Scala Breeze Dirichlet distribution parameter estimation - scala

I am trying to estimate parameters (Dirichlet distribution) for a data set using Scala's breeze lib. I already have a working python (pandas/dataframes) and R code for it but I was curious as to how to do it in Scala. Also I am new to Scala.
I cant seem to get it to work. I guess syntactically I don't have things right or something.
The code I trying to use is here: https://github.com/scalanlp/breeze/blob/master/math/src/main/scala/breeze/stats/distributions/Dirichlet.scala#L111
According to the code above: ExpFam[T,I] accepts two parameters T and I. I dont know what T and I are. Can T be a Dense Matrix ?
What I am doing is:
# Creating a matrix. The values are counts in my case.
val mat = DenseMatrix((1.0, 2.0, 3.0),(4.0, 5.0, 6.0))
# Then try to get sufficient stats and then MLE. I think this where I doing something wrong.
val diri = new ExpFam[DenseMatrix[Double],Int](mat)
println(diri.sufficientStatisticFor(mat))
Also if one has a data matrix like this DenseMatrix((1.0, 2.0, 3.0),(4.0, 5.0, 6.0)) how do estimate parameters (Dirichlet) in Scala.

I am not really very familiar with this aspect of breeze, but this works for me:
val data = Seq(
DenseVector(0.1, 0.1, 0.8),
DenseVector(0.2, 0.3, 0.5),
DenseVector(0.5, 0.1, 0.4),
DenseVector(0.3, 0.3, 0.4)
)
val expFam = new Dirichlet.ExpFam(DenseVector.zeros[Double](3))
val suffStat = data.foldLeft(expFam.emptySufficientStatistic){(a, x) =>
a + expFam.sufficientStatisticFor(x)
}
val alphaHat = expFam.mle(suffStat)
//DenseVector(2.9803000577558274, 2.325871404559782, 5.850530402841005)
The result is very close to but not exactly the same as what I get with my own code for maximum likelihood estimation of Dirichlets. The difference probably just comes down to differences in the optimizer being used (I'm using the fixed point iteration (9) in section 1 of this paper by T. Minka) and the stopping criteria.
Maybe there's a better way of doing this using the breeze api; if so, hopefully #dlwh or someone else more familiar with breeze will chime in.

T should be DenseVector and I should be Int. ExpFams aren't vectorized right now.

Related

Generating a random sequence using Scala

I need to get a random sequence of 100 values from 10^-10 to 10^10 and storing to an Array using Scala. I tried following but it didn't work
Array(scala.math.pow(10,-10).doubleValue to scala.math.pow(10,10).intValue by scala.math.pow(10,5).toLong)
Can anyone help me to figure out how to do this correctly?
So you need to fill() the array with Random elements.
import scala.util.Random
val rndm = new Random(1911L)
Array.fill(100)(rndm.between(math.pow(10,-10), math.pow(10,10)))
//res0: Array[Double] = Array(6.08868427907728E9
// , 3.29548545155816E9
// , 9.52802903383275E9
// , 7.981295238889314E9
// , 1.9462480080050848E9
// . . .
This works because the 2nd parameter to the fill() method is "by-name", i.e. re-evaluated for every element.
UPDATE
Things aren't quite as clean if you don't have the .between() method (Scala 2.13).
Array.fill(100)(rndm.nextDouble())
.map(_ * math.pow(10,10))
Note that this actually has a floor of 0.0 instead of the desired 0.0000000001. It's very unlikely you'd have an entry that's too small, especially when taking only 100 samples. Still, there are steps you could take to insure that can't happen.

What's the simplest way to get a Spark DataFrame from arbitrary Array Data in Scala?

I've been breaking my head about this one for a couple of days now. It feels like it should be intuitively easy... Really hope someone can help!
I've built an org.nd4j.linalg.api.ndarray.INDArray of word occurrence from some semi-structured data like this:
import org.nd4j.linalg.factory.Nd4j
import org.nd4s.Implicits._
val docMap = collection.mutable.Map[Int,Map[Int,Int]] //of the form Map(phrase -> Map(phrasePosition -> word)
val words = ArrayBuffer("word_1","word_2","word_3",..."word_n")
val windows = ArrayBuffer("$phrase,$phrasePosition_1","$phrase,$phrasePosition_2",..."$phrase,$phrasePosition_n")
var matrix = Nd4j.create(windows.length*words.length).reshape(windows.length,words.length)
for (row <- matrix.shape(0)){
for(column <- matrix.shape(1){
//+1 to (row,column) if word occurs at phrase, phrasePosition indicated by window_n.
}
}
val finalmatrix = matrix.T.dot(matrix) // to get co-occurrence matrix
So far so good...
Downstream of this point I need to integrate the data into an existing pipeline in Spark, and use that implementation of pca etc, so I need to create a DataFrame, or at least an RDD. If I knew the number of words and/or windows in advance I could do something like:
case class Row(window : String, word_1 : Double, word_2 : Double, ...etc)
val dfSeq = ArrayBuffer[Row]()
for (row <- matrix.shape(0)){
dfSeq += Row(windows(row),matrix.get(NDArrayIndex.point(row), NDArrayIndex.all()))
}
sc.parallelize(dfSeq).toDF("window","word_1","word_2",...etc)
but the number of windows and words is determined at runtime. I'm looking for a WindowsxWords org.apache.spark.sql.DataFrame as output, input is a WindowsxWords org.nd4j.linalg.api.ndarray.INDArray
Thanks in advance for any help you can offer.
Ok, so after several days work it looks like the simple answer is: there isn't one. In fact, it looks like trying to use Nd4j in this context at all is a bad idea for several reasons:
It's (really) hard to get data out of the native INDArray format once you've put it in.
Even using something like guava, the .data() method brings everything on heap which will quickly become expensive.
You've got the added hassle of having to compile an assembly jar or use hdfs etc to handle the library itself.
I did also consider using Breeze which may actually provide a viable solution but carries some of the same problems and can't be used on distributed data structures.
Unfortunately, using native Spark / Scala datatypes, although easier once you know how, is - for someone like me coming from Python + numpy + pandas heaven at least - painfully convoluted and ugly.
Nevertheless, I did implement this solution successfully:
import org.apache.spark.mllib.linalg.{Vectors,Vector,Matrix,DenseMatrix,DenseVector}
import org.apache.spark.mllib.linalg.distributed.RowMatrix
//first make a pseudo-matrix from Scala Array[Double]:
var rowSeq = Seq.fill(windows.length)(Array.fill(words.length)(0d))
//iterate through 'rows' and 'columns' to fill it:
for (row 0 until windows.length){
for (column 0 until words.length){
// rowSeq(row)(column) += 1 if word occurs at phrase, phrasePosition indicated by window_n.
}
}
//create Spark DenseMatrix
val rows : Array[Double] = rowSeq.transpose.flatten.toArray
val matrix = new DenseMatrix(windows.length,words.length,rows)
One of the main operations that I needed Nd4J for was matrix.T.dot(matrix) but it turns out that you can't multiply 2 matrices of Type org.apache.spark.mllib.linalg.DenseMatrix together, one of them (A) has to be a org.apache.spark.mllib.linalg.distributed.RowMatrix and - you guessed it - you can't call matrix.transpose() on a RowMatrix, only on a DenseMatrix! Since it's not really relevant to the question, I'll leave that part out, except to explain that what comes out of that step is a RowMatrix. Credit is also due here and here for the final part of the solution:
val rowMatrix : [RowMatrix] = transposeAndDotDenseMatrix(matrix)
// get DataFrame from RowMatrix via DenseMatrix
val newdense = new DenseMatrix(rowMatrix.numRows().toInt,rowMatrix.numCols().toInt,rowMatrix.rows.collect.flatMap(x => x.toArray)) // the call to collect() here is undesirable...
val matrixRows = newdense.rowIter.toSeq.map(_.toArray)
val df = spark.sparkContext.parallelize(matrixRows).toDF("Rows")
// then separate columns:
val df2 = (0 until words.length).foldLeft(df)((df, num) =>
df.withColumn(words(num), $"Rows".getItem(num)))
.drop("Rows")
Would love to hear improvements and suggestions on this, thanks.

chisel3 arithmetic operations on Doubles

Please I have problems manipulating arithmetic operations with doubles in chisel. I have been seeing examples that uses just the following types: Int,UInt,SInt.
I saw here that arithmetic operations where described only for SInt and UInt. What about Double?
I tried to declare my output out as Double, but didn't know how. Because the output of my code is Double.
Is there a way to declare in Bundle an input and an output of type Double?
Here is my code:
class hashfunc(val k:Int, val n: Int ) extends Module {
val a = k + k
val io = IO(new Bundle {
val b=Input(UInt(k.W))
val w=Input(UInt(k.W))
var out = Output(UInt(a.W))
})
val tabHash1 = new Array[Array[Double]](n)
val x = new ArrayBuffer[(Double, Data)]
val tabHash = new Array[Double](tabHash1.size)
for (ind <- tabHash1.indices){
var sum=0.0
for (ind2 <- 0 until x.size){
sum += ( x(ind2) * tabHash1(ind)(ind2) )
}
tabHash(ind) = ((sum + io.b) / io.w)
}
io.out := tabHash.reduce(_ + _)
}
When I compile the code, I get the following error:
code error
Thank you for your kind attention, looking forward to your responses.
Chisel does have a native FixedPoint type which maybe of use. It is in the experimental package
import chisel3.experimental.FixedPoint
There is also a project DspTools that has simulation support for Doubles. There are some nice features, e.g. it that allows modules to parameterized on the numeric types (Complex, Double, FixedPoint, SInt) so that you can run simulations on double to validate the desired mathematical behavior and then switch to a synthesizable number format that meets your precision criteria.
DspTools is an ongoing research projects and the team would appreciate outside users feedback.
Operations on floating point numbers (Double in this case) are not supported directly by any HDL. The reason for this is that while addition/subtraction/multiplication of fixed point numbers is well defined there are a lot of design space trade-offs for floating point hardware as it is a much more complex piece of hardware.
That is to say, a high performance floating point unit is a significant piece of hardware in it's own right and would be time shared in any realistic design.

filling a matrix with Scala library breeze

I'm new to Scala and I'm having a mental block on a seemingly easy problem. I'm using the Scala library breeze and need to take an array buffer (mutable) and put the results into a matrix. This... should be simple but? Scala is so insanely type casted breeze seems really picky about what data types it will take when making a DenseVector. This is just some prototype code, but can anyone help me come up with a solution?
Right now I have something like...
//9 elements that need to go into a 3x3 matrix, 1-3 as top row, 4-6 as middle row, etc)
val numbersForMatrix: ArrayBuffer[Double] = (1, 2, 3, 4, 5, 6, 7, 8, 9)
//the empty 3x3 matrix
var M: breeze.linalg.DenseMatrix[Double] = DenseMatrix.zeros(3,3)
In breeze you can do stuff like
M(0,0) = 100 and set the first value to 100 this way,
You can also do stuff like:
M(0, 0 to 2) := DenseVector(1, 2, 3)
which sets the first row to 1, 2, 3
But I cannot get it to do something like...
var dummyList: List[Double] = List(1, 2, 3) //this works
var dummyVec = DenseVector[Double](dummyList) //this works
M(0, 0 to 2) := dummyVec //this does not work
and successfully change the first row to the 1, 2,3.
And that's with a List, not even an ArrayBuffer.
Am willing to change datatypes from ArrayBuffer but just not sure how to approach this at all... could try updating the matrix values one by one but that seems like it would be VERY hacky to code up(?).
Note: I'm a Python programmer who is used to using numpy and just giving it arrays. The breeze documentation doesn't provide enough examples with other datatypes for me to have been able to figure this out yet.
Thanks!
Breeze is, in addition to pickiness over types, pretty picky about vector shape: DenseVectors are column vectors, but you are trying to assign to a subset of a row, which expects a transposed DenseVector:
M(0, 0 to 2) := dummyVec.t

How to use RowMatrix.columnSimilarities (similarity search)

TL;DR; I am trying to train off of an existing data set (Seq[Words] with corresponding categories), and use that trained dataset to filter another dataset using category similarity.
I am trying to train a corpus of data and then use it for text analysis*. I've tried using NaiveBayes, but that seems to only work with the data you have, so it's predict algorithm will always return something, even if it doesn't match anything.
So, I am now trying to use TFIDF and passing that output into a RowMatrix and computing the similarities. But, I'm not sure how to run my query (one word for now). Here's what I've tried:
val rddOfTfidfFromCorpus : RDD[Vector]
val query = "word"
val tf = new HashingTF().transform(List(query))
val tfIDF = new IDF().fit(sc.makeRDD(List(tf))).transform(tf)
val mergedVectors = rddOfTfidfFromCorpus.union(sc.makeRDD(List(tfIDF)))
val similarities = new RowMatrix(mergedVectors).columnSimilarities(1.0)
Here is where I'm stuck (if I've even done everything right until here). I tried filtering the similarities i and j down to the parts of my query's TFIDF and end up with an empty collection.
The gist is that I want to train on a corpus of data and find what category it falls in. The above code is at least trying to get it down to one category and checking if I can get a prediction from that at least....
*Note that this is a toy example, so I only need something that works well enough
*I am using Spark 1.4.0
Using columnSimilarities doesn't make sense here. Since each column in your matrix represents a set of terms you'll get a matrix of similarities between tokens not documents. You could transpose the matrix and then use columnSimilarities but as far as I understand what you want is a similarity between query and corpus. You can express that using matrix multiplication as follows:
For starters you'll need an IDFModel you've trained on a corpus. Lets assume it is called idf:
import org.apache.spark.mllib.feature.IDFModel
val idf: IDFModel = ??? // Trained using corpus data
and a small helper:
def toBlockMatrix(rdd: RDD[Vector]) = new IndexedRowMatrix(
rdd.zipWithIndex.map{case (v, i) => IndexedRow(i, v)}
).toCoordinateMatrix.toBlockMatrix
First lets convert query to an RDD and compute TF:
val query: Seq[String] = ???
val queryTf = new HashingTF().transform(query)
Next we can apply IDF model and convert result to matrix:
val queryTfidf = idf.transform(queryTf)
val queryMatrix = toBlockMatrix(queryTfidf)
We'll need a corpus matrix as well:
val corpusMatrix = toBlockMatrix(rddOfTfidfFromCorpus)
If you multiple both we get a matrix with number of rows equal to the number of docs in the query and number of columns equal to the number of documents in the corpus.
val dotProducts = queryMatrix.multiply(corpusMatrix.transpose)
To get a proper cosine similarity you have to divide by a product of magnitudes but if you can handle that.
There are two problems here. First of all it is rather expensive. Moreover I am not sure if it really useful. To reduce cost you can apply some dimensionality reduction algorithm first but lets leave it for now.
Judging from a following statement
NaiveBayes (...) seems to only work with the data you have, so it's predict algorithm will always return something, even if it doesn't match anything.
I guess you want some kind of unsupervised learning method. The simplest thing you can try is K-means:
import org.apache.spark.mllib.clustering.{KMeans, KMeansModel}
val numClusters: Int = ???
val numIterations = 20
val model = KMeans.train(rddOfTfidfFromCorpus, numClusters, numIterations)
val predictions = model.predict(queryTfidf)