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diags.go
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diags.go
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package seafan
// diags.go implements model diagnostics
import (
"fmt"
"math"
"sort"
"github.com/invertedv/utilities"
grob "github.com/MetalBlueberry/go-plotly/graph_objects"
"gonum.org/v1/gonum/stat"
)
const thresh = 0.5 // threshold for declaring y[i] to be a 1
// UnNormalize un-normalizes a slice, if need be
func UnNormalize(vals []float64, ft *FType) (unNorm []float64) {
outVal := vals
if ft != nil && ft.Normalized {
for ind, v := range vals {
outVal[ind] = v*ft.FP.Scale + ft.FP.Location
}
}
return outVal
}
// Coalesce combines columns of either a one-hot feature or a softmax output. In the case of a feature,
// it returns 1 if any of the target columns is 1. In the case of a softmax output, it sums the entries.
func Coalesce(vals []float64, nCat int, trg []int, binary, logodds bool, sl Slicer) ([]float64, error) {
if nCat < 1 {
return nil, Wrapper(ErrDiags, "Coalesce: nCat must be at least 1")
}
if trg == nil {
return nil, Wrapper(ErrDiags, "Coalesce: trg cannot be nil")
}
if len(vals)%nCat != 0 {
return nil, Wrapper(ErrDiags, "Coalesce: len y not multiple of nCat")
}
for _, t := range trg {
if t > nCat-1 {
return nil, Wrapper(ErrDiags, "Coalesce: trg index out of range")
}
}
if binary && logodds {
return nil, Wrapper(ErrDiags, "coalesce cannot have both binary and logodds")
}
n := len(vals) / nCat // # of observations
coalesced := make([]float64, 0)
for row := 0; row < n; row++ {
if sl != nil && !sl(row) {
continue
}
// index into y/pred which is stored by row
ind := row * nCat
den := 1.0
// if the input is log odds, we need to reconstruct probabilities
if logodds {
den = 0.0
for col := 0; col < nCat; col++ {
den += math.Exp(vals[ind+col])
}
}
outVal := 0.0
// We may be aggregating over categories of softmax
for _, col := range trg {
switch binary {
case true:
if vals[ind+col] > thresh {
outVal = 1.0
}
case false:
switch logodds {
case true:
outVal += math.Exp(vals[ind+col]) / den
case false:
outVal += vals[ind+col]
}
}
}
coalesced = append(coalesced, outVal)
}
return coalesced, nil
}
// KS finds the KS of a softmax model that is reduced to a binary outcome.
//
// xy XY struct where x is fitted value and y is the binary observed value
// plt PlotDef plot options. If plt is nil, no plot is produced.
//
// The ks statistic is returned as are Desc descriptions of the model for the two groups.
// Returns
//
// ks KS statistic
// notTarget Desc struct of fitted values of the non-target outcomes
// target Desc struct of fitted values of target outcomes
//
// Target: html plot file and/or plot in browser.
func KS(xy *XY, plt *utilities.PlotDef) (ks float64, notTarget *Desc, target *Desc, err error) {
const nPoints = 101 // # of points for ks plot
const divisor = float64(nPoints - 1)
n := len(xy.X)
// arrays to hold probabilities with observed 0's and 1's separately
probNotTarget, probTarget := make([]float64, 0), make([]float64, 0)
for row := 0; row < n; row++ {
// append to appropriate slice
switch {
case xy.Y[row] > thresh:
probTarget = append(probTarget, xy.X[row])
default:
probNotTarget = append(probNotTarget, xy.X[row])
}
}
if len(probTarget) == 0 || len(probNotTarget) == 0 {
return 0, nil, nil, fmt.Errorf("no 0's or no 1's in KS")
}
notTarget, _ = NewDesc(nil, "not target") // fmt.Sprintf("Value not in %v", trg))
target, _ = NewDesc(nil, "target") // fmt.Sprintf("Value in %v", trg))
notTarget.Populate(probNotTarget, false, nil) // side effect is probNotTarget is sorted
target.Populate(probTarget, false, nil)
// Min & max of probabilities
lower := math.Min(notTarget.Q[0], target.Q[0])
upper := math.Max(notTarget.Q[len(notTarget.Q)-1], target.Q[len(target.Q)-1])
// p is an array that is equally spaced between lower and upper
p := make([]float64, nPoints)
// these are cumulative distributions
for k := 0; k < nPoints; k++ {
p[k] = (float64(k)/divisor)*(upper-lower) + lower
}
sort.Float64s(probNotTarget)
sort.Float64s(probTarget)
upnt := make([]float64, len(probNotTarget))
for k := 0; k < len(upnt); k++ {
upnt[k] = float64(k+1) / float64(len(upnt))
}
upt := make([]float64, len(probTarget))
for k := 0; k < len(upt); k++ {
upt[k] = float64(k+1) / float64(len(upt))
}
xypt, _ := NewXY(probTarget, upt)
xypt.X = append(xypt.X, 0, 1)
xypt.Y = append(xypt.Y, 0, 1)
xypnt, _ := NewXY(probNotTarget, upnt)
xypnt.X = append(xypnt.X, 0, 1)
xypnt.Y = append(xypnt.Y, 0, 1)
cpt, _ := xypt.Interp(p)
cpnt, _ := xypnt.Interp(p)
ks, at := 0.0, 0.0
cumeNotTarget := cpnt.Y
cumeTarget := cpt.Y
for k := 0; k < nPoints; k++ {
if d := 100.0 * math.Abs(cumeTarget[k]-cumeNotTarget[k]); d > ks {
ks = d
at = p[k]
}
}
// plot, if requested
if plt != nil {
t0 := &grob.Scatter{
Type: grob.TraceTypeScatter,
X: p,
Y: cumeNotTarget,
Name: notTarget.Name,
Mode: grob.ScatterModeLines,
Line: &grob.ScatterLine{Color: "black"},
}
t1 := &grob.Scatter{
Type: grob.TraceTypeScatter,
X: p,
Y: cumeTarget,
Mode: grob.ScatterModeLines,
Name: target.Name,
Line: &grob.ScatterLine{Color: "red"},
}
fig := &grob.Fig{Data: grob.Traces{t0, t1}}
plt.Title = fmt.Sprintf("%s<br>KS %v at %v", plt.Title, math.Round(10.0*ks)/10.0, math.Round(1000*at)/1000)
if plt.XTitle == "" {
plt.XTitle = "Fitted Values"
}
if plt.YTitle == "" {
plt.YTitle = "Cumulative Score Distribution"
}
if plt.Title == "" {
plt.Title = "KS Plot"
}
lay := &grob.Layout{}
lay.Legend = &grob.LayoutLegend{X: target.Q[0], Y: 1.0}
err = utilities.Plotter(fig, lay, plt)
}
return ks, notTarget, target, err
}
// SegPlot generates a decile plot of the fields y and fit in pipe. The segments are based on the values of the field seg.
// If seg is continuous, the segments are based on quantiles: 0-.1, .1-.25, .25-.5, .5-.75, .9-1
//
// obs observed field (y-axis) name
// fit fitted field (x-axis) name
// seg segmenting field name
// plt PlotDef plot options. If plt is nil an error is generated.
func SegPlot(pipe Pipeline, obs, fit, seg string, plt *utilities.PlotDef, minVal, maxVal *float64) error {
const minCnt = 100 // min # of obs for each point
if plt == nil {
return Wrapper(ErrDiags, "Decile: plt cannot be nil")
}
fitFtype := pipe.GetFType(fit)
if fitFtype == nil {
return Wrapper(ErrDiags, fmt.Sprintf("no such field: %s", fit))
}
obsFit := pipe.GetFType(obs)
if obsFit == nil {
return Wrapper(ErrDiags, fmt.Sprintf("no such field: %s", obs))
}
if fitFtype.Role != FRCts || obsFit.Role != FRCts {
return Wrapper(ErrDiags, "decile Inputs must be type FRCts")
}
sliceGrp, e := NewSlice(seg, minCnt, pipe, nil)
if e != nil {
return e
}
fig := &grob.Fig{}
minV, maxV := math.MaxFloat64, -math.MaxFloat64
ind, mad, rowTot := 0, float64(0), float64(0)
bias := pipe.Get(fit).Summary.DistrC.Mean - pipe.Get(obs).Summary.DistrC.Mean
for sliceGrp.Iter() {
slicer := sliceGrp.MakeSlicer()
pipeSlice, e := pipe.Slice(slicer)
if e != nil {
continue
}
// for continuous fields, there is no check in slicer
if pipeSlice.Rows() < minCnt {
continue
}
nSqrt := math.Sqrt(float64(pipeSlice.Rows()))
distr := pipeSlice.Get(obs).Summary.DistrC
obsMean, obsStd := distr.Mean, distr.Std/nSqrt
fitMean := pipeSlice.Get(fit).Summary.DistrC.Mean - bias
mad += math.Abs(fitMean - obsMean)
rowTot++
ci := []float64{obsMean - 2.0*obsStd, obsMean + 2.0*obsStd}
maxV = math.Max(maxV, ci[1])
minV = math.Min(minV, ci[0])
ind++
trCI := &grob.Scatter{
Type: grob.TraceTypeScatter,
X: []float64{fitMean, fitMean},
Y: ci,
Name: fmt.Sprintf("%d: %v", pipeSlice.Rows(), sliceGrp.Value()),
Hoverlabel: &grob.ScatterHoverlabel{Namelength: -1},
Mode: grob.ScatterModeLines,
Line: &grob.ScatterLine{Color: "black"},
}
fig.AddTraces(trCI)
tr := &grob.Scatter{
Type: grob.TraceTypeScatter,
X: []float64{fitMean},
Y: []float64{obsMean},
Name: fmt.Sprintf("%v", sliceGrp.Value()),
Hoverlabel: &grob.ScatterHoverlabel{Namelength: -1},
Mode: grob.ScatterModeMarkers,
Line: &grob.ScatterLine{Color: "green"},
}
fig.AddTraces(tr)
}
// if user has supplied graph limits, use them
if minVal != nil {
minV = *minVal
}
if maxVal != nil {
maxV = *maxVal
}
tr := &grob.Scatter{
Type: grob.TraceTypeScatter,
X: []float64{minV, maxV},
Y: []float64{minV, maxV},
Name: "ref",
Mode: grob.ScatterModeLines,
Line: &grob.ScatterLine{Color: "red"},
}
fig.AddTraces(tr)
mad /= rowTot
plt.STitle = fmt.Sprintf("MAD (unbiased fit): %0.4f Bias: %0.4f", mad, bias)
if plt.XTitle == "" {
plt.XTitle = fit
}
if plt.YTitle == "" {
plt.YTitle = obs
}
if plt.Title == "" {
plt.Title = "Decile Plot"
}
plt.Title = fmt.Sprintf("%s<br>%s", plt.Title, "Bias Corrected")
err := utilities.Plotter(fig, &grob.Layout{}, plt)
return err
}
// Decile generates a decile plot based on xy
//
// XY values to base the plot on.
// plt PlotDef plot options. If plt is nil an error is generated.
//
// The deciles are created based on the values of xy.X
func Decile(xyIn *XY, plt *utilities.PlotDef) error {
if plt == nil {
return Wrapper(ErrDiags, "Decile: plt cannot be nil")
}
// preserve input data by making a copy
xCopy := make([]float64, xyIn.Len())
yCopy := make([]float64, xyIn.Len())
copy(xCopy, xyIn.X)
copy(yCopy, xyIn.Y)
xy, e := NewXY(xCopy, yCopy)
if e != nil {
return e
}
if ex := xy.Sort(); ex != nil {
return ex
}
deciles, e := NewDesc([]float64{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9}, "fitted")
if e != nil {
return e
}
deciles.Populate(xy.X, false, nil)
ng := len(deciles.U) + 1
fDec, yDec, nDec := make([]float64, ng), make([]float64, ng), make([]int, ng)
for row := 0; row < len(xy.X); row++ {
grp := ng - 1
for g := 0; g < len(deciles.U); g++ {
if xy.X[row] < deciles.Q[g] {
grp = g
break
}
}
fDec[grp] += xy.X[row]
yDec[grp] += xy.Y[row]
nDec[grp]++
}
for g := 0; g < ng; g++ {
if nDec[g] == 0 {
return Wrapper(ErrDiags, fmt.Sprintf("Decile: decile group %d has no observations", g))
}
nFloat := float64(nDec[g])
fDec[g] /= nFloat
yDec[g] /= nFloat
}
tr := &grob.Scatter{
Type: grob.TraceTypeScatter,
X: fDec,
Y: yDec,
Name: "decile averages",
Mode: grob.ScatterModeMarkers,
Line: &grob.ScatterLine{Color: "black"},
}
fig := &grob.Fig{Data: grob.Traces{tr}}
lower, upper := make([]float64, ng), make([]float64, ng)
minVal, maxVal := math.MaxFloat64, -math.MaxFloat64
for g := 0; g < ng; g++ {
nFloat := float64(nDec[g])
w := math.Sqrt(yDec[g] * (1.0 - yDec[g]) / nFloat)
lower[g] = yDec[g] - 2.0*w
upper[g] = yDec[g] + 2.0*w
minVal = math.Min(math.Min(minVal, lower[g]), fDec[g])
maxVal = math.Max(math.Max(maxVal, upper[g]), fDec[g])
trCI := &grob.Scatter{
Type: grob.TraceTypeScatter,
X: []float64{fDec[g], fDec[g]},
Y: []float64{lower[g], upper[g]},
Name: fmt.Sprintf("CI%d", g),
Mode: grob.ScatterModeLines,
Line: &grob.ScatterLine{Color: "black"},
}
fig.AddTraces(trCI)
}
tr = &grob.Scatter{
Type: grob.TraceTypeScatter,
X: []float64{minVal, maxVal},
Y: []float64{minVal, maxVal},
Name: "ref",
Mode: grob.ScatterModeLines,
Line: &grob.ScatterLine{Color: "red"},
}
fig.AddTraces(tr)
mFit := stat.Mean(xy.X, nil)
mObs := stat.Mean(xy.Y, nil)
n := xy.Len()
plt.STitle = fmt.Sprintf("95%% CI assuming independence<br># obs: %d means: Fit %0.3f actual %0.3f", n, mFit, mObs)
if plt.XTitle == "" {
plt.XTitle = "Fitted Values"
}
if plt.YTitle == "" {
plt.YTitle = "Actual Values"
}
if plt.Title == "" {
plt.Title = "Decile Plot"
}
err := utilities.Plotter(fig, &grob.Layout{}, plt)
return err
}
// Assess returns a selection of statistics of the fit
func Assess(xy *XY, cutoff float64) (n int, precision, recall, accuracy float64, obs, fit *Desc, err error) {
correctYes := 0
correct := 0
obsTot := 0
predTot := 0
for row := 0; row < len(xy.X); row++ {
predYes := xy.X[row] > cutoff
obsYes := xy.Y[row] > 0.999
if predYes && obsYes {
correctYes++
correct++
}
if !predYes && !obsYes {
correct++
}
if obsYes {
obsTot++
}
if predYes {
predTot++
}
}
if obsTot == 0 {
return 0, 0.0, 0.0, 0.0, nil, nil, Wrapper(ErrDiags, "Decile: there are not positive outcomes")
}
if obsTot == xy.Len() {
return 0, 0.0, 0.0, 0.0, nil, nil, Wrapper(ErrDiags, "Decile: there are not negative outcomes")
}
precision = float64(correctYes) / float64(predTot) // fraction of Yes corrects to total predicted Yes
recall = float64(correctYes) / float64(obsTot) // fraction of Yes corrects to total actual Yes
accuracy = float64(correct) / float64(len(xy.X)) // fraction of corrects
n = len(xy.X)
fit, err = NewDesc(nil, "fitted values")
if err != nil {
return
}
fit.Populate(xy.X, true, nil)
obs, err = NewDesc(nil, "observed values")
if err != nil {
return
}
obs.Populate(xy.Y, true, nil)
return n, precision, recall, accuracy, obs, fit, err
}
// AddFitted addes fitted values to a Pipeline. The features can be re-normalized/re-mapped to align pipeIn with
// the model build
// pipeIn -- input Pipeline to run the model on
// nnFile -- root directory of NNModel
// target -- target columns of the model output to coalesce
// name -- name of fitted value in Pipeline
// fts -- options FTypes to use for normalizing pipeIn
func AddFitted(pipeIn Pipeline, nnFile string, target []int, name string, fts FTypes, logodds bool, obsFit *FType) error {
// operate on all data
bSize := pipeIn.BatchSize()
WithBatchSize(0)(pipeIn) // all rows
nn1, e := PredictNNwFts(nnFile, pipeIn, false, fts)
if e != nil {
return e
}
// Coalesce the output
bigFit := nn1.FitSlice()
fit := make([]float64, pipeIn.Rows())
outCols := nn1.outCols // nn1.Cols()
for row := 0; row < len(fit); row++ {
for _, col := range target {
fit[row] += bigFit[row*outCols+col]
}
if logodds {
switch {
case fit[row] < 0.0:
return Wrapper(ErrDiags, "attempt to take log odds of value <0")
case fit[row] == 0.0:
fit[row] = -10.0
case fit[row] > 0.0 && fit[row] < 1.0:
fit[row] = math.Log(fit[row] / (1.0 - fit[row]))
case fit[row] == 1.0:
fit[row] = 10.0
case fit[row] > 1.0:
return Wrapper(ErrDiags, "attempt to take log odds of value >1")
}
}
}
gData := pipeIn.GData()
fitRaw := NewRawCast(UnNormalize(fit, obsFit), nil)
if e := gData.AppendField(fitRaw, name, FRCts, pipeIn.GetKeepRaw()); e != nil {
return e
}
WithBatchSize(bSize)(pipeIn)
return nil
}
// Marginal produces a set of plots to aid in understanding the effect of a feature.
// The plot takes the model output and creates six segments based on the quantiles of the model output:
// (<.1, .1-.25, .25-.5, .5-.75, .75-.9, .9-1).
//
// For each segment, the feature being analyzed various across its range within the quartile (continuous)
// its values (discrete).
// The bottom row shows the distribution of the feature within the quartile range.
func Marginal(nnFile string, feat string, target []int, pipe Pipeline, pd *utilities.PlotDef, obsFtype *FType) error {
const (
take = 1000 // # of obs to use for graph
maxCats = 10 // max # of levels of a categorical field to show in plot
cols = 6
)
var e error
name := feat
lay := &grob.Layout{}
lay.Grid = &grob.LayoutGrid{Rows: 2, Columns: cols, Pattern: grob.LayoutGridPatternIndependent, Roworder: grob.LayoutGridRoworderTopToBottom}
fig := &grob.Fig{}
bSize := pipe.BatchSize()
defer WithBatchSize(bSize)(pipe)
WithBatchSize(pipe.Rows())(pipe)
if e = AddFitted(pipe, nnFile, target, "fitted", nil, false, obsFtype); e != nil {
return Wrapper(e, "Marginal")
}
targFt := pipe.Get(feat) // feature we're working on
if targFt == nil {
return Wrapper(ErrDiags, fmt.Sprintf("Marginal: feature %s not in model", feat))
}
slice, e := NewSlice("fitted", 0, pipe, nil)
if e != nil {
return Wrapper(e, "Marginal")
}
plotNo := 12 // used as a basis to know which plot we're working on
for slice.Iter() {
sl := slice.MakeSlicer()
newPipe, e := pipe.Slice(sl)
if e != nil {
return Wrapper(e, "Marginal")
}
newPipe.Shuffle()
n := utilities.MinInt(newPipe.Rows(), take)
WithBatchSize(n)(newPipe)
xs1 := make([]string, n)
gd := newPipe.Get(feat)
// sets the plot to work on:
xAxis, yAxis := fmt.Sprintf("x%d", plotNo), fmt.Sprintf("y%d", plotNo)
switch gd.FT.Role {
case FRCts:
x := make([]float64, n)
for ind := 0; ind < n; ind++ {
x[ind] = gd.Data.([]float64)[ind]*gd.FT.FP.Scale + gd.FT.FP.Location
}
tr := &grob.Histogram{Xaxis: xAxis, Yaxis: yAxis, X: x, Type: grob.TraceTypeHistogram}
fig.AddTraces(tr)
qs := gd.Summary.DistrC.Q
dp := (qs[cols] - qs[0]) / 5
nper := n / 4
data := gd.Data
for row := 0; row < n; row++ {
grp := 1 + utilities.MinInt(row/nper, 3)
xx := qs[0] + dp*float64(grp)
data.([]float64)[row] = xx
xs1[row] = fmt.Sprintf("%0.2f", xx*gd.FT.FP.Scale+gd.FT.FP.Location)
}
case FROneHot, FREmbed:
gdFrom := newPipe.Get(gd.FT.From)
name = gd.FT.From
keys, vals := gdFrom.Summary.DistrD.Sort(false, false)
// convert counts to rates
rate := make([]float64, len(vals))
for ind := 0; ind < len(vals); ind++ {
rate[ind] = float64(vals[ind]) / float64(gd.Summary.NRows)
}
cats := utilities.MinInt(len(keys), maxCats)
tr := &grob.Bar{Xaxis: xAxis, Yaxis: yAxis, X: keys[0:cats], Y: rate[0:cats], Type: grob.TraceTypeBar}
fig.AddTraces(tr)
nper := n / cats
data := gd.Data
for row := 0; row < n; row++ {
grp := utilities.MinInt(row/nper, cats-1)
grpKey := keys[grp]
grpVal := int(gdFrom.FT.FP.Lvl[grpKey])
for c := 0; c < cats; c++ {
data.([]float64)[row*cats+c] = 0.0
}
data.([]float64)[row*cats+grpVal] = 1.0
xs1[row] = fmt.Sprintf("%v", grpKey)
}
default:
return Wrapper(ErrDiags, fmt.Sprintf("Marginal: feature %s is discrete -- need OneHot", feat))
}
// predict on data we just created
nn1, e := PredictNN(nnFile, newPipe, false)
if e != nil {
return Wrapper(e, "Marginal")
}
nCat := nn1.OutputCols() // nn1.Cols()
fit, e := Coalesce(UnNormalize(nn1.FitSlice(), obsFtype), nCat, target, false, false, nil)
if e != nil {
return Wrapper(e, "Marginal")
}
xAxis, yAxis = fmt.Sprintf("x%d", plotNo-cols), fmt.Sprintf("y%d", plotNo-cols)
plotNo--
tr := &grob.Box{X: xs1, Y: fit, Type: grob.TraceTypeBox, Xaxis: xAxis, Yaxis: yAxis}
fig.AddTraces(tr)
if plotNo == cols {
break
}
}
pd.Title = fmt.Sprintf("Marginal Effect of %s by Quartile of Fitted Value (High to Low)<br>%s", name, pd.Title)
if e := utilities.Plotter(fig, lay, pd); e != nil {
return Wrapper(e, "Marginal")
}
return nil
}
// R2 returns the model r-square. Returns -1 if an error.
func R2(y, yhat []float64) float64 {
if len(y) != len(yhat) {
return -1
}
my := stat.Mean(y, nil)
tss := 0.0
sse := 0.0
for ind := 0; ind < len(y); ind++ {
res := y[ind] - my
tss += res * res
res = y[ind] - yhat[ind]
sse += res * res
}
if tss == 0.0 {
return -1
}
return 100.0 * (1.0 - sse/tss)
}