Wrapped Normal Distribution

data.go

package main

import (
	"fmt"
	"math"
	"math/rand"
	"time"
)

func main() {
	rand.Seed(time.Now().UnixNano())
	for {
		variance := rand.Float64() * math.Pi * 2
		mean := randAngle()
		x := randAngle()

		// Bound the variance to prevent HUGE values.
		if variance < 0.05 {
			variance = 0.05
		}

		fmt.Println(mean, variance, x)

		logDensity := math.Inf(-1)
		for i := -15; i < 15; i++ {
			sqDist := math.Pow(2*math.Pi*float64(i)+mean-x, 2)
			logVal := -sqDist/(2*variance) - math.Log(2*math.Pi*variance)/2

			max := math.Max(logDensity, logVal)
			expSum := math.Exp(logVal-max) + math.Exp(logDensity-max)
			logDensity = math.Log(expSum) + max
		}

		fmt.Println(logDensity)
	}
}

func randAngle() float64 {
	return rand.Float64()*math.Pi*2 - math.Pi
}

make_plot.sh

#!/bin/bash
#
# Plot (in polar coordinates) an example distribution.

MEAN=2.356
VARIANCE=0.05
PLOT_FILE=plot.jpg

OCTAVE=octave
SCRIPT_FILE=plot_example.m

trap "rm -rf $SCRIPT_FILE octave-workspace" EXIT

xs=$($OCTAVE --eval "[0:2*pi/100:2*pi]'" | tr $'\n' ' ' | cut -f 3- -d ' ')
echo 'data = [' >$SCRIPT_FILE
for x in $xs
do
  y=$(echo $MEAN $VARIANCE $x | neurocli run -net network)
  echo $x $y \; >>$SCRIPT_FILE
done
echo '];' >>$SCRIPT_FILE
echo 'set(0, "defaultlinelinewidth", 2.0); ' >>$SCRIPT_FILE
echo 'polar(data(:,1), 1+exp(data(:,2)));' >>$SCRIPT_FILE
echo "print -djpg $PLOT_FILE" >>$SCRIPT_FILE

echo "Creating $PLOT_FILE..."
octave $SCRIPT_FILE

network.txt

Input(w=1, h=1, d=3)

FC(out=64)
Tanh
FC(out=64)
Tanh
FC(out=96)
Tanh
FC(out=1)

plot.jpg

train.sh

#!/bin/bash

make_samples() {
  # Avoid "signal: broken pipe" output.
  go run data.go 2>/dev/null
}

train_cmd="neurocli train -net network -cost mse -adam default -quiet"

if [ -f network ]; then
  echo 'Using existing network.'
else
  echo 'Creating network...'
  neurocli new -in network.txt -out network
fi

echo 'Stage 1: big learning rate...'
make_samples | $train_cmd -step 0.001 -batch 10 -stopsamples 400000

echo 'Stage 2: small learning rate...'
make_samples | $train_cmd -step 0.0001 -batch 10 -stopsamples 200000

echo 'Stage 3: refinements...'
make_samples | $train_cmd -step 0.00001 -batch 1000 -stopsamples 100000