If there are no `transpose()` in `self.theta`, a

*ValueError: matrices are not aligned*

is occurring. The former test case just ignore this situation.

Author: Xusen Yin <yinxusen@gmail.com>

Closes #463 from yinxusen/python-naive-bayes and squashes the following commits:

fcbe3bc [Xusen Yin] fix bugs of dot in python

This PR adds a SparseVector class in PySpark and updates all the regression, classification and clustering algorithms and models to support sparse data, similar to MLlib. I chose to add this class because SciPy is quite difficult to install in many environments (more so than NumPy), but I plan to add support for SciPy sparse vectors later too, and make the methods work transparently on objects of either type.

On the Scala side, we keep Python sparse vectors sparse and pass them to MLlib. We always return dense vectors from our models.

Some to-do items left:
- [x] Support SciPy's scipy.sparse matrix objects when SciPy is available. We can easily add a function to convert these to our own SparseVector.
- [x] MLlib currently uses a vector with one extra column on the left to represent what we call LabeledPoint in Scala. Do we really want this? It may get annoying once you deal with sparse data since you must add/subtract 1 to each feature index when training. We can remove this API in 1.0 and use tuples for labeling.
- [x] Explain how to use these in the Python MLlib docs.

CC @mengxr, @joshrosen

Author: Matei Zaharia <matei@databricks.com>

Closes #341 from mateiz/py-ml-update and squashes the following commits:

d52e763 [Matei Zaharia] Remove no-longer-needed slice code and handle review comments
ea5a25a [Matei Zaharia] Fix remaining uses of copyto() after merge
b9f97a3 [Matei Zaharia] Fix test
1e1bd0f [Matei Zaharia] Add MLlib logistic regression example in Python
88bc01f [Matei Zaharia] Clean up inheritance of LinearModel in Python, and expose its parametrs
37ab747 [Matei Zaharia] Fix some examples and docs due to changes in MLlib API
da0f27e [Matei Zaharia] Added a MLlib K-means example and updated docs to discuss sparse data
c48e85a [Matei Zaharia] Added some tests for passing lists as input, and added mllib/tests.py to run-tests script.
a07ba10 [Matei Zaharia] Fix some typos and calculation of initial weights
74eefe7 [Matei Zaharia] Added LabeledPoint class in Python
889dde8 [Matei Zaharia] Support scipy.sparse matrices in all our algorithms and models
ab244d1 [Matei Zaharia] Allow SparseVectors to be initialized using a dict
a5d6426 [Matei Zaharia] Add linalg.py to run-tests script
0e7a3d8 [Matei Zaharia] Keep vectors sparse in Java when reading LabeledPoints
eaee759 [Matei Zaharia] Update regression, classification and clustering models for sparse data
2abbb44 [Matei Zaharia] Further work to get linear models working with sparse data
154f45d [Matei Zaharia] Update docs, name some magic values
881fef7 [Matei Zaharia] Added a sparse vector in Python and made Java-Python format more compact

In PR https://github.com/apache/spark/pull/117, we added dense/sparse vector data model and updated KMeans to support sparse input. This PR is to replace all other `Array[Double]` usage by `Vector` in generalized linear models (GLMs) and Naive Bayes. Major changes:

1. `LabeledPoint` becomes `LabeledPoint(Double, Vector)`.
2. Methods that accept `RDD[Array[Double]]` now accept `RDD[Vector]`. We cannot support both in an elegant way because of type erasure.
3. Mark 'createModel' and 'predictPoint' protected because they are not for end users.
4. Add libSVMFile to MLContext.
5. NaiveBayes can accept arbitrary labels (introducing a breaking change to Python's `NaiveBayesModel`).
6. Gradient computation no longer creates temp vectors.
7. Column normalization and centering are removed from Lasso and Ridge because the operation will densify the data. Simple feature transformation can be done before training.

TODO:
1. ~~Use axpy when possible.~~
2. ~~Optimize Naive Bayes.~~

Author: Xiangrui Meng <meng@databricks.com>

Closes #245 from mengxr/vector and squashes the following commits:

eb6e793 [Xiangrui Meng] move libSVMFile to MLUtils and rename to loadLibSVMData
c26c4fc [Xiangrui Meng] update DecisionTree to use RDD[Vector]
11999c7 [Xiangrui Meng] Merge branch 'master' into vector
f7da54b [Xiangrui Meng] add minSplits to libSVMFile
da25e24 [Xiangrui Meng] revert the change to default addIntercept because it might change the behavior of existing code without warning
493f26f [Xiangrui Meng] Merge branch 'master' into vector
7c1bc01 [Xiangrui Meng] add a TODO to NB
b9b7ef7 [Xiangrui Meng] change default value of addIntercept to false
b01df54 [Xiangrui Meng] allow to change or clear threshold in LR and SVM
4addc50 [Xiangrui Meng] merge master
4ca5b1b [Xiangrui Meng] remove normalization from Lasso and update tests
f04fe8a [Xiangrui Meng] remove normalization from RidgeRegression and update tests
d088552 [Xiangrui Meng] use static constructor for MLContext
6f59eed [Xiangrui Meng] update libSVMFile to determine number of features automatically
3432e84 [Xiangrui Meng] update NaiveBayes to support sparse data
0f8759b [Xiangrui Meng] minor updates to NB
b11659c [Xiangrui Meng] style update
78c4671 [Xiangrui Meng] add libSVMFile to MLContext
f0fe616 [Xiangrui Meng] add a test for sparse linear regression
44733e1 [Xiangrui Meng] use in-place gradient computation
e981396 [Xiangrui Meng] use axpy in Updater
db808a1 [Xiangrui Meng] update JavaLR example
befa592 [Xiangrui Meng] passed scala/java tests
75c83a4 [Xiangrui Meng] passed test compile
1859701 [Xiangrui Meng] passed compile
834ada2 [Xiangrui Meng] optimized MLUtils.computeStats update some ml algorithms to use Vector (cont.)
135ab72 [Xiangrui Meng] merge glm
0e57aa4 [Xiangrui Meng] update Lasso and RidgeRegression to parse the weights correctly from GLM mark createModel protected mark predictPoint protected
d7f629f [Xiangrui Meng] fix a bug in GLM when intercept is not used
3f346ba [Xiangrui Meng] update some ml algorithms to use Vector

We've used camel case in other Spark methods so it felt reasonable to
keep using it here and make the code match Scala/Java as much as
possible. Note that parameter names matter in Python because it allows
passing optional parameters by name.

- Added a Python wrapper for Naive Bayes
- Updated the Scala Naive Bayes to match the style of our other
  algorithms better and in particular make it easier to call from Java
  (added builder pattern, removed default value in train method)
- Updated Python MLlib functions to not require a SparkContext; we can
  get that from the RDD the user gives
- Added a toString method in LabeledPoint
- Made the Python MLlib tests run as part of run-tests as well (before
  they could only be run individually through each file)