Golang : Markov chains to predict probability of next state example



Tags : golang trading markov-chain prediction probability matrix

Putting these two Golang codes here for my own future reference. The codes are adapted from the DataCamp's Markov Chains Python tutorial and writing the codes in Golang helps me to understand better about how Markov Chains works in predicting the next state or outcome. Useful in many situations and especially in trading. Can be used to predict the next trend of either bearish, bullish or stagnant.

If you've no idea about what these codes trying to do. Head over to DataCamp's Markov Chains Python tutorial to learn about Markov Chains first.

Here you go!

Part 1 :


 package main

 import (
 "fmt"
 "strconv"
 "strings"
 "time"

 "math/rand"

 "github.com/gonum/matrix/mat64"
 )

 // statespace
 var states = []string{"sleep", "icecream", "run"}

 // possible sequences of events
 var transitionFromSleep = []string{
 "SS",
 "SR",
 "SI",
 }

 var transitionFromRun = []string{
 "RS",
 "RR",
 "RI",
 }

 var transitionFromIceCream = []string{
 "IS",
 "IR",
 "II",
 }

 var transitionMatrix mat64.Matrix

 func main() {
 // probabilities matrix(transition matrix)
 // numbers are made up out of thin air...
 transitionMatrixString := "[0.2 0.6 0.2;0.1 0.6 0.3; 0.2 0.7 0.1]"
 transitionMatrix = matrix(transitionMatrixString)

 // print all transitionMatrix elements
 fmt.Printf("transitionMatrix :\n%v\n\n", mat64.Formatted(transitionMatrix, mat64.Prefix(""), mat64.Excerpt(0)))

 // perform simple sanity check.
 // all probabilities must sum up to 1, therefore we have 3 rows and the final
 // result must be equal to 3
 s := mat64.Sum(transitionMatrix)
 s1 := fmt.Sprintf("%0.1f", s)

 if s1 != "3.0" {
 panic("Probabilites sum up must be equal to 3, each row sum up to 1. Check your transition matrix")
 } else {
 fmt.Println("Transition matrix checked out and proceeding to next stage!")
 }

 activityForecast(2)
 }

 func matrixByRow(a mat64.Matrix, rowNumber int) []float64 {
 dst := []float64{0.0, 0.0, 0.0}
 mat64.Row(dst, rowNumber, a)
 return dst
 }

 func sampleSet(cdf []float64) int {
 // https://stackoverflow.com/questions/50507513/golang-choice-number-from-slice-array-with-given-probability

 rand.Seed(time.Now().UnixNano())
 r := rand.Float64()

 bucket := 0

 for r > cdf[bucket] {
 bucket++
 if bucket == len(cdf) {
 bucket--
 break // need this to prevent runtime error: index out of range
 }
 }
 return bucket
 }

 func activityForecast(days int) {
 // default state
 todayActivity := "sleep"
 fmt.Println("Start state : ", todayActivity)

 activityList := []string{}
 activityList = append(activityList, todayActivity)

 i := 0
 // calculate the probability of the activityList
 prob := 1.0

 for i < days {
 if todayActivity == "sleep" {
 sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 0)

 randomChoice := sampleSet(sleepNextProbabilityDistribution)
 change := transitionFromSleep[randomChoice]

 if change == "SS" {
 prob = prob * 0.2
 activityList = append(activityList, "sleep")
 } else if change == "SR" {
 prob = prob * 0.6
 todayActivity = "run"
 activityList = append(activityList, "run")
 } else {
 prob = prob * 0.2
 todayActivity = "icecream"
 activityList = append(activityList, "icecream")
 }

 } else if todayActivity == "run" {
 runNextProbabilityDistribution := matrixByRow(transitionMatrix, 1)

 randomChoice := sampleSet(runNextProbabilityDistribution)
 change := transitionFromRun[randomChoice]

 if change == "RR" {
 prob = prob * 0.5
 activityList = append(activityList, "run")
 } else if change == "RS" {
 prob = prob * 0.2
 todayActivity = "sleep"
 activityList = append(activityList, "sleep")
 } else {
 prob = prob * 0.3
 todayActivity = "icecream"
 activityList = append(activityList, "icecream")
 }

 } else {
 sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 2)

 randomChoice := sampleSet(sleepNextProbabilityDistribution)
 change := transitionFromIceCream[randomChoice]

 if change == "II" {
 prob = prob * 0.1
 activityList = append(activityList, "icecream")
 } else if change == "IS" {
 prob = prob * 0.2
 todayActivity = "sleep"
 activityList = append(activityList, "sleep")
 } else {
 prob = prob * 0.7
 todayActivity = "run"
 activityList = append(activityList, "run")
 }

 }

 i = i + 1
 }

 fmt.Println("Possible states : ", activityList)
 fmt.Println("End state after " + strconv.Itoa(days) + " days : " + todayActivity)
 fmt.Println("Probability of the possible sequence of states : ", strconv.FormatFloat(prob, 'f', 6, 64))
 }

 // from https://www.socketloop.com/tutorials/golang-emulate-numpy-way-of-creating-matrix-example

 // WARNING: this function does not perform error checking on input string
 // You probably need to modify this function to perform sanity check on stuff such as:

 // such as only 1 pair of [ ]
 // all columns and rows have number or 0
 // all rows are same size [pynum will throw "ValueError: Rows not the same size."]

 func matrix(str string) *mat64.Dense {

 // remove [ and ]
 str = strings.Replace(str, "[", "", -1)
 str = strings.Replace(str, "]", "", -1)

 // calculate total number of rows
 parts := strings.SplitN(str, ";", -1)
 rows := len(parts)

 // calculate total number of columns
 colSlice := strings.Fields(parts[0])
 columns := len(colSlice)

 // replace all ; with space
 str = strings.Replace(str, ";", " ", -1)

 // convert str to slice
 // taken from https://www.socketloop.com/tutorials/golang-convert-string-to-array-slice
 elements := strings.Fields(str)

 // populate data for the new matrix(Dense type)
 data := make([]float64, rows*columns)
 for i := range data {
 floatValue, _ := strconv.ParseFloat(elements[i], 64)
 data[i] = floatValue
 }

 M := mat64.NewDense(rows, columns, data)
 return M
 }

Sample output:

transitionMatrix :

⎡0.2 0.6 0.2⎤

⎢0.1 0.6 0.3⎥

⎣0.2 0.7 0.1⎦

Transition matrix checked out and proceeding to next stage!

Start state : sleep

Possible states : [sleep run run]

End state after 2 days : run

Probability of the possible sequence of states : 0.300000

Part 2 :


 package main

 import (
  "fmt"
  "strconv"
  "strings"
  "time"

  "math/rand"

  "github.com/gonum/matrix/mat64"
 )

 // statespace
 var states = []string{"sleep", "icecream", "run"}

 // possible sequences of events
 var transitionFromSleep = []string{
  "SS",
  "SR",
  "SI",
 }

 var transitionFromRun = []string{
  "RS",
  "RR",
  "RI",
 }

 var transitionFromIceCream = []string{
  "IS",
  "IR",
  "II",
 }

 var transitionMatrix mat64.Matrix

 func main() {
  // probabilities matrix(transition matrix)
  // numbers are made up out of thin air...
  transitionMatrixString := "[0.2 0.6 0.2;0.1 0.6 0.3; 0.2 0.7 0.1]"
  transitionMatrix = matrix(transitionMatrixString)

  // print all transitionMatrix elements
  fmt.Printf("transitionMatrix :\n%v\n\n", mat64.Formatted(transitionMatrix, mat64.Prefix(""), mat64.Excerpt(0)))

  // perform simple sanity check.
  // all probabilities must sum up to 1, therefore we have 3 rows and the final
  // result must be equal to 3
  s := mat64.Sum(transitionMatrix)
  s1 := fmt.Sprintf("%0.1f", s)

  if s1 != "3.0" {
 panic("Probabilites sum up must be equal to 3, each row sum up to 1. Check your transition matrix")
  } else {
 fmt.Println("Transition matrix checked out and proceeding to next stage!")
  }

  // to save every activityList
  activityListSlice := [][]string{}
  count := 0
  numberOfIterations := 10000

  // iterations
  for i := 1; i < numberOfIterations; i++ {
 activityListSlice = append(activityListSlice, activityForecast(2))
  }

  // check out all the 'activityList' we collected
  //fmt.Println(activityListSlice)

  // iterate through the list to get a count of all activities ending in the state : "Run"
  for _, v := range activityListSlice {
 if v[2] == "run" {
 count++

 }
  }

  // calculate the probability of starting from state: "sleep" and ending at state "run"
  inner := float64(count) / float64(numberOfIterations)
  percentage := inner * 100.00
  fmt.Printf("Probability of starting at state: 'sleep' and ending at state 'run' : %0.2f%%\n", percentage)
 }

 func matrixByRow(a mat64.Matrix, rowNumber int) []float64 {
  dst := []float64{0.0, 0.0, 0.0}
  mat64.Row(dst, rowNumber, a)
  return dst
 }

 func sampleSet(cdf []float64) int {
  // https://stackoverflow.com/questions/50507513/golang-choice-number-from-slice-array-with-given-probability

  rand.Seed(time.Now().UnixNano())
  r := rand.Float64()

  bucket := 0

  for r > cdf[bucket] {
 bucket++
 if bucket == len(cdf) {
 bucket--
 break // need this to prevent runtime error: index out of range
 }
  }
  return bucket
 }

 func activityForecast(days int) []string {
  // default state
  todayActivity := "sleep"
  activityList := []string{}
  activityList = append(activityList, todayActivity)

  i := 0
  // calculate the probability of the activityList
  prob := 1.0

  for i < days {
 if todayActivity == "sleep" {
 sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 0)

 randomChoice := sampleSet(sleepNextProbabilityDistribution)
 change := transitionFromSleep[randomChoice]

 if change == "SS" {
 prob = prob * 0.2
 activityList = append(activityList, "sleep")
 } else if change == "SR" {
 prob = prob * 0.6
 todayActivity = "run"
 activityList = append(activityList, "run")
 } else {
 prob = prob * 0.2
 todayActivity = "icecream"
 activityList = append(activityList, "icecream")
 }

 } else if todayActivity == "run" {
 runNextProbabilityDistribution := matrixByRow(transitionMatrix, 1)

 randomChoice := sampleSet(runNextProbabilityDistribution)
 change := transitionFromRun[randomChoice]

 if change == "RR" {
 prob = prob * 0.5
 activityList = append(activityList, "run")
 } else if change == "RS" {
 prob = prob * 0.2
 todayActivity = "sleep"
 activityList = append(activityList, "sleep")
 } else {
 prob = prob * 0.3
 todayActivity = "icecream"
 activityList = append(activityList, "icecream")
 }

 } else {
 sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 2)

 randomChoice := sampleSet(sleepNextProbabilityDistribution)
 change := transitionFromIceCream[randomChoice]

 if change == "II" {
 prob = prob * 0.1
 activityList = append(activityList, "icecream")
 } else if change == "IS" {
 prob = prob * 0.2
 todayActivity = "sleep"
 activityList = append(activityList, "sleep")
 } else {
 prob = prob * 0.7
 todayActivity = "run"
 activityList = append(activityList, "run")
 }

 }

 i++

  }
  return activityList
 }

 // from https://www.socketloop.com/tutorials/golang-emulate-numpy-way-of-creating-matrix-example

 // WARNING: this function does not perform error checking on input string
 // You probably need to modify this function to perform sanity check on stuff such as:

 // such as only 1 pair of [ ]
 // all columns and rows have number or 0
 // all rows are same size [pynum will throw "ValueError: Rows not the same size."]

 func matrix(str string) *mat64.Dense {

  // remove [ and ]
  str = strings.Replace(str, "[", "", -1)
  str = strings.Replace(str, "]", "", -1)

  // calculate total number of rows
  parts := strings.SplitN(str, ";", -1)
  rows := len(parts)

  // calculate total number of columns
  colSlice := strings.Fields(parts[0])
  columns := len(colSlice)

  // replace all ; with space
  str = strings.Replace(str, ";", " ", -1)

  // convert str to slice
  // taken from https://www.socketloop.com/tutorials/golang-convert-string-to-array-slice
  elements := strings.Fields(str)

  // populate data for the new matrix(Dense type)
  data := make([]float64, rows*columns)
  for i := range data {
 floatValue, _ := strconv.ParseFloat(elements[i], 64)
 data[i] = floatValue
  }

  M := mat64.NewDense(rows, columns, data)
  return M
 }

Sample output:

transitionMatrix :

⎡0.2 0.6 0.2⎤

⎢0.1 0.6 0.3⎥

⎣0.2 0.7 0.1⎦

Transition matrix checked out and proceeding to next stage!

Probability of starting at state: 'sleep' and ending at state 'run' : 47.54%

References :

https://www.socketloop.com/tutorials/golang-linear-algebra-and-matrix-calculation-example

https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.choice.html

https://stackoverflow.com/questions/50507513/golang-choice-number-from-slice-array-with-given-probability

https://www.datacamp.com/community/tutorials/markov-chains-python-tutorial

  See also : Golang : Create matrix with Gonum Matrix package example



Tags : golang trading markov-chain prediction probability matrix

By Adam Ng(黃武俊)

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