/
irls.go
248 lines (202 loc) · 4.61 KB
/
irls.go
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package glm
import (
"fmt"
"math"
"strings"
"sync"
"github.com/kshedden/statmodel/statmodel"
"gonum.org/v1/gonum/mat"
)
func (glm *GLM) fitIRLS(start []float64, maxiter int) []float64 {
// TODO make this configurable
dtol := 1e-8
linpred := glm.getNslice()
mn := glm.getNslice()
va := glm.getNslice()
lderiv := glm.getNslice()
irlsw := glm.getNslice()
adjy := glm.getNslice()
var nparam mat.VecDense
nvar := glm.NumParams()
xty := make([]float64, nvar)
xtx := make([]float64, nvar*nvar)
var params []float64
if start == nil {
params = make([]float64, nvar)
} else {
params = start
}
var dev []float64
xdat := make([][]statmodel.Dtype, len(glm.xpos))
for j, k := range glm.xpos {
xdat[j] = glm.data[k]
}
// IRLS iterations
for iter := 0; iter < maxiter; iter++ {
zero(xtx)
zero(xty)
var devi float64
// Loop over data chunks
var wgt, off []statmodel.Dtype
yda := glm.data[glm.ypos]
if glm.weightpos != -1 {
wgt = glm.data[glm.weightpos]
}
if glm.offsetpos != -1 {
off = glm.data[glm.offsetpos]
}
zero(linpred)
for j := range glm.xpos {
for i := range linpred {
linpred[i] += float64(xdat[j][i]) * params[j]
}
}
if off != nil {
for i := range linpred {
linpred[i] += float64(off[i])
}
}
if iter == 0 {
glm.startingMu(yda, mn)
} else {
glm.link.InvLink(linpred, mn)
}
glm.link.Deriv(mn, lderiv)
glm.vari.Var(mn, va)
devi += glm.fam.Deviance(yda, mn, wgt, 1)
// Create weights for WLS
if wgt != nil {
for i := range yda {
irlsw[i] = float64(wgt[i]) / (lderiv[i] * lderiv[i] * va[i])
}
} else {
for i := range yda {
irlsw[i] = 1 / (lderiv[i] * lderiv[i] * va[i])
}
}
// Create an adjusted response for WLS
if off == nil {
for i := range yda {
adjy[i] = linpred[i] + lderiv[i]*(float64(yda[i])-mn[i])
}
} else {
for i := range yda {
adjy[i] = linpred[i] + lderiv[i]*(float64(yda[i])-mn[i]) - float64(off[i])
}
}
// Update the weighted moment matrices. For large data sets, this is by far the
// most expensive step.
glm.irlsXprod(xdat, adjy, irlsw, xty, xtx)
// Fill in the unfilled triangle of xtx
for j1 := range glm.xpos {
for j2 := j1 + 1; j2 < nvar; j2++ {
xtx[j1*nvar+j2] = xtx[j2*nvar+j1]
}
}
// Update the parameters
xtxm := mat.NewDense(nvar, nvar, xtx)
xtyv := mat.NewVecDense(nvar, xty)
err := nparam.SolveVec(xtxm, xtyv)
if err != nil {
for j := 0; j < nvar; j++ {
fmt.Printf("%8d %12.4f %12.4f\n", j, xty[j], xtx[j*nvar+j])
}
panic(err)
}
params = nparam.RawVector().Data
// Check convergence
dev = append(dev, devi)
if len(dev) > 3 && math.Abs(dev[len(dev)-1]-dev[len(dev)-2]) < dtol {
break
}
if glm.log != nil {
msg := fmt.Sprintf("Iteration %d: deviance=%.10f\n", iter+1, devi)
glm.log.Print(msg)
}
}
if glm.log != nil {
glm.log.Print("IRLS converged\n")
}
glm.putNslice(linpred)
glm.putNslice(mn)
glm.putNslice(va)
glm.putNslice(lderiv)
glm.putNslice(irlsw)
glm.putNslice(adjy)
return params
}
func (glm *GLM) irlsXprod(xdat [][]statmodel.Dtype, adjy, irlsw, xty, xtx []float64) {
if len(adjy) >= glm.concurrentIRLS {
glm.irlsXprodConcurrent(xdat, adjy, irlsw, xty, xtx)
return
}
nvar := len(xdat)
for j1 := range glm.xpos {
// Update x' w^-1 yadj
xda := xdat[j1]
var u float64
for i := range adjy {
u += adjy[i] * float64(xda[i]) * irlsw[i]
}
xty[j1] += u
// Update x' w^-1 x
for j2 := 0; j2 <= j1; j2++ {
xdb := xdat[j2]
var u float64
for i := range xda {
u += float64(xda[i]*xdb[i]) * irlsw[i]
}
xtx[j1*nvar+j2] += u
}
}
}
// irlsXprodConcurrent is a concurrent version of irlsXprod
func (glm *GLM) irlsXprodConcurrent(xdat [][]statmodel.Dtype, adjy, irlsw, xty, xtx []float64) {
nvar := len(xdat)
var wg sync.WaitGroup
for j1 := range glm.xpos {
// Update x' w^-1 yadj
xda := xdat[j1]
wg.Add(1)
go func(j1 int) {
var u float64
for i := range adjy {
u += adjy[i] * float64(xda[i]) * irlsw[i]
}
xty[j1] += u
wg.Done()
}(j1)
// Update x' w^-1 x
for j2 := 0; j2 <= j1; j2++ {
xdb := xdat[j2]
wg.Add(1)
go func(j1, j2 int) {
var u float64
for i := range xda {
u += float64(xda[i]*xdb[i]) * irlsw[i]
}
xtx[j1*nvar+j2] += u
wg.Done()
}(j1, j2)
}
}
wg.Wait()
}
func (glm *GLM) startingMu(y []statmodel.Dtype, mn []float64) {
var q float64
name := strings.ToLower(glm.fam.Name)
if name == "binomial" {
q = 0.5
} else {
for i := range y {
q += float64(y[i])
}
q /= float64(len(y))
}
for i := range mn {
mn[i] = (float64(y[i]) + q) / 2
if mn[i] < 0.1 {
mn[i] = 0.1
}
}
}