How was this patch tested?
Docs change, no new tests.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14633 from yanboliang/lr-typo.

## What changes were proposed in this pull request?

Replaces custom choose function with o.a.commons.math3.CombinatoricsUtils.binomialCoefficient

## How was this patch tested?

Spark unit tests

Author: zero323 <zero323@users.noreply.github.com>

Closes #14614 from zero323/SPARK-17027.

## What changes were proposed in this pull request?
```GaussianMixture``` should use ```treeAggregate``` rather than ```aggregate``` to improve performance and scalability. In my test of dataset with 200 features and 1M instance, I found there is 20% increased performance.
BTW, we should destroy broadcast variable ```compute``` at the end of each iteration.

## How was this patch tested?
Existing tests.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14621 from yanboliang/spark-17033.

## What changes were proposed in this pull request?
Training GLMs on weighted dataset is very important use cases, but it is not supported by SparkR currently. Users can pass argument ```weights``` to specify the weights vector in native R. For ```spark.glm```, we can pass in the ```weightCol``` which is consistent with MLlib.

## How was this patch tested?
Unit test.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14346 from yanboliang/spark-16710.

## What changes were proposed in this pull request?
Similar to ```LeastSquaresAggregator``` in #14109, ```AFTAggregator``` used for ```AFTSurvivalRegression``` ends up serializing the ```parameters``` and ```featuresStd```, which is not necessary and can cause performance issues for high dimensional data. This patch removes this serialization. This PR is highly inspired by #14109.

## How was this patch tested?
I tested this locally and verified the serialization reduction.

Before patch
![image](https://cloud.githubusercontent.com/assets/1962026/17512035/abb93f04-5dda-11e6-97d3-8ae6b61a0dfd.png)

After patch
![image](https://cloud.githubusercontent.com/assets/1962026/17512024/9e0dc44c-5dda-11e6-93d0-6e130ba0d6aa.png)

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14519 from yanboliang/spark-16933.

[SPARK-16779][TRIVIAL] Avoid using postfix operators where they do not add much and remove whitelisting

## What changes were proposed in this pull request?

Avoid using postfix operation for command execution in SQLQuerySuite where it wasn't whitelisted and audit existing whitelistings removing postfix operators from most places. Some notable places where postfix operation remains is in the XML parsing & time units (seconds, millis, etc.) where it arguably can improve readability.

## How was this patch tested?

Existing tests.

Author: Holden Karau <holden@us.ibm.com>

Closes #14407 from holdenk/SPARK-16779.

## What changes were proposed in this pull request?
Similar to `LogisticAggregator`, `LeastSquaresAggregator` used for linear regression ends up serializing the coefficients and the features standard deviations, which is not necessary and can cause performance issues for high dimensional data. This patch removes this serialization.

In https://github.com/apache/spark/pull/13729 the approach was to pass these values directly to the add method. The approach used here, initially, is to mark these fields as transient instead which gives the benefit of keeping the signature of the add method simple and interpretable. The downside is that it requires the use of `transient lazy val`s which are difficult to reason about if one is not quite familiar with serialization in Scala/Spark.

## How was this patch tested?

**MLlib**
![image](https://cloud.githubusercontent.com/assets/7275795/16703660/436f79fa-4524-11e6-9022-ef00058ec718.png)

**ML without patch**
![image](https://cloud.githubusercontent.com/assets/7275795/16703831/c4d50b9e-4525-11e6-80cb-9b58c850cd41.png)

**ML with patch**
![image](https://cloud.githubusercontent.com/assets/7275795/16703675/63e0cf40-4524-11e6-9120-1f512a70e083.png)

Author: sethah <seth.hendrickson16@gmail.com>

Closes #14109 from sethah/LIR_serialize.

[SPARK-16750][FOLLOW-UP][ML] Add transformSchema for StringIndexer/VectorAssembler and fix failed tests.

## What changes were proposed in this pull request?
This is follow-up for #14378. When we add ```transformSchema``` for all estimators and transformers, I found there are tests failed for ```StringIndexer``` and ```VectorAssembler```. So I moved these parts of work separately in this PR, to make it more clear to review.
The corresponding tests should throw ```IllegalArgumentException``` at schema validation period after we add ```transformSchema```. It's efficient that to throw exception at the start of ```fit``` or ```transform``` rather than during the process.

## How was this patch tested?
Modified unit tests.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14455 from yanboliang/transformSchema.

## What changes were proposed in this pull request?

Add threshoulds' length checking for Classifiers which extends ProbabilisticClassifier

## How was this patch tested?

unit tests and manual tests

Author: Zheng RuiFeng <ruifengz@foxmail.com>

Closes #14470 from zhengruifeng/classifier_check_setThreshoulds_length.

## What changes were proposed in this pull request?

To Make sure ANN layer input training data to be persisted,
so that it can avoid overhead cost if the RDD need to be computed from lineage.

## How was this patch tested?

Existing Tests.

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #14483 from WeichenXu123/add_ann_persist_training_data.

## What changes were proposed in this pull request?

Support using latex in scaladoc by adding MathJax javascript to the js template.

## How was this patch tested?

Generated scaladoc.  Preview:

- LogisticGradient: [before](https://spark.apache.org/docs/2.0.0/api/scala/index.html#org.apache.spark.mllib.optimization.LogisticGradient) and [after](https://sparkdocs.lins05.pw/spark-16822/api/scala/index.html#org.apache.spark.mllib.optimization.LogisticGradient)

- MinMaxScaler: [before](https://spark.apache.org/docs/2.0.0/api/scala/index.html#org.apache.spark.ml.feature.MinMaxScaler) and [after](https://sparkdocs.lins05.pw/spark-16822/api/scala/index.html#org.apache.spark.ml.feature.MinMaxScaler)

Author: Shuai Lin <linshuai2012@gmail.com>

Closes #14438 from lins05/spark-16822-support-latex-in-scaladoc.

## What changes were proposed in this pull request?
Add a length checking for threshoulds' length in method `setThreshoulds()`  of classification models.

## How was this patch tested?
unit tests

Author: Zheng RuiFeng <ruifengz@foxmail.com>

Closes #14457 from zhengruifeng/check_setThresholds.

## What changes were proposed in this pull request?

Removed useless latex in a log messge.

## How was this patch tested?

Check generated scaladoc.

Author: Shuai Lin <linshuai2012@gmail.com>

Closes #14380 from lins05/fix-docs-formatting.

[SPARK-16696][ML][MLLIB] destroy KMeans bcNewCenters when loop finished and update code where should release unused broadcast/RDD in proper time

## What changes were proposed in this pull request?

update unused broadcast in KMeans/Word2Vec,
use destroy(false) to release memory in time.

and several place destroy() update to destroy(false) so that it will be async-called,
it will better than blocking called.

and update bcNewCenters in KMeans to make it destroy in correct time.
I use a list to store all historical `bcNewCenters` generated in each loop iteration and delay them to release at the end of loop.

fix TODO in `BisectingKMeans.run` "unpersist old indices",
Implements the pattern "persist current step RDD, and unpersist previous one" in the loop iteration.

## How was this patch tested?

Existing tests.

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #14333 from WeichenXu123/broadvar_unpersist_to_destroy.

[SPARK-16694][CORE] Use for/foreach rather than map for Unit expressions whose side effects are required

## What changes were proposed in this pull request?

Use foreach/for instead of map where operation requires execution of body, not actually defining a transformation

## How was this patch tested?

Jenkins

Author: Sean Owen <sowen@cloudera.com>

Closes #14332 from srowen/SPARK-16694.

## What changes were proposed in this pull request?
ML ```GaussianMixture``` training failed due to feature column type mistake. The feature column type should be ```ml.linalg.VectorUDT``` but got ```mllib.linalg.VectorUDT``` by mistake.
See [SPARK-16750](https://issues.apache.org/jira/browse/SPARK-16750) for how to reproduce this bug.
Why the unit tests did not complain this errors? Because some estimators/transformers missed calling ```transformSchema(dataset.schema)``` firstly during ```fit``` or ```transform```. I will also add this function to all estimators/transformers who missed in this PR.

## How was this patch tested?
No new tests, should pass existing ones.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14378 from yanboliang/spark-16750.

## What changes were proposed in this pull request?
Updated ML pipeline Cross Validation Scaladoc & PyDoc.

## How was this patch tested?

Documentation update

(If this patch involves UI changes, please attach a screenshot; otherwise, remove this)

Author: krishnakalyan3 <krishnakalyan3@gmail.com>

Closes #13894 from krishnakalyan3/kfold-cv.

## What changes were proposed in this pull request?
Fix some mistake in ```LinearRegression``` formula.

## How was this patch tested?
Documents change, no tests.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14369 from yanboliang/LiR-formula.

## What changes were proposed in this pull request?

In `LDAOptimizer.submitMiniBatch`, do persist on `stats: RDD[(BDM[Double], List[BDV[Double]])]`
and also move the place of unpersisting `expElogbetaBc` broadcast variable,
to avoid the `expElogbetaBc` broadcast variable to be unpersisted too early,
and update previous `expElogbetaBc.unpersist()` into `expElogbetaBc.destroy(false)`

## How was this patch tested?

Existing test.

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #14335 from WeichenXu123/improve_LDA.

## What changes were proposed in this pull request?

replace ANN convergence tolerance param default
from 1e-4 to 1e-6

so that it will be the same with other algorithms in MLLib which use LBFGS as optimizer.

## How was this patch tested?

Existing Test.

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #14286 from WeichenXu123/update_ann_tol.

## What changes were proposed in this pull request?

renaming var names to make code more clear:
nnz => weightSum
weightSum => totalWeightSum

and add a new member vector `nnz` (not `nnz` in previous code, which renamed to `weightSum`) to count each dimensions non-zero value number.
using `nnz` which I added above instead of `weightSum` when calculating min/max so that it fix several numerical error in some extreme case.

## How was this patch tested?

A new testcase added.

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #14216 from WeichenXu123/multivarOnlineSummary.

## What changes were proposed in this pull request?
Forgotten broadcasted variables were persisted into a previous #PR 14153). This PR turns those `unpersist()` into `destroy()` so that memory is freed even on the driver.

## How was this patch tested?
Unit Tests in Word2VecSuite were run locally.

This contribution is done on behalf of Criteo, according to the
terms of the Apache license 2.0.

Author: Anthony Truchet <a.truchet@criteo.com>

Closes #14268 from AnthonyTruchet/SPARK-16440.

## What changes were proposed in this pull request?
breeze 0.12 has been released for more than half a year, and it brings lots of new features, performance improvement and bug fixes.
One of the biggest features is ```LBFGS-B``` which is an implementation of ```LBFGS``` with box constraints and much faster for some special case.
We would like to implement Huber loss function for ```LinearRegression``` ([SPARK-3181](https://issues.apache.org/jira/browse/SPARK-3181)) and it requires ```LBFGS-B``` as the optimization solver. So we should bump up the dependent breeze version to 0.12.
For more features, improvements and bug fixes of breeze 0.12, you can refer the following link:
https://groups.google.com/forum/#!topic/scala-breeze/nEeRi_DcY5c

## How was this patch tested?
No new tests, should pass the existing ones.

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #14150 from yanboliang/spark-16494.

## What changes were proposed in this pull request?

`\partial\x` ==> `\partial x`
`har{x_i}` ==> `hat{x_i}`

## How was this patch tested?

N/A

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #14246 from WeichenXu123/fix_formular_err.

[SPARK-16535][BUILD] In pom.xml, remove groupId which is redundant definition and inherited from the parent

https://issues.apache.org/jira/browse/SPARK-16535

## What changes were proposed in this pull request?

When I scan through the pom.xml of sub projects, I found this warning as below and attached screenshot
```
Definition of groupId is redundant, because it's inherited from the parent
```
![screen shot 2016-07-13 at 3 13 11 pm](https://cloud.githubusercontent.com/assets/3925641/16823121/744f893e-4916-11e6-8a52-042f83b9db4e.png)

I've tried to remove some of the lines with groupId definition, and the build on my local machine is still ok.
```
<groupId>org.apache.spark</groupId>
```
As I just find now `<maven.version>3.3.9</maven.version>` is being used in Spark 2.x, and Maven-3 supports versionless parent elements: Maven 3 will remove the need to specify the parent version in sub modules. THIS is great (in Maven 3.1).

ref: http://stackoverflow.com/questions/3157240/maven-3-worth-it/3166762#3166762

## How was this patch tested?

I've tested by re-building the project, and build succeeded.

Author: Xin Ren <iamshrek@126.com>

Closes #14189 from keypointt/SPARK-16535.