func (fm *FeatureMatrix) Mat64(header, transpose bool) *mat64.Dense {
var (
idx int
iter fmIt
dense *mat64.Dense
)
ncol := len(fm.Data)
nrow := len(fm.CaseLabels)
if !transpose {
iter = rowIter(fm, header)
dense = mat64.NewDense(nrow, ncol, nil)
} else {
iter = colIter(fm, header)
dense = mat64.NewDense(ncol, nrow+1, nil)
}
for row, ok := iter(); ok; idx++ {
for j, val := range row {
flt, _ := strconv.ParseFloat(val, 64)
dense.Set(idx, j, flt)
}
row, ok = iter()
}
return dense
}
// LatinHypercube generates rows(batch) samples using Latin hypercube sampling
// from the given distribution. If src is not nil, it will be used to generate
// random numbers, otherwise rand.Float64 will be used.
//
// Latin hypercube sampling divides the cumulative distribution function into equally
// spaced bins and guarantees that one sample is generated per bin. Within each bin,
// the location is randomly sampled. The distmv.UnitNormal variable can be used
// for easy generation from the unit interval.
func LatinHypercube(batch *mat64.Dense, q distmv.Quantiler, src *rand.Rand) {
r, c := batch.Dims()
var f64 func() float64
var perm func(int) []int
if src != nil {
f64 = src.Float64
perm = src.Perm
} else {
f64 = rand.Float64
perm = rand.Perm
}
r64 := float64(r)
for i := 0; i < c; i++ {
p := perm(r)
for j := 0; j < r; j++ {
var v float64
v = f64()
v = v/r64 + float64(j)/r64
batch.Set(p[j], i, v)
}
}
p := make([]float64, c)
for i := 0; i < r; i++ {
copy(p, batch.RawRowView(i))
q.Quantile(batch.RawRowView(i), p)
}
}
// Generate generates a list of n random features given an input dimension d
func (iso IsoSqExp) Generate(n int, dim int, features *mat64.Dense) {
scale := math.Exp(iso.LogScale)
for i := 0; i < n; i++ {
for j := 0; j < dim; j++ {
features.Set(i, j, rand.NormFloat64()*scale)
}
}
}
// Add adds a new point to the gaussian process
func (gp *Trainer) Add(newInput []float64, newOutput []float64) {
gp.nData++
// See if we need to allocate new memory
var inputAtCap bool
if len(gp.inputData) == cap(gp.inputData) {
inputAtCap = true
}
/*
var outputAtCap bool
if len(gp.outputData) == cap(gp.outputData) {
outputAtCap = true
}
*/
gp.inputData = append(gp.inputData, newInput)
gp.outputData = append(gp.outputData, newOutput)
// If we had to allocate memory, allocate new memory for the kernel matrix
if gp.Implicit {
// If it's implicit, just need to update matrix size, because the kernel
// is computed on the fly
//gp.kernelMat =
panic("not coded")
}
var newKernelMatrix *mat64.Dense
if inputAtCap {
oldKernelMatrix := gp.kernelMatrix
// If we had to allocate new memory for the inputs, then need to expand
// the size of the matrix as well
newKernelData := make([]float64, cap(gp.inputData)*cap(gp.inputData))
panic("Need to use raw matrix")
//newKernelMatrix = mat64.NewDense(gp.nData, gp.nData, newKernelData)
// Copy the old kernel data into the new one. View and newKernelMatrix share
// the same underlying array
view := &mat64.Dense{}
view.View(newKernelMatrix, 0, 0, gp.nData-1, gp.nData-1)
view.Copy(oldKernelMatrix)
gp.kernelData = newKernelData
} else {
// We aren't at capacity, so just need to increase the size
newKernelMatrix = mat64.NewDense(nData, nData, gp.kernelData)
}
// Set the new values of the kernel matrix
for i := 0; i < nData; i++ {
oldInput := gp.inputData[i*gp.inputDim : (i+1)*gp.inputDim]
ker := gp.Kernel(oldData, newInput)
newKernelMatrix.Set(i, gp.nData, ker)
newKernelMatrix.Set(gp.nData, i, ker)
}
gp.kernelMatrix = newKernelMatrix
}
func (SquaredDistance) LossDerivHess(prediction, truth, derivative []float64, hessian *mat64.Dense) (loss float64) {
if len(prediction) != len(truth) || len(prediction) != len(derivative) {
panic(lenMismatch)
}
n, m := hessian.Dims()
if len(prediction) != n {
panic(lenMismatch)
}
if len(prediction) != m {
panic(lenMismatch)
}
for i := range prediction {
diff := prediction[i] - truth[i]
derivative[i] = diff
loss += diff * diff
}
nFloat := float64(n)
loss /= nFloat
corr := 2 / nFloat
for i := range derivative {
derivative[i] *= corr
}
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if i == j {
hessian.Set(i, j, corr)
} else {
hessian.Set(i, j, 0)
}
}
}
return loss
}
// Rejection generates rows(batch) samples using the rejection sampling algorithm and
// stores them in place into samples.
// Sampling continues until batch is filled. Rejection returns the total number of proposed
// locations and a boolean indicating if the rejection sampling assumption is
// violated (see details below). If the returned boolean is false, all elements
// of samples are set to NaN. If src != nil, it will be used to generate random
// numbers, otherwise rand.Float64 will be used.
//
// Rejection sampling generates points from the target distribution by using
// the proposal distribution. At each step of the algorithm, the proposaed point
// is accepted with probability
// p = target(x) / (proposal(x) * c)
// where target(x) is the probability of the point according to the target distribution
// and proposal(x) is the probability according to the proposal distribution.
// The constant c must be chosen such that target(x) < proposal(x) * c for all x.
// The expected number of proposed samples is len(samples) * c.
//
// Target may return the true (log of) the probablity of the location, or it may return
// a value that is proportional to the probability (logprob + constant). This is
// useful for cases where the probability distribution is only known up to a normalization
// constant.
func Rejection(batch *mat64.Dense, target distmv.LogProber, proposal distmv.RandLogProber, c float64, src *rand.Rand) (nProposed int, ok bool) {
if c < 1 {
panic("rejection: acceptance constant must be greater than 1")
}
f64 := rand.Float64
if src != nil {
f64 = src.Float64
}
r, dim := batch.Dims()
v := make([]float64, dim)
var idx int
for {
nProposed++
proposal.Rand(v)
qx := proposal.LogProb(v)
px := target.LogProb(v)
accept := math.Exp(px-qx) / c
if accept > 1 {
// Invalidate the whole result and return a failure.
for i := 0; i < r; i++ {
for j := 0; j < dim; j++ {
batch.Set(i, j, math.NaN())
}
}
return nProposed, false
}
if accept > f64() {
batch.SetRow(idx, v)
idx++
if idx == r {
break
}
}
}
return nProposed, true
}
