grad.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Distributions\n",
    "using LightGraphs, SimpleWeightedGraphs\n",
    "using GraphPlot\n",
    "using LightGraphs: smallgraph\n",
    "using Flux\n",
    "using LinearAlgebra\n",
    "using ProximalOperators\n",
    "using Zygote: @adjoint\n",
    "using StatsBase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "edge_probability (generic function with 1 method)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1(x) = 1/(1+exp(x))\n",
    "f1prime(x) = -exp(x)/((exp(x)+1)^2)\n",
    "\n",
    "\n",
    "function edge_probability(f1, i::Int, j::Int, coordinates) \n",
    "    yi, yj = coordinates[[i,j], :]\n",
    "    return f1((norm(yi - yj))^2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "function biased_sample(n, k, p)\n",
    "    \"\"\"\n",
    "    n is the number of samples to draw\n",
    "    k is the number of catergories, here is just the number of nodes\n",
    "    p is the corresponding probability of k, everything in p sums to 1\n",
    "    \"\"\"\n",
    "    returna =[0 for b in 1:n]\n",
    "    a = 1\n",
    "    r = 1\n",
    "    #a = Vector{Int}()\n",
    "    for i in 1:k\n",
    "        q = rand(Binomial(n,p[i]/r))\n",
    "        x = fill(i,q)\n",
    "        if q != 0 && n ==1 \n",
    "            return x[1]\n",
    "        elseif q!=0 && n != 1 \n",
    "            returna[a:a+q] = x\n",
    "            a  =a +q\n",
    "        end\n",
    "        #append!(a, x)\n",
    "        n = n - q\n",
    "        r = r - p[i]\n",
    "    end\n",
    "    \n",
    "    return returna\n",
    "end\n",
    "@adjoint biased_sample(n, k, p) = biased_sample(n, k, p), del -> (del)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "likelihood (generic function with 1 method)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function likelihood(coordinates)  \n",
    "    g =  smallgraph(:karate)\n",
    "    A = adjacency_matrix(g)\n",
    "    A =  Matrix(A)\n",
    "    B = -1*(A.-1)\n",
    "    g2 = Graph(B) \n",
    "    nodes = [x for x  in vertices(g)]\n",
    "    negsource = [src(x) for x in edges(g2)]\n",
    "    negdestin = [dst(x) for x in edges(g2)]\n",
    "    weight2 = fill(1,ne(g2))\n",
    "    weight2_norm = weight2./sum(weight2)\n",
    "    num_negative_edges::Int=10\n",
    "    γ = 0.5\n",
    "    lik = 0\n",
    "\n",
    "    for ed in edges(g)\n",
    "        ei, ej = src(ed), dst(ed)\n",
    "        indi = findall(x->x==ei, nodes)[1]\n",
    "        indj = findall(x->x==ej, nodes)[1]\n",
    "        lik += log(edge_probability(f1, indi, indj, coordinates))\n",
    "        \n",
    "        \n",
    "        neg_ind = findall(x->x==ej,negdestin)\n",
    "\n",
    "        num_of_neg_ej = length(neg_ind)\n",
    "        neg_ind_weight = weight2_norm[neg_ind]\n",
    "        neg_ind_weight_norm = neg_ind_weight./(sum(neg_ind_weight)+0.000001)\n",
    "        \n",
    "        for i in 1:num_negative_edges\n",
    "            edge_ind = sample(neg_ind, Weights(neg_ind_weight_norm))\n",
    "            indii = findall(x->x==negsource[edge_ind][1], nodes)[1]\n",
    "            indjj = findall(x->x==negdestin[edge_ind][1], nodes)[1]\n",
    "            lik += γ * log(1 - edge_probability(f1, indii, indjj, coordinates))\n",
    "        end\n",
    "    \n",
    "    end\n",
    "    return -lik\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "diff_likelihood (generic function with 4 methods)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function diff_likelihood(coordinates,g,nodes, γ, weight2,num_negative_edges,negsource,negdestin)  \n",
    "    coordinates_revised = [[0.0,0.0] for x in nodes]\n",
    "    for ed in edges(g)\n",
    "        ei, ej = src(ed), dst(ed)\n",
    "        \n",
    "        indi = findall(x->x==ei, nodes)[1]\n",
    "        indj = findall(x->x==ej, nodes)[1]\n",
    "        \n",
    "        yi = coordinates[indi, :]\n",
    "        yj = coordinates[indj, :]\n",
    "        \n",
    "        x1 = diff_log_sig(yi,yj) \n",
    "        x2 = diff_log_sig(yj,yi)        \n",
    "        \n",
    "        neg_ind = findall(x->x==ej,negdestin)\n",
    "        \n",
    "        num_of_neg_ej = length(neg_ind)\n",
    "        neg_ind_weight = weight2[neg_ind]\n",
    "        neg_ind_weight_norm = neg_ind_weight./(sum(neg_ind_weight)+0.000001)\n",
    "        \n",
    "        for i in 1:num_negative_edges\n",
    "            edge_ind = sample(neg_ind, Weights(neg_ind_weight_norm))\n",
    "            \n",
    "            indii = findall(x->x==negsource[edge_ind][1], nodes)[1]\n",
    "            indjj = findall(x->x==negdestin[edge_ind][1], nodes)[1]\n",
    "            \n",
    "            yii = coordinates[indii, :]\n",
    "            yjj = coordinates[indjj, :]\n",
    "            \n",
    "            x2 = x2 .+ diff_log_sig(yj,yii)\n",
    "        end\n",
    "        \n",
    "        coordinates_revised[indi] = coordinates_revised[indi] .+ x1\n",
    "        coordinates_revised[indj] = coordinates_revised[indj] .+ x2 \n",
    "    \n",
    "    end\n",
    "    \n",
    "    coordinates_revised = [[x[1]/ne(g),x[2]/ne(g)] for x in coordinates_revised]\n",
    "    \n",
    "    return coordinates_revised\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "diff_f (generic function with 1 method)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function diff_f(x,y,neg_sample)\n",
    "    x1 = diff_log_sig(x,y) \n",
    "    x2 = diff_log_sig(y,x)\n",
    "    for sample in neg_sample\n",
    "        x2 = x2 + diff_log_sig(y,sample)\n",
    "    end\n",
    "    return [x1,x2]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "diff_log_sig (generic function with 1 method)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function diff_log_sig(x,y)\n",
    "    z = (norm(x - y))^2\n",
    "    return (f1prime(z)/f1(z))*2*(x-y) \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
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Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.5820413570978247cx, -0.8115349761364531cy), (0.13735354056939106cx, -0.2940198900303217cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.5781227039866929cx, -0.8153636797161948cy), (-0.05604938054836464cx, -0.24431178732996373cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.5817288219682605cx, -0.8267627706016659cy), (-0.9719349378798151cx, 0.9675872311841798cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.5782786168426642cx, -0.8301062562384217cy), (-0.056395165956855994cx, -0.2446912009052931cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.4968309620102168cx, -0.6448891910935602cy), (-0.9711438039934682cx, 0.9682895088945273cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.49140835677177797cx, -0.6508470303098498cy), (-0.053631631957666535cx, -0.24137456961541176cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.081097167489459cx, -0.22930575509253587cy), (-0.9716860264632087cx, 0.967804438245691cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(0.06765045536250544cx, -0.2517915059830054cy), (-0.04614974753889219cx, -0.22533172859006806cy)]), Compose.LinePrimitive{Tuple{Measures.Measure,Measures.Measure}}(Tuple{Measures.Measure,Measures.Measure}[(-0.974268475726742cx, 0.9657053363816995cy), (-0.11364195747589516cx, -0.1813272541079282cy)])], Symbol(\"\"))]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.5144957554275265mm)]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.8274509803921568,0.8274509803921568,0.8274509803921568,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}},Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.5144957554275265mm)]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.8274509803921568,0.8274509803921568,0.8274509803921568,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}},Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([]), List([Compose.Property{Compose.FontSizePrimitive}(Compose.FontSizePrimitive[Compose.FontSizePrimitive(4.0mm)]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}},Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}}(Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}[Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.2974989897999194cx, -0.7772449740747198cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.2695093110182383cx, -0.8192415772470569cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.33990001208951526cx, -0.7532443675180053cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.11791941034735798cx, -0.7091734045211355cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.23222819369952408cx, -0.7926961705176067cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.2315139529710477cx, -0.5546604881892906cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.5533299532943934cx, -0.6726872802444586cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((-0.2688539751034821cx, -0.756368889018564cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((1.0cx, -0.6733292727707192cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.3054133480198358cx, -0.7223900062187055cy), 0.017149858514250882w)  …  Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.19923166303742557cx, -0.7453381501534355cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.6711230735353155cx, -1.0cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.2336743500404055cx, -0.7127971823029025cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.9783203299384478cx, -0.58838785225548cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.6099837566409654cx, -0.8440535493199299cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.6097938840884454cx, -0.8591755394174861cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.5256871580167486cx, -0.676599682199033cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((0.10941114102625038cx, -0.26150131684684486cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((-1.0cx, 1.0cy), 0.017149858514250882w), Compose.CirclePrimitive{Tuple{Measures.Measure,Measures.Measure},Measures.Measure}((-0.08791043320263714cx, -0.21562191772622863cy), 0.017149858514250882w)], Symbol(\"\"))]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.0mm)]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(0.25098039215686274,0.8784313725490196,0.8156862745098039,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}},Tuple{Measures.Length{:w,Float64},Measures.Length{:h,Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([]), List([Compose.Property{Compose.FontSizePrimitive}(Compose.FontSizePrimitive[Compose.FontSizePrimitive(4.0mm)]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g =  smallgraph(:karate) \n",
    "\n",
    "A = adjacency_matrix(g)\n",
    "A =  Matrix(A)\n",
    "B = -1*(A.-1)\n",
    "g2 = Graph(B) \n",
    "nodes = [x for x  in vertices(g)]\n",
    "negsource = [src(x) for x in edges(g2)]\n",
    "negdestin = [dst(x) for x in edges(g2)]\n",
    "weight2 = fill(1,ne(g2))\n",
    "weight2_norm = weight2./sum(weight2)\n",
    "num_negative_edges = 10\n",
    "Y = rand(nv(g), 2) # I think julia is faster columnwise. Not sure\n",
    "γ = 0.5\n",
    "revised_Y = diff_likelihood(Y,g,nodes, γ, weight2,num_negative_edges,negsource,negdestin)  \n",
    "\n",
    "am = Matrix(adjacency_matrix(g))\n",
    "loc_x = [x[1] for x in revised_Y]\n",
    "loc_y = [x[2] for x in revised_Y]\n",
    "gplot(g,loc_x,loc_y)\n",
    "\n",
    "\n",
    "#likelihood(Y)"
   ]
  }
 ],
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