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// Copyright ©2016 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package samplemv
import (
"errors"
"math"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/mat"
"gonum.org/v1/gonum/stat/distmv"
)
const errLengthMismatch = "samplemv: slice length mismatch"
var (
_ Sampler = LatinHypercube{}
_ Sampler = (*Rejection)(nil)
_ Sampler = IID{}
_ WeightedSampler = SampleUniformWeighted{}
_ WeightedSampler = Importance{}
)
func min(a, b int) int {
if a < b {
return a
}
return b
}
// Sampler generates a batch of samples according to the rule specified by the
// implementing type. The number of samples generated is equal to rows(batch),
// and the samples are stored in-place into the input.
type Sampler interface {
Sample(batch *mat.Dense)
}
// WeightedSampler generates a batch of samples and their relative weights
// according to the rule specified by the implementing type. The number of samples
// generated is equal to rows(batch), and the samples and weights
// are stored in-place into the inputs. The length of weights must equal
// rows(batch), otherwise SampleWeighted will panic.
type WeightedSampler interface {
SampleWeighted(batch *mat.Dense, weights []float64)
}
// SampleUniformWeighted wraps a Sampler type to create a WeightedSampler where all
// weights are equal.
type SampleUniformWeighted struct {
Sampler
}
// SampleWeighted generates rows(batch) samples from the embedded Sampler type
// and sets all of the weights equal to 1. If rows(batch) and len(weights)
// of weights are not equal, SampleWeighted will panic.
func (w SampleUniformWeighted) SampleWeighted(batch *mat.Dense, weights []float64) {
r, _ := batch.Dims()
if r != len(weights) {
panic(errLengthMismatch)
}
w.Sample(batch)
for i := range weights {
weights[i] = 1
}
}
// LatinHypercube is a type for sampling 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.NewUnitUniform function can be used
// for easy sampling from the unit hypercube.
type LatinHypercube struct {
Q distmv.Quantiler
Src rand.Source
}
// Sample generates rows(batch) samples using the LatinHypercube generation
// procedure.
func (l LatinHypercube) Sample(batch *mat.Dense) {
latinHypercube(batch, l.Q, l.Src)
}
func latinHypercube(batch *mat.Dense, q distmv.Quantiler, src rand.Source) {
r, c := batch.Dims()
var f64 func() float64
var perm func(int) []int
if src != nil {
r := rand.New(src)
f64 = r.Float64
perm = r.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++ {
v := f64()/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)
}
}
// Importance is a type for performing importance sampling using the given
// Target and Proposal distributions.
//
// Importance sampling is a variance reduction technique where samples are
// generated from a proposal distribution, q(x), instead of the target distribution
// p(x). This allows relatively unlikely samples in p(x) to be generated more frequently.
//
// The importance sampling weight at x is given by p(x)/q(x). To reduce variance,
// a good proposal distribution will bound this sampling weight. This implies the
// support of q(x) should be at least as broad as p(x), and q(x) should be "fatter tailed"
// than p(x).
type Importance struct {
Target distmv.LogProber
Proposal distmv.RandLogProber
}
// SampleWeighted generates rows(batch) samples using the Importance sampling
// generation procedure.
//
// The length of weights must equal the length of batch, otherwise Importance will panic.
func (l Importance) SampleWeighted(batch *mat.Dense, weights []float64) {
importance(batch, weights, l.Target, l.Proposal)
}
func importance(batch *mat.Dense, weights []float64, target distmv.LogProber, proposal distmv.RandLogProber) {
r, _ := batch.Dims()
if r != len(weights) {
panic(errLengthMismatch)
}
for i := 0; i < r; i++ {
v := batch.RawRowView(i)
proposal.Rand(v)
weights[i] = math.Exp(target.LogProb(v) - proposal.LogProb(v))
}
}
// ErrRejection is returned when the constant in Rejection is not sufficiently high.
var ErrRejection = errors.New("rejection: acceptance ratio above 1")
// Rejection is a type for sampling using the rejection sampling algorithm.
//
// Rejection sampling generates points from the target distribution by using
// the proposal distribution. At each step of the algorithm, the proposed 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.
//
// The number of proposed locations during sampling can be found with a call to
// Proposed. If there was an error during sampling, all elements of samples are
// set to NaN and the error can be accesssed with the Err method. If src != nil,
// it will be used to generate random numbers, otherwise rand.Float64 will be used.
//
// 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.
type Rejection struct {
C float64
Target distmv.LogProber
Proposal distmv.RandLogProber
Src rand.Source
err error
proposed int
}
// Err returns nil if the most recent call to sample was successful, and returns
// ErrRejection if it was not.
func (r *Rejection) Err() error {
return r.err
}
// Proposed returns the number of samples proposed during the most recent call to
// Sample.
func (r *Rejection) Proposed() int {
return r.proposed
}
// Sample generates rows(batch) using the Rejection sampling generation procedure.
// Rejection sampling may fail if the constant is insufficiently high, as described
// in the type comment for Rejection. If the generation fails, the samples
// are set to math.NaN(), and a call to Err will return a non-nil value.
func (r *Rejection) Sample(batch *mat.Dense) {
r.err = nil
r.proposed = 0
proposed, ok := rejection(batch, r.Target, r.Proposal, r.C, r.Src)
if !ok {
r.err = ErrRejection
}
r.proposed = proposed
}
func rejection(batch *mat.Dense, target distmv.LogProber, proposal distmv.RandLogProber, c float64, src rand.Source) (nProposed int, ok bool) {
if c < 1 {
panic("rejection: acceptance constant must be greater than 1")
}
f64 := rand.Float64
if src != nil {
f64 = rand.New(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
}
// IID generates a set of independently and identically distributed samples from
// the input distribution.
type IID struct {
Dist distmv.Rander
}
// Sample generates a set of identically and independently distributed samples.
func (iid IID) Sample(batch *mat.Dense) {
r, _ := batch.Dims()
for i := 0; i < r; i++ {
iid.Dist.Rand(batch.RawRowView(i))
}
}
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