7
मैं गिब्स नमूनाकरण का उपयोग कर बेयसियन अनुमान के लिए एक पैकेज लिख रहा हूं। चूंकि ये विधियां आम तौर पर कम्प्यूटेशनल रूप से महंगी होती हैं, इसलिए मैं अपने कोड के प्रदर्शन के बारे में बहुत चिंतित हूं। वास्तव में, मैं पाइथन से जूलिया तक जाने का कारण था।जूलिया मेमोरी आवंटन और कोड कवरेज परिणाम का विश्लेषण कैसे करें
Dirichlet Process Model लागू करने के बाद मैंने Coverage.jl और --track-allocation=user कमांडलाइन विकल्प का उपयोग करके कोड का विश्लेषण किया। ,
- #=
- DPM
-
- Dirichlet Process Mixture Models
-
- 25/08/2015
- Adham Beyki, [email protected]
-
- =#
-
- type DPM{T}
- bayesian_component::T
- K::Int64
- aa::Float64
- a1::Float64
- a2::Float64
- K_hist::Vector{Int64}
- K_zz_dict::Dict{Int64, Vector{Int64}}
-
- DPM{T}(c::T, K::Int64, aa::Float64, a1::Float64, a2::Float64) = new(c, K, aa, a1, a2,
- Int64[], (Int64 => Vector{Int64})[])
- end
0 DPM{T}(c::T, K::Int64, aa::Real, a1::Real, a2::Real) = DPM{typeof(c)}(c, K, convert(Float64, aa),
- convert(Float64, a1), convert(Float64, a2))
-
- function Base.show(io::IO, dpm::DPM)
- println(io, "Dirichlet Mixture Model with $(dpm.K) $(typeof(dpm.bayesian_component)) components")
- end
-
- function initialize_gibbs_sampler!(dpm::DPM, zz::Vector{Int64})
- # populates the cluster labels randomly
0 zz[:] = rand(1:dpm.K, length(zz))
- end
-
- function DPM_sample_hyperparam(aa::Float64, a1::Float64, a2::Float64, K::Int64, NN::Int64, iters::Int64)
-
- # resampling concentration parameter based on Escobar and West 1995
0 for n = 1:iters
0 eta = rand(Distributions.Beta(aa+1, NN))
0 rr = (a1+K-1)/(NN*(a2-log(NN)))
0 pi_eta = rr/(1+rr)
-
0 if rand() < pi_eta
0 aa = rand(Distributions.Gamma(a1+K, 1/(a2-log(eta))))
- else
0 aa = rand(Distributions.Gamma(a1+K-1, 1/(a2-log(eta))))
- end
- end
0 aa
- end
-
- function DPM_sample_pp{T1, T2}(
- bayesian_components::Vector{T1},
- xx::T2,
- nn::Vector{Float64},
- pp::Vector{Float64},
- aa::Float64)
-
0 K = length(nn)
0 @inbounds for kk = 1:K
0 pp[kk] = log(nn[kk]) + logpredictive(bayesian_components[kk], xx)
- end
0 pp[K+1] = log(aa) + logpredictive(bayesian_components[K+1], xx)
0 normalize_pp!(pp, K+1)
0 return sample(pp[1:K+1])
- end
-
-
- function collapsed_gibbs_sampler!{T1, T2}(
- dpm::DPM{T1},
- xx::Vector{T2},
- zz::Vector{Int64},
- n_burnins::Int64, n_lags::Int64, n_samples::Int64, n_internals::Int64; max_clusters::Int64=100)
-
-
191688 NN = length(xx) # number of data points
96 nn = zeros(Float64, dpm.K) # count array
0 n_iterations = n_burnins + (n_samples)*(n_lags+1)
384 bayesian_components = [deepcopy(dpm.bayesian_component) for k = 1:dpm.K+1]
2864 dpm.K_hist = zeros(Int64, n_iterations)
176 pp = zeros(Float64, max_clusters)
-
48 tic()
0 for ii = 1:NN
0 kk = zz[ii]
0 additem(bayesian_components[kk], xx[ii])
0 nn[kk] += 1
- end
0 dpm.K_hist[1] = dpm.K
0 elapsed_time = toq()
-
0 for iteration = 1:n_iterations
-
5329296 println("iteration: $iteration, KK: $(dpm.K), KK mode: $(indmax(hist(dpm.K_hist,
- 0.5:maximum(dpm.K_hist)+0.5)[2])), elapsed time: $elapsed_time")
-
16800 tic()
28000000 @inbounds for ii = 1:NN
0 kk = zz[ii]
0 nn[kk] -= 1
0 delitem(bayesian_components[kk], xx[ii])
-
- # remove the cluster if empty
0 if nn[kk] == 0
161880 println("\tcomponent $kk has become inactive")
0 splice!(nn, kk)
0 splice!(bayesian_components, kk)
0 dpm.K -= 1
-
- # shifting the labels one cluster back
69032 idx = find(x -> x>kk, zz)
42944 zz[idx] -= 1
- end
-
0 kk = DPM_sample_pp(bayesian_components, xx[ii], nn, pp, dpm.aa)
-
0 if kk == dpm.K+1
158976 println("\tcomponent $kk activated.")
14144 push!(bayesian_components, deepcopy(dpm.bayesian_component))
4872 push!(nn, 0)
0 dpm.K += 1
- end
-
0 zz[ii] = kk
0 nn[kk] += 1
0 additem(bayesian_components[kk], xx[ii])
- end
-
0 dpm.aa = DPM_sample_hyperparam(dpm.aa, dpm.a1, dpm.a2, dpm.K, NN, n_internals)
0 dpm.K_hist[iteration] = dpm.K
14140000 dpm.K_zz_dict[dpm.K] = deepcopy(zz)
0 elapsed_time = toq()
- end
- end
-
- function truncated_gibbs_sampler{T1, T2}(dpm::DPM{T1}, xx::Vector{T2}, zz::Vector{Int64},
- n_burnins::Int64, n_lags::Int64, n_samples::Int64, n_internals::Int64, K_truncation::Int64)
-
- NN = length(xx) # number of data points
- nn = zeros(Int64, K_truncation) # count array
- bayesian_components = [deepcopy(dpm.bayesian_component) for k = 1:K_truncation]
- n_iterations = n_burnins + (n_samples)*(n_lags+1)
- dpm.K_hist = zeros(Int64, n_iterations)
- states = (ASCIIString => Int64)[]
- n_states = 0
-
- tic()
- for ii = 1:NN
- kk = zz[ii]
- additem(bayesian_components[kk], xx[ii])
- nn[kk] += 1
- end
- dpm.K_hist[1] = dpm.K
-
- # constructing the sticks
- beta_VV = rand(Distributions.Beta(1.0, dpm.aa), K_truncation)
- beta_VV[end] = 1.0
- π = ones(Float64, K_truncation)
- π[2:end] = 1 - beta_VV[1:K_truncation-1]
- π = log(beta_VV) + log(cumprod(π))
-
- elapsed_time = toq()
-
- for iteration = 1:n_iterations
-
- println("iteration: $iteration, # active components: $(length(findn(nn)[1])), mode: $(indmax(hist(dpm.K_hist,
- 0.5:maximum(dpm.K_hist)+0.5)[2])), elapsed time: $elapsed_time \n", nn)
-
- tic()
- for ii = 1:NN
- kk = zz[ii]
- nn[kk] -= 1
- delitem(bayesian_components[kk], xx[ii])
-
- # resampling label
- pp = zeros(Float64, K_truncation)
- for kk = 1:K_truncation
- pp[kk] = π[kk] + logpredictive(bayesian_components[kk], xx[ii])
- end
- pp = exp(pp - maximum(pp))
- pp /= sum(pp)
-
- # sample from pp
- kk = sampleindex(pp)
- zz[ii] = kk
- nn[kk] += 1
- additem(bayesian_components[kk], xx[ii])
-
- for kk = 1:K_truncation-1
- gamma1 = 1 + nn[kk]
- gamma2 = dpm.aa + sum(nn[kk+1:end])
- beta_VV[kk] = rand(Distributions.Beta(gamma1, gamma2))
- end
- beta_VV[end] = 1.0
- π = ones(Float64, K_truncation)
- π[2:end] = 1 - beta_VV[1:K_truncation-1]
- π = log(beta_VV) + log(cumprod(π))
-
- # resampling concentration parameter based on Escobar and West 1995
- for internal_iters = 1:n_internals
- eta = rand(Distributions.Beta(dpm.aa+1, NN))
- rr = (dpm.a1+dpm.K-1)/(NN*(dpm.a2-log(NN)))
- pi_eta = rr/(1+rr)
-
- if rand() < pi_eta
- dpm.aa = rand(Distributions.Gamma(dpm.a1+dpm.K, 1/(dpm.a2-log(eta))))
- else
- dpm.aa = rand(Distributions.Gamma(dpm.a1+dpm.K-1, 1/(dpm.a2-log(eta))))
- end
- end
- end
-
- nn_string = nn2string(nn)
- if !haskey(states, nn_string)
- n_states += 1
- states[nn_string] = n_states
- end
- dpm.K_hist[iteration] = states[nn_string]
- dpm.K_zz_dict[states[nn_string]] = deepcopy(zz)
- elapsed_time = toq()
- end
- return states
- end
-
-
- function posterior{T1, T2}(dpm::DPM{T1}, xx::Vector{T2}, K::Int64, K_truncation::Int64=0)
0 n_components = 0
0 if K_truncation == 0
0 n_components = K
- else
0 n_components = K_truncation
- end
-
0 bayesian_components = [deepcopy(dpm.bayesian_component) for kk=1:n_components]
0 zz = dpm.K_zz_dict[K]
-
0 NN = length(xx)
0 nn = zeros(Int64, n_components)
-
0 for ii = 1:NN
0 kk = zz[ii]
0 additem(bayesian_components[kk], xx[ii])
0 nn[kk] += 1
- end
-
0 return([posterior(bayesian_components[kk]) for kk=1:n_components], nn)
- end
-
क्या मुझे समझ में ही नहीं आता कि क्यों उदाहरण के लिए एक सरल काम है जो केवल दो बार चलाता है:
यहाँ कवरेज परिणाम
- #=
- DPM
-
- Dirichlet Process Mixture Models
-
- 25/08/2015
- Adham Beyki, [email protected]
-
- =#
-
- type DPM{T}
- bayesian_component::T
- K::Int64
- aa::Float64
- a1::Float64
- a2::Float64
- K_hist::Vector{Int64}
- K_zz_dict::Dict{Int64, Vector{Int64}}
-
- DPM{T}(c::T, K::Int64, aa::Float64, a1::Float64, a2::Float64) = new(c, K, aa, a1, a2,
- Int64[], (Int64 => Vector{Int64})[])
- end
1 DPM{T}(c::T, K::Int64, aa::Real, a1::Real, a2::Real) = DPM{typeof(c)}(c, K, convert(Float64, aa),
- convert(Float64, a1), convert(Float64, a2))
-
- function Base.show(io::IO, dpm::DPM)
- println(io, "Dirichlet Mixture Model with $(dpm.K) $(typeof(dpm.bayesian_component)) components")
- end
-
- function initialize_gibbs_sampler!(dpm::DPM, zz::Vector{Int64})
- # populates the cluster labels randomly
1 zz[:] = rand(1:dpm.K, length(zz))
- end
-
- function DPM_sample_hyperparam(aa::Float64, a1::Float64, a2::Float64, K::Int64, NN::Int64, iters::Int64)
-
- # resampling concentration parameter based on Escobar and West 1995
352 for n = 1:iters
3504 eta = rand(Distributions.Beta(aa+1, NN))
3504 rr = (a1+K-1)/(NN*(a2-log(NN)))
3504 pi_eta = rr/(1+rr)
-
3504 if rand() < pi_eta
0 aa = rand(Distributions.Gamma(a1+K, 1/(a2-log(eta))))
- else
3504 aa = rand(Distributions.Gamma(a1+K-1, 1/(a2-log(eta))))
- end
- end
352 aa
- end
-
- function DPM_sample_pp{T1, T2}(
- bayesian_components::Vector{T1},
- xx::T2,
- nn::Vector{Float64},
- pp::Vector{Float64},
- aa::Float64)
-
1760000 K = length(nn)
1760000 @inbounds for kk = 1:K
11384379 pp[kk] = log(nn[kk]) + logpredictive(bayesian_components[kk], xx)
- end
1760000 pp[K+1] = log(aa) + logpredictive(bayesian_components[K+1], xx)
1760000 normalize_pp!(pp, K+1)
1760000 return sample(pp[1:K+1])
- end
-
-
- function collapsed_gibbs_sampler!{T1, T2}(
- dpm::DPM{T1},
- xx::Vector{T2},
- zz::Vector{Int64},
- n_burnins::Int64, n_lags::Int64, n_samples::Int64, n_internals::Int64; max_clusters::Int64=100)
-
-
2 NN = length(xx) # number of data points
2 nn = zeros(Float64, dpm.K) # count array
2 n_iterations = n_burnins + (n_samples)*(n_lags+1)
2 bayesian_components = [deepcopy(dpm.bayesian_component) for k = 1:dpm.K+1]
2 dpm.K_hist = zeros(Int64, n_iterations)
2 pp = zeros(Float64, max_clusters)
-
2 tic()
2 for ii = 1:NN
10000 kk = zz[ii]
10000 additem(bayesian_components[kk], xx[ii])
10000 nn[kk] += 1
- end
2 dpm.K_hist[1] = dpm.K
2 elapsed_time = toq()
-
2 for iteration = 1:n_iterations
-
352 println("iteration: $iteration, KK: $(dpm.K), KK mode: $(indmax(hist(dpm.K_hist,
- 0.5:maximum(dpm.K_hist)+0.5)[2])), elapsed time: $elapsed_time")
-
352 tic()
352 @inbounds for ii = 1:NN
1760000 kk = zz[ii]
1760000 nn[kk] -= 1
1760000 delitem(bayesian_components[kk], xx[ii])
-
- # remove the cluster if empty
1760000 if nn[kk] == 0
166 println("\tcomponent $kk has become inactive")
166 splice!(nn, kk)
166 splice!(bayesian_components, kk)
166 dpm.K -= 1
-
- # shifting the labels one cluster back
830166 idx = find(x -> x>kk, zz)
166 zz[idx] -= 1
- end
-
1760000 kk = DPM_sample_pp(bayesian_components, xx[ii], nn, pp, dpm.aa)
-
1760000 if kk == dpm.K+1
171 println("\tcomponent $kk activated.")
171 push!(bayesian_components, deepcopy(dpm.bayesian_component))
171 push!(nn, 0)
171 dpm.K += 1
- end
-
1760000 zz[ii] = kk
1760000 nn[kk] += 1
1760000 additem(bayesian_components[kk], xx[ii])
- end
-
352 dpm.aa = DPM_sample_hyperparam(dpm.aa, dpm.a1, dpm.a2, dpm.K, NN, n_internals)
352 dpm.K_hist[iteration] = dpm.K
352 dpm.K_zz_dict[dpm.K] = deepcopy(zz)
352 elapsed_time = toq()
- end
- end
-
- function truncated_gibbs_sampler{T1, T2}(dpm::DPM{T1}, xx::Vector{T2}, zz::Vector{Int64},
- n_burnins::Int64, n_lags::Int64, n_samples::Int64, n_internals::Int64, K_truncation::Int64)
-
- NN = length(xx) # number of data points
- nn = zeros(Int64, K_truncation) # count array
- bayesian_components = [deepcopy(dpm.bayesian_component) for k = 1:K_truncation]
- n_iterations = n_burnins + (n_samples)*(n_lags+1)
- dpm.K_hist = zeros(Int64, n_iterations)
- states = (ASCIIString => Int64)[]
- n_states = 0
-
- tic()
- for ii = 1:NN
- kk = zz[ii]
- additem(bayesian_components[kk], xx[ii])
- nn[kk] += 1
- end
- dpm.K_hist[1] = dpm.K
-
- # constructing the sticks
- beta_VV = rand(Distributions.Beta(1.0, dpm.aa), K_truncation)
- beta_VV[end] = 1.0
- π = ones(Float64, K_truncation)
- π[2:end] = 1 - beta_VV[1:K_truncation-1]
- π = log(beta_VV) + log(cumprod(π))
-
- elapsed_time = toq()
-
- for iteration = 1:n_iterations
-
- println("iteration: $iteration, # active components: $(length(findn(nn)[1])), mode: $(indmax(hist(dpm.K_hist,
- 0.5:maximum(dpm.K_hist)+0.5)[2])), elapsed time: $elapsed_time \n", nn)
-
- tic()
- for ii = 1:NN
- kk = zz[ii]
- nn[kk] -= 1
- delitem(bayesian_components[kk], xx[ii])
-
- # resampling label
- pp = zeros(Float64, K_truncation)
- for kk = 1:K_truncation
- pp[kk] = π[kk] + logpredictive(bayesian_components[kk], xx[ii])
- end
- pp = exp(pp - maximum(pp))
- pp /= sum(pp)
-
- # sample from pp
- kk = sampleindex(pp)
- zz[ii] = kk
- nn[kk] += 1
- additem(bayesian_components[kk], xx[ii])
-
- for kk = 1:K_truncation-1
- gamma1 = 1 + nn[kk]
- gamma2 = dpm.aa + sum(nn[kk+1:end])
- beta_VV[kk] = rand(Distributions.Beta(gamma1, gamma2))
- end
- beta_VV[end] = 1.0
- π = ones(Float64, K_truncation)
- π[2:end] = 1 - beta_VV[1:K_truncation-1]
- π = log(beta_VV) + log(cumprod(π))
-
- # resampling concentration parameter based on Escobar and West 1995
- for internal_iters = 1:n_internals
- eta = rand(Distributions.Beta(dpm.aa+1, NN))
- rr = (dpm.a1+dpm.K-1)/(NN*(dpm.a2-log(NN)))
- pi_eta = rr/(1+rr)
-
- if rand() < pi_eta
- dpm.aa = rand(Distributions.Gamma(dpm.a1+dpm.K, 1/(dpm.a2-log(eta))))
- else
- dpm.aa = rand(Distributions.Gamma(dpm.a1+dpm.K-1, 1/(dpm.a2-log(eta))))
- end
- end
- end
-
- nn_string = nn2string(nn)
- if !haskey(states, nn_string)
- n_states += 1
- states[nn_string] = n_states
- end
- dpm.K_hist[iteration] = states[nn_string]
- dpm.K_zz_dict[states[nn_string]] = deepcopy(zz)
- elapsed_time = toq()
- end
- return states
- end
-
-
- function posterior{T1, T2}(dpm::DPM{T1}, xx::Vector{T2}, K::Int64, K_truncation::Int64=0)
2 n_components = 0
1 if K_truncation == 0
1 n_components = K
- else
0 n_components = K_truncation
- end
-
1 bayesian_components = [deepcopy(dpm.bayesian_component) for kk=1:n_components]
1 zz = dpm.K_zz_dict[K]
-
1 NN = length(xx)
1 nn = zeros(Int64, n_components)
-
1 for ii = 1:NN
5000 kk = zz[ii]
5000 additem(bayesian_components[kk], xx[ii])
5000 nn[kk] += 1
- end
-
1 return([posterior(bayesian_components[kk]) for kk=1:n_components], nn)
- end
-
और यहाँ स्मृति आवंटन है 1 9 1688 इकाइयों को आवंटित करता है (मुझे लगता है कि यूनिट बाइट्स है, मुझे यकीन नहीं है)।
.cov:
2 NN = length(xx) # number of data points
.mem:
191688 NN = length(xx) # number of data points
या इस एक भी बदतर है:
cov:
352 @inbounds for ii = 1:NN
मेम:
28000000 @inbounds for ii = 1:NN
'एनएन' का मूल्य क्या है? मैं स्मृति आवंटन से पहले धीमी भागों की पहचान करने के लिए प्रोफाइलर का उपयोग करने की सलाह दूंगा। – IainDunning
मैंने प्रोफाइलर का उपयोग किया है और 'एनएन = लंबाई (xx)' एक बाधा नहीं है। 'xx'' :: वेक्टर {Float64} है 'इस प्रकार एनएन बस एक पूर्णांक है, इस प्रयोग में 5000 के बराबर है। – Adham