Ejemplo n.º 1
0
// MetropolisHastings generates rows(batch) samples using the Metropolis Hastings
// algorithm (http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm),
// with the given target and proposal distributions, starting at the intial location
// and storing the results in-place into samples. If src != nil, it will be used to generate random
// numbers, otherwise rand.Float64 will be used.
//
// Metropolis-Hastings is a Markov-chain Monte Carlo algorithm that generates
// samples according to the distribution specified by target by using the Markov
// chain implicitly defined by the proposal distribution. At each
// iteration, a proposal point is generated randomly from the current location.
// This proposal point is accepted with probability
//  p = min(1, (target(new) * proposal(current|new)) / (target(current) * proposal(new|current)))
// If the new location is accepted, it is stored into batch and becomes the
// new current location. If it is rejected, the current location remains and
// is stored into samples. Thus, a location is stored into batch at every iteration.
//
// The samples in Metropolis Hastings are correlated with one another through the
// Markov chain. As a result, the initial value can have a significant influence
// on the early samples, and so, typically, the first samples generated by the chain
// are ignored. This is known as "burn-in", and can be accomplished with slicing.
// The best choice for burn-in length will depend on the sampling and target
// distributions.
//
// Many choose to have a sampling "rate" where a number of samples
// are ignored in between each kept sample. This helps decorrelate
// the samples from one another, but also reduces the number of available samples.
// A sampling rate can be implemented with successive calls to MetropolisHastings.
func MetropolisHastings(batch *mat64.Dense, initial []float64, target distmv.LogProber, proposal MHProposal, src *rand.Rand) {
	f64 := rand.Float64
	if src != nil {
		f64 = src.Float64
	}
	if len(initial) == 0 {
		panic("metropolishastings: zero length initial")
	}
	r, _ := batch.Dims()
	current := make([]float64, len(initial))
	copy(current, initial)
	proposed := make([]float64, len(initial))
	currentLogProb := target.LogProb(initial)
	for i := 0; i < r; i++ {
		proposal.ConditionalRand(proposed, current)
		proposedLogProb := target.LogProb(proposed)
		probTo := proposal.ConditionalLogProb(proposed, current)
		probBack := proposal.ConditionalLogProb(current, proposed)

		accept := math.Exp(proposedLogProb + probBack - probTo - currentLogProb)
		if accept > f64() {
			copy(current, proposed)
			currentLogProb = proposedLogProb
		}
		batch.SetRow(i, current)
	}
}
Ejemplo n.º 2
0
// Sample generates rows(batch) samples using the Metropolis Hastings sample
// generation method. The initial location is NOT updated during the call to Sample.
//
// The number of columns in batch must equal len(m.Initial), otherwise Sample
// will panic.
func (m MetropolisHastingser) Sample(batch *mat64.Dense) {
	burnIn := m.BurnIn
	rate := m.Rate
	if rate == 0 {
		rate = 1
	}
	r, c := batch.Dims()
	if len(m.Initial) != c {
		panic("metropolishastings: length mismatch")
	}

	// Use the optimal size for the temporary memory to allow the fewest calls
	// to MetropolisHastings. The case where tmp shadows samples must be
	// aligned with the logic after burn-in so that tmp does not shadow samples
	// during the rate portion.
	tmp := batch
	if rate > r {
		tmp = mat64.NewDense(rate, c, nil)
	}
	rTmp, _ := tmp.Dims()

	// Perform burn-in.
	remaining := burnIn
	initial := make([]float64, c)
	copy(initial, m.Initial)
	for remaining != 0 {
		newSamp := min(rTmp, remaining)
		MetropolisHastings(tmp.View(0, 0, newSamp, c).(*mat64.Dense), initial, m.Target, m.Proposal, m.Src)
		copy(initial, tmp.RawRowView(newSamp-1))
		remaining -= newSamp
	}

	if rate == 1 {
		MetropolisHastings(batch, initial, m.Target, m.Proposal, m.Src)
		return
	}

	if rTmp <= r {
		tmp = mat64.NewDense(rate, c, nil)
	}

	// Take a single sample from the chain.
	MetropolisHastings(batch.View(0, 0, 1, c).(*mat64.Dense), initial, m.Target, m.Proposal, m.Src)

	copy(initial, batch.RawRowView(0))
	// For all of the other samples, first generate Rate samples and then actually
	// accept the last one.
	for i := 1; i < r; i++ {
		MetropolisHastings(tmp, initial, m.Target, m.Proposal, m.Src)
		v := tmp.RawRowView(rate - 1)
		batch.SetRow(i, v)
		copy(initial, v)
	}
}
Ejemplo n.º 3
0
// 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
}