From c4f1986a9f57e2afa6e3af31c74289a34040facb Mon Sep 17 00:00:00 2001 From: Leigh-Anne Mathieson Date: Thu, 21 Mar 2019 12:38:08 +0000 Subject: [PATCH] add minmax scaling and tidy up especially gradient descent app --- notes/week1-written.pdf | Bin 0 -> 82176 bytes src/main/scala/app/GradientDescentApp.scala | 30 ++++--- src/main/scala/util/FeatureScaler.scala | 44 ++++++--- src/main/scala/util/GradientDescent.scala | 15 ++-- test/main/scala/util/FeatureScalerTest.scala | 46 ++++++++-- .../main/scala/util/GradientDescentTest.scala | 84 +++++------------ tex/week1.log | 85 +++++++++--------- tex/week1.pdf | Bin 1875274 -> 1874991 bytes tex/week1.synctex.gz | Bin 42579 -> 42802 bytes tex/week1.tex | 26 +++--- 10 files changed, 165 insertions(+), 165 deletions(-) create mode 100644 notes/week1-written.pdf diff --git a/notes/week1-written.pdf b/notes/week1-written.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6a92d5410eccfb6972d6f5ec03e2d5a902521606 GIT binary patch literal 82176 zcmV)4K+3-*P((&8F)lO;CGFw{FG6W_b5Lb+LvL+xZ*FC7 zbRaPbFGFu^Z*o&`VPj<=FGOW_X=7zaa$$K2FHB`_XLM*FGBq|hG72w7X>4?5av(2C zLPVma%Ev{3IG5A05AXn0000J000Jd000Dy00000000000RR91 z0003d00IC1|Nj6026g}d1dRXy00000000001ONU10{;H~tMxC*fRQ}Jr^lSA_89qg zR|EX7`N=2|Z#4&S;MZx1y9t`3v|rjqTQXE%=bbgTsh6mHFZc{RB46gh9#{@ZKjBtg zXW8z%aQlnH@lmvwevsR1cPr#Y-%cIlf?BXqQ_~|kz{S3w&}0Q#aAJD=gw1rr0QqX) z%E_$3J%X-b5l;f)OBqQUJW^N)`f6?X;5^FwVZ9TUW$kee2lT)y2y4g+RvuOQm~KPq z|7DlTkF6`@R&#EkqPi7#qW=-xKv{Jx5%J}uP%90QouGq% zELS=4=hGQU3>rNIov?Jfmu{4t#fkiB%)Ffo+
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z-vs}=2tG>suMq5<8UC&UgNeN@qlb~hhkM{(?mu+6MLt%}#Z>g;#m@|6;-Uw#&@(fs zGW}goW;Qw?@T01{jQ^qezh>GysoLAy@JpJy+nBnz&?|l{zmXFNASbT)Z!4?Nn~o5TN2Rpku$3(m^$ zjQ>O`;BS2Y`_A!jGBtw-0+?9ff&Y2{>}+f-YydOB|CDh8xmZ8;>t7GR?jN#`G1CWC z)qjyOvvG2K93}rD0}8QlurLd=ax!!A|KBzKK6RX3jGSElUI9)f O4h~j$3JNg=@&5q^u<)+{ literal 0 HcmV?d00001 diff --git a/src/main/scala/app/GradientDescentApp.scala b/src/main/scala/app/GradientDescentApp.scala index 90f3f83..fbeb12b 100644 --- a/src/main/scala/app/GradientDescentApp.scala +++ b/src/main/scala/app/GradientDescentApp.scala @@ -7,28 +7,34 @@ import main.scala.util.GradientDescent.LearnedParameterSet import main.scala.util._ object GradientDescentApp { - def arrayToHeightWeight(strings: Array[String]) = HeightWeight(strings(0), strings(1).toDouble, strings(2).toDouble) - def heightWeightTo2dPoint(data: List[HeightWeight]) = data.map(dataPoint => SimplePoint(dataPoint.height, dataPoint.weight)) - val heightWeights = CsvReader.asCaseClassList("/nlys-train.csv", true, arrayToHeightWeight) - val data = heightWeightTo2dPoint(heightWeights) + def main(args: Array[String]): Unit = { - val learnedParameters: LearnedParameterSet = GradientDescent.gradientDescent(data, 0, 1, 3, 500) + def arrayToHeightWeight(strings: Array[String]) = HeightWeight(strings(0), strings(1).toDouble, strings(2).toDouble) + def heightWeightTo2dPoint(data: List[HeightWeight]) = data.map(dataPoint => SimplePoint(dataPoint.height, dataPoint.weight)) - def main(args: Array[String]): Unit = { + //load in the training data + val heightWeights = CsvReader.asCaseClassList("/nlys-train.csv", true, arrayToHeightWeight) + val data = heightWeightTo2dPoint(heightWeights) + val normalisedData = FeatureScaler.meanNormalisedData(data) + + //run gradient descent + val learnedParameters: LearnedParameterSet = GradientDescent.gradientDescent(normalisedData, 0, 1, 3, 500) + //load in test data val heightWeightsTestData = CsvReader.asCaseClassList("/nlys-test.csv", true, arrayToHeightWeight) val heightWeightsTestDataPoints = heightWeightTo2dPoint(heightWeightsTestData) + val heightWeightTestDataScaled = FeatureScaler.meanNormalisedData(heightWeightsTestDataPoints) - val heightWeightScaled = FeatureScaler.scaledFeatures(data) - val heightWeightTestDataScaled = FeatureScaler.scaledFeatures(heightWeightsTestDataPoints) - + //plot the trend of cost vs iteration so we know if gradient descent is working displayPlot(Plotter.costItersPlot(learnedParameters.history, None)) - displayPlot(Plotter.heightWeightPlot(heightWeightScaled.map(p => HeightWeight("", p.x, p.y)), learnedParameters.theta0, learnedParameters.theta1, Some("Height vs weight TRAINING data and line fit via linear regression"))) + //plot our training data, and the line that we fit with gradient descent + displayPlot(Plotter.heightWeightPlot(normalisedData.map(p => HeightWeight("", p.x, p.y)), learnedParameters.theta0, learnedParameters.theta1, Some("Height vs weight TRAINING data and line fit via linear regression"))) + //plot our test data, and the line that we fit with gradient descent displayPlot(Plotter.heightWeightPlot(heightWeightTestDataScaled.map(p => HeightWeight("", p.x, p.y)), learnedParameters.theta0, learnedParameters.theta1, Some("Height vs weight TEST data and line fit via linear regression"))) - - val meanAbsoluteError = LinearErrorCalculator.linearMeanAbsoluteError(heightWeightScaled, learnedParameters.theta0, learnedParameters.theta1) + //just print out the mean absolute error for the line we fit when we compare to the test set + val meanAbsoluteError = LinearErrorCalculator.linearMeanAbsoluteError(normalisedData, learnedParameters.theta0, learnedParameters.theta1) println(s"Hello, world! This is the absolute error: $meanAbsoluteError") } diff --git a/src/main/scala/util/FeatureScaler.scala b/src/main/scala/util/FeatureScaler.scala index 741cf10..84a9278 100644 --- a/src/main/scala/util/FeatureScaler.scala +++ b/src/main/scala/util/FeatureScaler.scala @@ -21,21 +21,39 @@ object FeatureScaler { } } - def scaledFeatures(data: List[SimplePoint]): List[SimplePoint] = { - - def sum(xs: List[Double]): Double = { - @tailrec - def inner(xs: List[Double], accum: Double): Double = { - xs match { - case x :: tail => inner(tail, accum + x) - case Nil => accum - } - } + def minMaxScaledData(data: List[SimplePoint]): List[SimplePoint] = { + val xList = data.map(_.x) + val yList = data.map(_.y) + + val maxX = xList.max + val maxY = yList.max + val minX = yList.min + val minY = yList.min + + data.map { point => + SimplePoint( + (point.x - minX) / (maxX - minX), + (point.y - minY) / (maxY - minY) + ) + } + + } - inner(xs, 0) + def sum(xs: List[Double]): Double = { + @tailrec + def inner(xs: List[Double], accum: Double): Double = { + xs match { + case x :: tail => inner(tail, accum + x) + case Nil => accum + } } - def avg(nums: List[Double]): Double = sum(nums) / nums.length.toDouble + inner(xs, 0) + } + + def avg(nums: List[Double]): Double = sum(nums) / nums.length.toDouble + + def meanNormalisedData(data: List[SimplePoint]): List[SimplePoint] = { def scaled(min: Double, max: Double, avg: Double, dataPoint: Double): Double = { val range = max - min @@ -52,9 +70,7 @@ object FeatureScaler { val maxY = yList.max val xAvg = avg(xList) - println(xAvg) val yAvg = avg(yList) - println(yAvg) data.map { point => SimplePoint( diff --git a/src/main/scala/util/GradientDescent.scala b/src/main/scala/util/GradientDescent.scala index 512aacf..4216b8b 100644 --- a/src/main/scala/util/GradientDescent.scala +++ b/src/main/scala/util/GradientDescent.scala @@ -36,12 +36,9 @@ object GradientDescent { learningRate: Double, iters: Int): LearnedParameterSet = { - val scaledData = FeatureScaler.scaledFeatures(data) -// val scaledData = FeatureScaler.scaledDividedByMax(data) - var theta0 = startingTheta0 var theta1 = startingTheta1 - var cost = LinearErrorCalculator.linearMSE(scaledData, theta0, theta1) + var cost = LinearErrorCalculator.linearMSE(data, theta0, theta1) var gradientDescentHistory = new ListBuffer[GradientDescentHistoryPoint] println(s"starting cost ${cost}") @@ -51,16 +48,16 @@ object GradientDescent { println(s"old theta 0 ${theta0}") println(s"old theta 1 ${theta1}") - println(s"theta 0 iter ${theta0Updated(scaledData, theta0, theta1, learningRate)}") - println(s"theta 1 iter ${theta1Updated(scaledData, theta0, theta1, learningRate)}") + println(s"theta 0 iter ${theta0Updated(data, theta0, theta1, learningRate)}") + println(s"theta 1 iter ${theta1Updated(data, theta0, theta1, learningRate)}") - val tempTheta0 = theta0Updated(scaledData, theta0, theta1, learningRate) - val tempTheta1 = theta1Updated(scaledData, theta0, theta1, learningRate) + val tempTheta0 = theta0Updated(data, theta0, theta1, learningRate) + val tempTheta1 = theta1Updated(data, theta0, theta1, learningRate) theta0 = tempTheta0 theta1 = tempTheta1 - cost = LinearErrorCalculator.linearMSE(scaledData, theta0, theta1) + cost = LinearErrorCalculator.linearMSE(data, theta0, theta1) println(s"new theta 0 ${theta0}") println(s"new theta 1 ${theta1}") println(s"new cost ${cost}") diff --git a/test/main/scala/util/FeatureScalerTest.scala b/test/main/scala/util/FeatureScalerTest.scala index bd8ed92..b42ccfc 100644 --- a/test/main/scala/util/FeatureScalerTest.scala +++ b/test/main/scala/util/FeatureScalerTest.scala @@ -5,8 +5,8 @@ import org.specs2.mutable.Specification class FeatureScalerTest extends Specification { - "FeatureScalerTest" should { - "scaledFeatures" in { + "scaledFeatures" should { + "scale the data in " in { val inputData = List( SimplePoint(78, 90), SimplePoint(55, 50), @@ -16,16 +16,46 @@ class FeatureScalerTest extends Specification { ) val expected = List( - SimplePoint(0.22352941176470573,0.3949999999999999), - SimplePoint(-0.4529411764705884,-0.6050000000000001), - SimplePoint(-0.48235294117647076,-0.45500000000000007), - SimplePoint(0.19411764705882337,0.2699999999999999), - SimplePoint(0.5176470588235292,0.3949999999999999) + SimplePoint(0.22352941176470573, 0.3949999999999999), + SimplePoint(-0.4529411764705884, -0.6050000000000001), + SimplePoint(-0.48235294117647076, -0.45500000000000007), + SimplePoint(0.19411764705882337, 0.2699999999999999), + SimplePoint(0.5176470588235292, 0.3949999999999999) ) - val scaled = FeatureScaler.scaledFeatures(inputData) + val scaled = FeatureScaler.meanNormalisedData(inputData) + scaled shouldEqual (expected) + } + } + + "minMaxScaledData" should { + "scale the data" in { + val inputData = List( + SimplePoint(78, 90), + SimplePoint(55, 50), + SimplePoint(54, 56), + SimplePoint(77, 85), + SimplePoint(88, 90) + ) + + val expected = List( + SimplePoint(0.7368421052631579,1.0), + SimplePoint(0.13157894736842105,0.0), + SimplePoint(0.10526315789473684,0.15), + SimplePoint(0.7105263157894737,0.875), + SimplePoint(1.0,1.0) + ) + + val scaled = FeatureScaler.minMaxScaledData(inputData) scaled shouldEqual(expected) } + } + "avg" should { + "give the average of a list of values" in { + val inputValues = List(78.0, 55.0, 54.0, 77.0, 88.0) + + FeatureScaler.avg(inputValues) shouldEqual (70.4) + } } } diff --git a/test/main/scala/util/GradientDescentTest.scala b/test/main/scala/util/GradientDescentTest.scala index 0b06557..ff6f9e0 100644 --- a/test/main/scala/util/GradientDescentTest.scala +++ b/test/main/scala/util/GradientDescentTest.scala @@ -1,83 +1,41 @@ package main.scala.util -import main.scala.model.{HeightWeight, House, SimplePoint} +import main.scala.model.SimplePoint import org.specs2.mutable.Specification -import main.scala.util.GradientDescent.LearnedParameterSet class GradientDescentTest extends Specification{ - "theta0Iter" should { - "probably not be zero" in { - - val expected = List( - HeightWeight("Male",174.0,96.0), - HeightWeight("Male",189.0,87.0) + "updatedTheta0" should { + "be updated from the value passed in" in { + val normalisedData = List( + SimplePoint(0.22352941176470573, 0.3949999999999999), + SimplePoint(-0.4529411764705884, -0.6050000000000001), + SimplePoint(-0.48235294117647076, -0.45500000000000007), + SimplePoint(0.19411764705882337, 0.2699999999999999), + SimplePoint(0.5176470588235292, 0.3949999999999999) ) - val data = expected.map(dataPoint => SimplePoint(dataPoint.height, dataPoint.weight)) - val gmm: Double = GradientDescent.theta0Updated(data, 1, 1, 1) + val updatedTheta0: Double = GradientDescent.theta0Updated(normalisedData, 1, 1, 0.01) - gmm shouldEqual (-90) + updatedTheta0 shouldEqual (0.99) } } - "theta1iter" should { - "probably not be zero" in { + "updatedTheta1" should { + "be updated from the value passed in" in { - val expected = List( - HeightWeight("Female",185.0,110.0), - HeightWeight("Female",195.0,104.0) + val normalisedData = List( + SimplePoint(0.22352941176470573, 0.3949999999999999), + SimplePoint(-0.4529411764705884, -0.6050000000000001), + SimplePoint(-0.48235294117647076, -0.45500000000000007), + SimplePoint(0.19411764705882337, 0.2699999999999999), + SimplePoint(0.5176470588235292, 0.3949999999999999) ) - val data = expected.map(dataPoint => SimplePoint(dataPoint.height, dataPoint.weight)) - val gmm: Double = GradientDescent.theta1Updated(data, 1, 1, 1) + val updatedTheta1: Double = GradientDescent.theta1Updated(normalisedData, 1, 1, 0.01) - gmm shouldEqual (-15999) + updatedTheta1 shouldEqual (1.0000905017301038) } } - "gradientDescent" should { -// "get closer to the right answer" in { -// -// def transformer(strings: Array[String]) = House(strings(0), strings(4).toDouble, strings(80).toDouble) -// val housePrices = CsvReader.asCaseClassList("house-prices-training-resources.data-test.csv", true, transformer) -// -// val resources.data = housePrices.map(dataPoint => SimplePoint(dataPoint.lotArea, dataPoint.salePrice)) -// val gmm = GradientDescent.gradientDescent(resources.data, 0, 1, 2, 1000) -// -// gmm shouldEqual (LearnedParameterSet(5, 5)) -// } - - "get closer to the right answer" in { - - def transformer(strings: Array[String]) = HeightWeight(strings(0), strings(1).toDouble, strings(2).toDouble) - val heightWeights = CsvReader.asCaseClassListFromTestResource("height-weight-test.csv", true, transformer) - - val data = heightWeights.map(dataPoint => SimplePoint(dataPoint.height, dataPoint.weight)) - val learnedParams = GradientDescent.gradientDescent(data, 0, 1, 0.001, 1000) - - learnedParams.theta0 shouldEqual (-0.009308274850941753) - learnedParams.theta1 shouldEqual (0.9889333098394358) - - } - -// "pass the coursera test case" in { -// -// //[1 5; 1 2; 1 4; 1 5],[1 6 4 2]',[0 0]',0.01,1000 -// -// def transformer(strings: Array[String]) = House(strings(0), strings(4).toDouble, strings(80).toDouble) -// val housePrices: Seq[House] = CsvReader.asCaseClassList("house-prices-training-resources.data-test.csv", true, transformer) -// -// val resources.data = List( -// SimplePoint(1, 5), -// SimplePoint(1, 2), -// SimplePoint(1, 4), -// SimplePoint(1, 5), -// ) -//// val resources.data: Seq[SimplePoint] = housePrices.map(dataPoint => SimplePoint(dataPoint.lotArea, dataPoint.salePrice)) -// val gmm = GradientDescent.gradientDescent(resources.data, 0, 1, 2, 1000) -// -// gmm shouldEqual (LearnedParameterSet(5, 5)) -// } - } } diff --git a/tex/week1.log b/tex/week1.log index 6be64ab..241e5c5 100644 --- a/tex/week1.log +++ b/tex/week1.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2019.3.20) 20 MAR 2019 18:56 +This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2019.3.20) 21 MAR 2019 11:53 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -160,27 +160,27 @@ s/spam.png> <./images/photo-search.png>] <./images/algo-abstract.png, id=13, 1098.1025pt x 339.2675pt> File: ./images/algo-abstract.png Graphic file (type png) -Package pdftex.def Info: ./images/algo-abstract.png used on input line 41. +Package pdftex.def Info: ./images/algo-abstract.png used on input line 38. 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(pdftex.def) Requested size: 390.0pt x 202.24997pt. -Overfull \hbox (17.62482pt too wide) in paragraph at lines 70--71 +Overfull \hbox (17.62482pt too wide) in paragraph at lines 63--64 [][] [] @@ -188,15 +188,15 @@ Overfull \hbox (17.62482pt too wide) in paragraph at lines 70--71 <./images/tumour-size.png, id=26, 696.6025pt x 377.41pt> File: ./images/tumour-size.png Graphic file (type png) -Package pdftex.def Info: ./images/tumour-size.png used on input line 84. +Package pdftex.def Info: ./images/tumour-size.png used on input line 77. 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zMWEUdg+VKf?4(I}r;`{aCvuxHJE_;ocs9i(Su68*@x9(IC!asv!5$2gj7QH74 zZ`Vv(qCSnekr~|Lx~Qdbj2qHVuN6Pskk0Qu`pu_DzxgANetB1rSER#t|MJ(r|MO=^ z@%e}U_0yMs{Pe?r|MI7=-+udF|N7T2|L1@F`17|vefjBcfBoSPfBWN?AO7*>>p#By z^wXd4_s?H``Qdjz{J$?>-t6yw{O2#<{ic}j{^#F*`uWGd{Og~;eE#mg{q3KB{rNNZ jkKg?Ut3E0J<)=UV<4=G8`JaFJ{N4Wt%w`W`9moOzbQE>0 diff --git a/tex/week1.tex b/tex/week1.tex index 94c1d19..7d2148b 100644 --- a/tex/week1.tex +++ b/tex/week1.tex @@ -24,13 +24,10 @@ \subsection{Introduction} \subsection{What is Machine Learning?} According to wikipedia: -Machine learning (ML) is the scientific study of algorithms and statistical models that computer systems use to -effectively perform a specific task without using explicit instructions, relying on patterns and inference instead. +Machine learning (ML) is the scientific study of algorithms and statistical models that computer systems use to effectively perform a specific task without using explicit instructions, relying on patterns and inference instead. -Machine learning algorithms can learn to do a particular task without being explicitly programmed by building a -mathematical model based on sample data, known as "training data". Then, that model can be applied to new data -not previously used to build the model. +Machine learning algorithms can learn to do a particular task without being explicitly programmed by building a mathematical model based on sample data, known as "training data". Then, that model can be applied to new data not previously used to build the model. \subsection{What is an algorithm?} @@ -43,13 +40,9 @@ \subsection{What is an algorithm?} An algorithm is a way to solve a computational problem, and a computational problem just specifies valid input and desired output. -For example, for the problem of spam filtering the input would be an email message, and the output would be a -classification (spam/not spam). The algorithm could be a set of steps. We could compose a series of regular expressions to -the message that are based on previous messages that we know have turned out to be spam. +For example, for the problem of spam filtering the input would be an email message, and the output would be a classification (spam/not spam). The algorithm could be a set of steps. We could compose a series of regular expressions to the message that are based on previous messages that we know have turned out to be spam. -We could also train a model based on a dataset of emails and classifications, to learn patterns of what spam messages -look like without explicitly writing spam identification rules. Then, we could use the model for new data without a -classification. That's the approach we're more interested in here, but both approaches are algorithms. +We could also train a model based on a dataset of emails and classifications, to learn patterns of what spam messages look like without explicitly writing spam identification rules. Then, we could use the model for new data without aclassification. That's the approach we're more interested in here, but both approaches are algorithms. \subsection{What is a machine learning algorithm?} @@ -205,11 +198,11 @@ \subsubsection{Training and Test Sets} \textbf{Hypothesis}: $h_\theta(x) = \theta_0 + \theta_1x$ (we think that a line will fit our data) -\textbf{Parameters}: $\theta_0$, $theta_1$ +\textbf{Parameters}: $\theta_0$, $\theta_1$ \textbf{Cost function}: \[J(\theta_0, \theta_1) = \frac{1}{2m} \sum^m_{i=1}(h_\theta(x^{(i)}) - y^{(i)})^2\] -\textbf{Goal}: minimise $J(\theta_0, \theta_1)$. Once we have $\theta_0$, $theta_1$, we can plug them into our hypothesis and make predictions! +\textbf{Goal}: minimise $J(\theta_0, \theta_1)$. Once we have $\theta_0$, $\theta_1$, we can plug them into our hypothesis and make predictions! \subsection{Gradient Descent} @@ -226,6 +219,7 @@ \subsection{Gradient Descent} More formally: set some initial values for $\theta_0, \theta_1$ + repeat until convergence \{ \[\theta_0 := \theta_0 - \alpha \frac{\delta}{\delta \theta_0} J(\theta_0, \theta_1)\] @@ -237,6 +231,8 @@ \subsection{Gradient Descent} $\alpha$ is the learning rate, and it represents the size of the step you take in each iteration. More on that later. $\frac{\delta}{\delta \theta_0} J(\theta_0, \theta_1) $ and $\frac{\delta}{\delta \theta_1} J(\theta_0, \theta_1) $ are partial derivatives for the cost function, and they represent the direction we need to go if we want $J(\theta_0, \theta_1)$ to decrease in the next iteration. Here is the algorithm with the partial derivatives for our cost function subbed in: +set some initial values for $\theta_0, \theta_1$ + repeat until convergence \{ \[\theta_0 := \theta_0 - \alpha \frac{1}{m} \sum^m_{i=1} (h_\theta(x^{(i)}) - y^{(i)} )\] @@ -271,8 +267,8 @@ \subsubsection{Feature scaling} For some feature $x_i$, we find the mean $\mu_i$ and the range $s_i$ (max value - min value). Then for each point $j$ in $x_i$: \[ -x_i^{(j)} \leftarrow \frac{x_i - \mu_i}{s_i} +x_i^{(j)} \leftarrow \frac{x_i^{(j)} - \mu_i^{(j)}}{s_i^{(j)}} \] -and then for each $x_i$, $-0.5 \leq x_i \leq 0.5$ +and then for each $x_i^{(j)} $, $-0.5 \leq x_i^{(j)} \leq 0.5$ \end{document} \ No newline at end of file