-
Notifications
You must be signed in to change notification settings - Fork 41
/
Copy pathvbmc.m
1153 lines (1010 loc) · 55.2 KB
/
vbmc.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
function [vp,elbo,elbo_sd,exitflag,output,samples,optimState,stats,vp_train] = ...
vbmc(fun,x0,LB,UB,PLB,PUB,options,varargin)
%VBMC Posterior and model inference via Variational Bayesian Monte Carlo (v1.0.12).
% VBMC computes a variational approximation of the full posterior and a
% lower bound on the normalization constant (marginal likelhood or model
% evidence) for a provided unnormalized log posterior. As of v1.0, VBMC
% also supports noisy evaluations of the log posterior (see below).
%
% VP = VBMC(FUN,X0,LB,UB) initializes the variational posterior in the
% proximity of X0 (ideally, a posterior mode) and iteratively computes
% a variational approximation for a given target log posterior FUN.
% FUN accepts input X and returns the value of the target log-joint, that
% is the unnormalized log-posterior density, at X. LB and UB define a set
% of strict lower and upper bounds coordinate vector, X, so that the
% posterior has support on LB < X < UB. LB and UB can be scalars or
% vectors. If scalars, the bound is replicated in each dimension. Use
% empty matrices for LB and UB if no bounds exist. Set LB(i) = -Inf and
% UB(i) = Inf if the i-th coordinate is unbounded (while other coordinates
% may be bounded). Note that if LB and UB contain unbounded variables,
% the respective values of PLB and PUB need to be specified (see below).
% VBMC returns a variational posterior solution VP, which can then be
% manipulated via other functions in the VBMC toolbox (see examples below).
%
% VP = VBMC(FUN,X0,LB,UB,PLB,PUB) specifies a set of plausible lower and
% upper bounds such that LB < PLB < PUB < UB. Both PLB and PUB
% need to be finite. PLB and PUB represent a "plausible" range, which
% should denote a region of high posterior probability mass. Among other
% things, the plausible box is used to draw initial samples and to set
% priors over hyperparameters of the algorithm. When in doubt, we found
% that setting PLB and PUB using the topmost ~68% percentile range of the
% prior (e.g, mean +/- 1 SD for a Gaussian prior) works well in many
% cases (but note that additional information might afford a better guess).
%
% VP = VBMC(FUN,X0,LB,UB,PLB,PUB,OPTIONS) performs variational inference
% with the default parameters replaced by values in the structure OPTIONS.
% VBMC('defaults') returns the default OPTIONS struct.
%
% VP = VBMC(FUN,X0,LB,UB,PLB,PUB,OPTIONS,...) passes additional arguments
% to FUN.
%
% VBMC also supports noisy/stochastic estimates of the log-posterior,
% obtained through techniques such as Inverse Binomial Sampling (see
% examples and references below). For noisy evaluations, FUN should
% return as second agument the estimated SD (standard deviation) of the
% log-likelihood noise at X.
% Set OPTIONS.SpecifyTargetNoise = 1 to activate support for noisy
% inference (this is not automatic).
%
% VP = VBMC(FUN,VP0,...) uses variational posterior VP0 (from a previous
% run of VBMC) to initialize the current run. You can leave PLB and PUB
% empty, in which case they will be set using VP0 (recommended).
%
% [VP,ELBO] = VBMC(...) returns an estimate of the ELBO, the variational
% expected lower bound on the log marginal likelihood (log model evidence).
% This estimate is computed via Bayesian quadrature.
%
% [VP,ELBO,ELBO_SD] = VBMC(...) returns the standard deviation of the
% estimate of the ELBO, as computed via Bayesian quadrature. Note that
% this standard deviation is *not* representative of the error between the
% ELBO and the true log marginal likelihood.
%
% [VP,ELBO,ELBO_SD,EXITFLAG] = VBMC(...) returns an EXITFLAG that describes
% the exit condition. Possible values of EXITFLAG and the corresponding
% exit conditions are
%
% 1 Change in the variational posterior, in the ELBO and its uncertainty
% have reached a satisfactory level of stability across recent
% iterations, suggesting convergence of the variational solution.
% 0 Maximum number of function evaluations or iterations reached. Note
% that the returned solution has *not* stabilized.
%
% [VP,ELBO,ELBO_SD,EXITFLAG,OUTPUT] = VBMC(...) returns a structure OUTPUT
% with the following information:
% function: <Target probability density function name>
% iterations: <Total iterations>
% funccount: <Total function evaluations>
% bestiter: <Iteration of returned solution>
% trainsetsize: <Size of training set for returned solution>
% components: <Number of mixture components of returned solution>
% rindex: <Reliability index (< 1 is good)>
% convergencestatus: <"probable" or "no" convergence>
% overhead: <Fractional overhead (total runtime / total fcn time - 1)>
% rngstate: <Status of random number generator>
% algorithm: <Variational Bayesian Monte Carlo>
% message: <VBMC termination message>
% elbo: <Estimated ELBO for returned solution>
% elbo_sd: <Estimated standard deviation of ELBO at returned solution>
% retried: <"yes", "no", or "failed" if a retry run was performed>
%
% OPTIONS = VBMC('defaults') returns a basic default OPTIONS structure.
%
% EXITFLAG = VBMC('test') runs a battery of tests. Here EXITFLAG is 0 if
% everything works correctly.
%
% Examples:
% FUN can be a function handle (using @)
% vp = vbmc(@rosenbrock_test, ...)
% In this case, F = rosenbrock_test(X) returns the scalar log pdf F of
% the target pdf evaluated at X.
%
% An example with no hard bounds, only plausible bounds
% plb = [-5 -5]; pub = [5 5]; options.Plot = 'on';
% [vp,elbo,elbo_sd] = vbmc(@rosenbrock_test,[0 0],[],[],plb,pub,options);
%
% FUN can also be an anonymous function:
% lb = [0 0]; ub = [pi 5]; plb = [0.1 0.1]; pub = [3 4]; options.Plot = 'on';
% vp = vbmc(@(x) 3*sin(x(1))*exp(-x(2)),[1 1],lb,ub,plb,pub,options)
%
% See VBMC_EXAMPLES for an extended tutorial with more examples.
% The most recent version of the algorithm and additional documentation
% can be found here: https://github.com/acerbilab/vbmc
% Also, check out the FAQ: https://github.com/acerbilab/vbmc/wiki
%
% References (please cite both):
%
% 1) Acerbi, L. (2018). "Variational Bayesian Monte Carlo". In Advances
% in Neural Information Processing Systems 31 (NeurIPS 2018), pp. 8213-8223.
% 2) Acerbi, L. (2020). "Variational Bayesian Monte Carlo with Noisy
% Likelihoods". In Advances in Neural Information Processing Systems 33
% (NeurIPS 2020).
%
% Additional references:
%
% 3) Acerbi, L. (2019). "An Exploration of Acquisition and Mean Functions
% in Variational Bayesian Monte Carlo". In Proc. Machine Learning
% Research 96: 1-10. 1st Symposium on Advances in Approximate Bayesian
% Inference, Montréal, Canada.
% 4) van Opheusden, B.*, Acerbi, L.* & Ma, W. J. (2020). "Unbiased and
% Efficient Log-Likelihood Estimation with Inverse Binomial Sampling".
% PLoS Computational Biology 16(12): e1008483. (* equal contribution)
%
% See also VBMC_EXAMPLES, VBMC_KLDIV, VBMC_MODE, VBMC_MOMENTS, VBMC_MTV,
% VBMC_PDF, VBMC_RND, VBMC_DIAGNOSTICS, @.
%--------------------------------------------------------------------------
% VBMC: Variational Bayesian Monte Carlo for posterior and model inference.
% To be used under the terms of the GNU General Public License
% (http://www.gnu.org/copyleft/gpl.html).
%
% Author (copyright): Luigi Acerbi, 2018-2022
% e-mail: luigi.acerbi@{helsinki.fi,gmail.com}
% URL: http://luigiacerbi.com
% Version: 1.0.12
% Release date: Oct 26, 2022
% Code repository: https://github.com/acerbilab/vbmc
%--------------------------------------------------------------------------
%% Start timer
t0 = tic;
vbmc_version = '1.0.12';
% Check that all VBMC subfolders are on the MATLAB path
add2path();
%% Basic default options
defopts.Display = 'iter % Level of display ("iter", "notify", "final", or "off")';
defopts.Plot = 'off % Plot marginals of variational posterior at each iteration';
defopts.MaxIter = '50*(2+nvars) % Max number of iterations';
defopts.MaxFunEvals = '50*(2+nvars) % Max number of target fcn evals';
defopts.FunEvalsPerIter = '5 % Number of target fcn evals per iteration';
defopts.TolStableCount = '60 % Required stable fcn evals for termination';
defopts.RetryMaxFunEvals = '0 % Max number of target fcn evals on retry (0 = no retry)';
defopts.MinFinalComponents = '50 % Number of variational components to refine posterior at termination';
defopts.SpecifyTargetNoise = 'no % Target log joint function returns noise estimate (SD) as second output';
%% If called with no arguments or with 'defaults', return default options
if nargout <= 1 && (nargin == 0 || (nargin == 1 && ischar(fun) && strcmpi(fun,'defaults')))
if nargin < 1
fprintf('Basic default options returned (type "help vbmc" for help).\n');
end
vp = defopts;
return;
end
%% If called with one argument which is 'test', run test
if nargout <= 1 && (nargin == 1 || nargin == 2) && ischar(fun) && strcmpi(fun,'test')
% Can run a test with a specific OPTIONS struct (otherwise use defaults)
if nargin == 2; options = x0; else; options = []; end
vp = runtest_vbmc(options);
return;
end
%% If called with one argument which is 'version', return version
if nargout <= 1 && nargin == 1 && ischar(fun) && strcmpi(fun,'version')
vp = vbmc_version;
return;
end
%% Advanced options (do not modify unless you *know* what you are doing)
defopts.UncertaintyHandling = '[] % Explicit noise handling';
defopts.IntegerVars = '[] % Array with indices of integer variables';
defopts.NoiseSize = '[] % Base observation noise magnitude (standard deviation)';
defopts.MaxRepeatedObservations = '0 % Max number of consecutive repeated measurements for noisy inputs';
defopts.RepeatedAcqDiscount = '1 % Multiplicative discount on acquisition fcn to repeat measurement at the same location';
defopts.FunEvalStart = '10*ceil((D+1)/10) % Number of initial target fcn evals';
defopts.SGDStepSize = '0.005 % Base step size for stochastic gradient descent';
defopts.SkipActiveSamplingAfterWarmup = 'no % Skip active sampling the first iteration after warmup';
defopts.RankCriterion = 'yes % Use ranking criterion to pick best non-converged solution';
defopts.TolStableEntropyIters = '6 % Required stable iterations to switch entropy approximation';
defopts.VariableMeans = 'yes % Use variable component means for variational posterior';
defopts.VariableWeights = 'yes % Use variable mixture weight for variational posterior';
defopts.WeightPenalty = '0.1 % Penalty multiplier for small mixture weights';
defopts.Diagnostics = 'off % Run in diagnostics mode, get additional info';
defopts.OutputFcn = '[] % Output function';
defopts.TolStableExcptFrac = '0.2 % Fraction of allowed exceptions when computing iteration stability';
defopts.Fvals = '[] % Evaluated fcn values at X0';
defopts.OptimToolbox = '[] % Use Optimization Toolbox (if empty, determine at runtime)';
defopts.ProposalFcn = '[] % Weighted proposal fcn for uncertainty search';
defopts.NonlinearScaling = 'on % Automatic nonlinear rescaling of variables';
defopts.SearchAcqFcn = '@acqf_vbmc % Fast search acquisition fcn(s)';
defopts.NSsearch = '2^13 % Samples for fast acquisition fcn eval per new point';
defopts.NSent = '@(K) 100*K.^(2/3) % Total samples for Monte Carlo approx. of the entropy';
defopts.NSentFast = '0 % Total samples for preliminary Monte Carlo approx. of the entropy';
defopts.NSentFine = '@(K) 2^12*K % Total samples for refined Monte Carlo approx. of the entropy';
defopts.NSentBoost = '@(K) 200*K.^(2/3) % Total samples for Monte Carlo approx. of the entropy (final boost)';
defopts.NSentFastBoost = '[] % Total samples for preliminary Monte Carlo approx. of the entropy (final boost)';
defopts.NSentFineBoost = '[] % Total samples for refined Monte Carlo approx. of the entropy (final boost)';
defopts.NSentActive = '@(K) 20*K.^(2/3) % Total samples for Monte Carlo approx. of the entropy (active sampling)';
defopts.NSentFastActive = '0 % Total samples for preliminary Monte Carlo approx. of the entropy (active sampling)';
defopts.NSentFineActive = '@(K) 200*K % Total samples for refined Monte Carlo approx. of the entropy (active sampling)';
defopts.NSelbo = '@(K) 50*K % Samples for fast approximation of the ELBO';
defopts.NSelboIncr = '0.1 % Multiplier to samples for fast approx. of ELBO for incremental iterations';
defopts.ElboStarts = '2 % Starting points to refine optimization of the ELBO';
defopts.NSgpMax = '80 % Max GP hyperparameter samples (decreases with training points)';
defopts.NSgpMaxWarmup = '8 % Max GP hyperparameter samples during warmup';
defopts.NSgpMaxMain = 'Inf % Max GP hyperparameter samples during main algorithm';
defopts.WarmupNoImproThreshold = '20 + 5*nvars % Fcn evals without improvement before stopping warmup';
defopts.WarmupCheckMax = 'yes % Also check for max fcn value improvement before stopping warmup';
defopts.StableGPSampling = '200 + 10*nvars % Force stable GP hyperparameter sampling (reduce samples or start optimizing)';
defopts.StableGPvpK = 'Inf % Force stable GP hyperparameter sampling after reaching this number of components';
defopts.StableGPSamples = '0 % Number of GP samples when GP is stable (0 = optimize)';
defopts.GPSampleThin = '5 % Thinning for GP hyperparameter sampling';
defopts.GPTrainNinit = '1024 % Initial design points for GP hyperparameter training';
defopts.GPTrainNinitFinal = '64 % Final design points for GP hyperparameter training';
defopts.GPTrainInitMethod = 'rand % Initial design method for GP hyperparameter training';
defopts.GPTolOpt = '1e-5 % Tolerance for optimization of GP hyperparameters';
defopts.GPTolOptMCMC = '1e-2 % Tolerance for optimization of GP hyperparameters preliminary to MCMC';
defopts.GPTolOptActive = '1e-4 % Tolerance for optimization of GP hyperparameters during active sampling';
defopts.GPTolOptMCMCActive = '1e-2 % Tolerance for optimization of GP hyperparameters preliminary to MCMC during active sampling';
defopts.TolGPVar = '1e-4 % Threshold on GP variance used by regulatized acquisition fcns';
defopts.TolGPVarMCMC = '1e-4 % Threshold on GP variance, used to stabilize sampling';
defopts.gpMeanFun = 'negquad % GP mean function';
defopts.gpIntMeanFun = '0 % GP integrated mean function';
defopts.KfunMax = '@(N) N.^(2/3) % Max variational components as a function of training points';
defopts.Kwarmup = '2 % Variational components during warmup';
defopts.AdaptiveK = '2 % Added variational components for stable solution';
defopts.HPDFrac = '0.8 % High Posterior Density region (fraction of training inputs)';
defopts.ELCBOImproWeight = '3 % Uncertainty weight on ELCBO for computing lower bound improvement';
defopts.TolLength = '1e-6 % Minimum fractional length scale';
defopts.CacheSize = '500 % Size of cache for storing fcn evaluations';
defopts.CacheFrac = '0.5 % Fraction of search points from starting cache (if nonempty)';
defopts.StochasticOptimizer = 'adam % Stochastic optimizer for varational parameters';
defopts.TolFunStochastic = '1e-3 % Stopping threshold for stochastic optimization';
defopts.MaxIterStochastic = '100*(2+nvars) % Max iterations for stochastic optimization';
defopts.TolSD = '0.1 % Tolerance on ELBO uncertainty for stopping (iff variational posterior is stable)';
defopts.TolsKL = '0.01*sqrt(nvars) % Stopping threshold on change of variational posterior per training point';
defopts.TolStableWarmup = '15 % Number of stable fcn evals for stopping warmup';
defopts.VariationalSampler = 'malasample % MCMC sampler for variational posteriors';
defopts.TolImprovement = '0.01 % Required ELCBO improvement per fcn eval before termination';
defopts.KLgauss = 'yes % Use Gaussian approximation for symmetrized KL-divergence b\w iters';
defopts.TrueMean = '[] % True mean of the target density (for debugging)';
defopts.TrueCov = '[] % True covariance of the target density (for debugging)';
defopts.MinFunEvals = '5*nvars % Min number of fcn evals';
defopts.MinIter = 'nvars % Min number of iterations';
defopts.HeavyTailSearchFrac = '0.25 % Fraction of search points from heavy-tailed variational posterior';
defopts.MVNSearchFrac = '0.25 % Fraction of search points from multivariate normal';
defopts.HPDSearchFrac = '0 % Fraction of search points from multivariate normal fitted to HPD points';
defopts.BoxSearchFrac = '0.25 % Fraction of search points from uniform random box based on training inputs';
defopts.SearchCacheFrac = '0 % Fraction of search points from previous iterations';
defopts.AlwaysRefitVarPost = 'no % Always fully refit variational posterior';
defopts.Warmup = 'on % Perform warm-up stage';
defopts.WarmupOptions = '[] % Special OPTIONS struct for warmup stage';
defopts.StopWarmupThresh = '0.2 % Stop warm-up when ELCBO increase below threshold (per fcn eval)';
defopts.WarmupKeepThreshold = '10*nvars % Max log-likelihood difference for points kept after warmup';
defopts.WarmupKeepThresholdFalseAlarm = '100*(nvars+2) % Max log-likelihood difference for points kept after a false-alarm warmup stop';
defopts.StopWarmupReliability = '100 % Reliability index required to stop warmup';
defopts.SearchOptimizer = 'cmaes % Optimization method for active sampling';
defopts.SearchCMAESVPInit = 'yes % Initialize CMA-ES search SIGMA from variational posterior';
defopts.SearchCMAESbest = 'no % Take bestever solution from CMA-ES search';
defopts.SearchMaxFunEvals = '500*(nvars+2) % Max number of acquisition fcn evaluations during search';
defopts.MomentsRunWeight = '0.9 % Weight of previous trials (per trial) for running avg of variational posterior moments';
defopts.GPRetrainThreshold = '1 % Upper threshold on reliability index for full retraining of GP hyperparameters';
defopts.ELCBOmidpoint = 'on % Compute full ELCBO also at best midpoint';
defopts.GPSampleWidths = '5 % Multiplier to widths from previous posterior for GP sampling (Inf = do not use previous widths)';
defopts.HypRunWeight = '0.9 % Weight of previous trials (per trial) for running avg of GP hyperparameter covariance';
defopts.WeightedHypCov = 'on % Use weighted hyperparameter posterior covariance';
defopts.TolCovWeight = '0 % Minimum weight for weighted hyperparameter posterior covariance';
defopts.GPHypSampler = 'slicesample % MCMC sampler for GP hyperparameters';
defopts.CovSampleThresh = '10 % Switch to covariance sampling below this threshold of stability index';
defopts.DetEntTolOpt = '1e-3 % Optimality tolerance for optimization of deterministic entropy';
defopts.EntropySwitch = 'off % Switch from deterministic entropy to stochastic entropy when reaching stability';
defopts.EntropyForceSwitch = '0.8 % Force switch to stochastic entropy at this fraction of total fcn evals';
defopts.DetEntropyAlpha = '0 % Alpha value for lower/upper deterministic entropy interpolation';
defopts.UpdateRandomAlpha = 'no % Randomize deterministic entropy alpha during active sample updates';
defopts.AdaptiveEntropyAlpha = 'no % Online adaptation of alpha value for lower/upper deterministic entropy interpolation';
defopts.DetEntropyMinD = '5 % Start with deterministic entropy only with this number of vars or more';
defopts.TolConLoss = '0.01 % Fractional tolerance for constraint violation of variational parameters';
defopts.BestSafeSD = '5 % SD multiplier of ELCBO for computing best variational solution';
defopts.BestFracBack = '0.25 % When computing best solution, lacking stability go back up to this fraction of iterations';
defopts.TolWeight = '1e-2 % Threshold mixture component weight for pruning';
defopts.PruningThresholdMultiplier = '@(K) 1/sqrt(K) % Multiplier to threshold for pruning mixture weights';
defopts.AnnealedGPMean = '@(N,NMAX) 0 % Annealing for hyperprior width of GP negative quadratic mean';
defopts.ConstrainedGPMean = 'no % Strict hyperprior for GP negative quadratic mean';
defopts.TolGPNoise = 'sqrt(1e-5) % Minimum GP observation noise';
defopts.GPLengthPriorMean = 'sqrt(D/6) % Prior mean over GP input length scale (in plausible units)';
defopts.GPLengthPriorStd = '0.5*log(1e3) % Prior std over GP input length scale (in plausible units)';
defopts.UpperGPLengthFactor = '0 % Upper bound on GP input lengths based on plausible box (0 = ignore)';
defopts.InitDesign = 'plausible % Initial samples ("plausible" is uniform in the plausible box)';
defopts.gpQuadraticMeanBound = 'yes % Stricter upper bound on GP negative quadratic mean function';
defopts.Bandwidth = '0 % Bandwidth parameter for GP smoothing (in units of plausible box)';
defopts.FitnessShaping = 'no % Heuristic output warping ("fitness shaping")';
defopts.OutwarpThreshBase = '10*nvars % Output warping starting threshold';
defopts.OutwarpThreshMult = '1.25 % Output warping threshold multiplier when failed sub-threshold check';
defopts.OutwarpThreshTol = '0.8 % Output warping base threshold tolerance (fraction of current threshold)';
defopts.Temperature = '1 % Temperature for posterior tempering (allowed values T = 1,2,3,4)';
defopts.SeparateSearchGP = 'no % Use separate GP with constant mean for active search';
defopts.NoiseShaping = 'no % Discount observations from from extremely low-density regions';
defopts.NoiseShapingThreshold = '10*nvars % Threshold from max observed value to start discounting';
defopts.NoiseShapingFactor = '0.05 % Proportionality factor of added noise wrt distance from threshold';
defopts.AcqHedge = 'no % Hedge on multiple acquisition functions';
defopts.AcqHedgeIterWindow = '4 % Past iterations window to judge acquisition fcn improvement';
defopts.AcqHedgeDecay = '0.9 % Portfolio value decay per function evaluation';
defopts.ActiveVariationalSamples = '0 % MCMC variational steps before each active sampling';
defopts.ScaleLowerBound = 'yes % Apply lower bound on variational components scale during variational sampling';
defopts.ActiveSampleVPUpdate = 'no % Perform variational optimization after each active sample';
defopts.ActiveSampleGPUpdate = 'no % Perform GP training after each active sample';
defopts.ActiveSampleFullUpdatePastWarmup = '2 % # iters past warmup to continue update after each active sample';
defopts.ActiveSampleFullUpdateThreshold = '3 % Perform full update during active sampling if stability above threshold';
defopts.VariationalInitRepo = 'no % Use previous variational posteriors to initialize optimization';
defopts.SampleExtraVPMeans = '0 % Extra variational components sampled from GP profile';
defopts.OptimisticVariationalBound = '0 % Uncertainty weight on ELCBO during active sampling';
defopts.ActiveImportanceSamplingVPSamples = '100 % # importance samples from smoothed variational posterior';
defopts.ActiveImportanceSamplingBoxSamples = '100 % # importance samples from box-uniform centered on training inputs';
defopts.ActiveImportanceSamplingMCMCSamples = '100 % # importance samples through MCMC';
defopts.ActiveImportanceSamplingMCMCThin = '1 % Thinning for importance sampling MCMC';
defopts.ActiveSamplefESSThresh = '1 % fractional ESS threhsold to update GP and VP';
defopts.ActiveImportanceSamplingfESSThresh = '0.9 % % fractional ESS threhsold to do MCMC while active importance sampling';
defopts.ActiveSearchBound = '2 % Active search bound multiplier';
defopts.TolBoundX = '1e-5 % Tolerance on closeness to bound constraints (fraction of total range)';
defopts.RecomputeLCBmax = 'yes % Recompute LCB max for each iteration based on current GP estimate';
defopts.BoundedTransform = 'logit % Input transform for bounded variables';
defopts.WarpEveryIters = '5 % Warp every this number of iterations';
defopts.IncrementalWarpDelay = 'yes % Increase delay between warpings';
defopts.WarpTolReliability = '3 % Threshold on reliability index to perform warp';
defopts.WarpRotoScaling = 'yes % Rotate and scale input';
defopts.WarpCovReg = '0 % Regularization weight towards diagonal covariance matrix for N training inputs';
defopts.WarpRotoCorrThresh = '0.05 % Threshold on correlation matrix for roto-scaling';
defopts.WarpMinK = '5 % Min number of variational components to perform warp';
defopts.WarpUndoCheck = 'yes % Immediately undo warp if not improving ELBO';
defopts.WarpTolImprovement = '0.1 % Improvement of ELBO required to keep a warp proposal';
defopts.WarpTolSDMultiplier = '2 % Multiplier tolerance of ELBO SD after warp proposal';
defopts.WarpTolSDBase = '1 % Base tolerance on ELBO SD after warp proposal';
%% Advanced options for unsupported/untested features (do *not* modify)
defopts.WarpNonlinear = 'off % Nonlinear input warping';
defopts.ELCBOWeight = '0 % Uncertainty weight during ELCBO optimization';
defopts.VarParamsBack = '0 % Check variational posteriors back to these previous iterations';
defopts.AltMCEntropy = 'no % Use alternative Monte Carlo computation for the entropy';
defopts.VarActiveSample = 'no % Variational active sampling';
defopts.FeatureTest = 'no % Test a new experimental feature';
defopts.BOWarmup = 'no % Bayesian-optimization-like warmup stage';
defopts.gpOutwarpFun = '[] % GP default output warping function';
%% If called with 'all', return all default options
if strcmpi(fun,'all')
vp = defopts;
return;
end
%% Input arguments
if nargin < 3 || isempty(LB); LB = -Inf; end
if nargin < 4 || isempty(UB); UB = Inf; end
if nargin < 5; PLB = []; end
if nargin < 6; PUB = []; end
if nargin < 7; options = []; end
%% Initialize display printing options
if ~isfield(options,'Display') || isempty(options.Display)
options.Display = defopts.Display;
end
switch lower(options.Display(1:min(end,3)))
case {'not'} % notify
prnt = 1;
case {'no','non','off'} % none
prnt = 0;
case {'ite','all','on','yes'} % iter
prnt = 3;
case {'fin','end'} % final
prnt = 2;
otherwise
prnt = 3;
end
%% Initialize variables and algorithm structures
if isempty(x0)
if prnt > 2
fprintf('X0 not specified. Taking the number of dimensions from PLB and PUB...');
end
if isempty(PLB) || isempty(PUB)
error('vbmc:UnknownDims', ...
'If no starting point is provided, PLB and PUB need to be specified.');
end
x0 = NaN(size(PLB));
if prnt > 2
fprintf(' D = %d.\n', numel(x0));
end
end
% Initialize from variational posterior
if vbmc_isavp(x0)
init_from_vp_flag = true;
vp0 = x0;
[x0,LB,UB,PLB,PUB,Xvp] = initFromVP(vp0,LB,UB,PLB,PUB,prnt);
else
init_from_vp_flag = false;
end
D = size(x0,2); % Number of variables
optimState = [];
% Setup algorithm options
options = setupoptions_vbmc(D,defopts,options);
if options.Warmup
options_main = options;
% Use special options during Warmup
if isfield(options,'WarmupOptions')
WarmupOptions = options.WarmupOptions;
% Copy these fields to avoid re-update in SETUPOPTIONS_VBMC
copyfields = {'MaxFunEvals','TolStableCount','ActiveSampleGPUpdate','ActiveSampleVPUpdate','SearchAcqFcn'};
for f = copyfields
if ~isfield(WarmupOptions,f{:})
WarmupOptions.(f{:}) = options.(f{:});
end
end
options = setupoptions_vbmc(D,options,WarmupOptions);
end
end
if init_from_vp_flag % Finish initialization from variational posterior
x0 = [x0; robustSampleFromVP(vp0,options.FunEvalStart-1,Xvp)];
clear Xvp vp0;
end
% Check/fix boundaries and starting points
[x0,LB,UB,PLB,PUB] = boundscheck_vbmc(x0,LB,UB,PLB,PUB,prnt);
% Convert from char to function handles
if ischar(fun); fun = str2func(fun); end
% Setup and transform variables, prepare OPTIMSTATE settings struct
K = options.Kwarmup;
[vp,optimState] = ...
setupvars_vbmc(x0,LB,UB,PLB,PUB,K,optimState,options,prnt);
% Store target density function
optimState.fun = fun;
funwrapper = @(u_) fun(u_,varargin{:});
% Get information from acquisition function(s)
optimState.acqInfo = getAcqInfo(options.SearchAcqFcn);
% GP struct and GP hyperparameters
gp = []; hypstruct = []; hypstruct_search = [];
% Initialize function logger
[~,optimState] = funlogger_vbmc([],D,optimState,'init',options.CacheSize);
if optimState.Cache.active
displayFormat = ' %5.0f %5.0f /%5.0f %12.2f %12.2f %12.2f %4.0f %10.3g %s\n';
displayFormat_warmup = ' %5.0f %5.0f /%5.0f %s\n';
elseif optimState.UncertaintyHandlingLevel > 0 && options.MaxRepeatedObservations > 0
displayFormat = ' %5.0f %5.0f %5.0f %12.2f %12.2f %12.2f %4.0f %10.3g %s\n';
displayFormat_warmup = ' %5.0f %5.0f %12.2f %s\n';
else
displayFormat = ' %5.0f %5.0f %12.2f %12.2f %12.2f %4.0f %10.3g %s\n';
displayFormat_warmup = ' %5.0f %5.0f %12.2f %s\n';
end
if prnt > 2
if optimState.UncertaintyHandlingLevel > 0
fprintf('Beginning variational optimization assuming NOISY observations of the log-joint.\n');
else
fprintf('Beginning variational optimization assuming EXACT observations of the log-joint.\n');
end
if optimState.Cache.active
fprintf(' Iteration f-count/f-cache Mean[ELBO] Std[ELBO] sKL-iter[q] K[q] Convergence Action\n');
else
if options.BOWarmup
fprintf(' Iteration f-count Max[f] Action\n');
elseif optimState.UncertaintyHandlingLevel > 0 && options.MaxRepeatedObservations > 0
fprintf(' Iteration f-count (x-count) Mean[ELBO] Std[ELBO] sKL-iter[q] K[q] Convergence Action\n');
else
fprintf(' Iteration f-count Mean[ELBO] Std[ELBO] sKL-iter[q] K[q] Convergence Action\n');
end
end
end
%% Variational optimization loop
iter = 0;
isFinished_flag = false;
exitflag = 0; output = []; stats = [];
while ~isFinished_flag
t_iter = tic;
timer = timer_init(); % Initialize iteration timer
iter = iter + 1;
optimState.iter = iter;
vp_old = vp;
action = '';
optimState.redoRotoscaling = false;
if iter == 1 && optimState.Warmup; action = 'start warm-up'; end
% Switch to stochastic entropy towards the end if still on deterministic
if optimState.EntropySwitch && ...
optimState.funccount >= options.EntropyForceSwitch*options.MaxFunEvals
optimState.EntropySwitch = false;
if isempty(action); action = 'entropy switch'; else; action = [action ', entropy switch']; end
end
%% Input warping / reparameterization
if options.IncrementalWarpDelay
WarpDelay = options.WarpEveryIters*max(1,optimState.WarpingCount);
else
WarpDelay = options.WarpEveryIters;
end
DoWarping = (options.WarpRotoScaling || options.WarpNonlinear) && ...
iter > 1 && ~optimState.Warmup && ...
(iter - optimState.LastWarping) > WarpDelay && ...
vp.K >= options.WarpMinK && stats.rindex(iter-1) < options.WarpTolReliability && ...
vp.D > 1;
% (stats.stable(iter-1) || optimState.funccount >= options.MaxFunEvals*2/3);
if DoWarping
t = tic;
[vp_tmp,~,~,idx_best] = ...
best_vbmc(stats,iter-1,options.BestSafeSD,options.BestFracBack,options.RankCriterion,0);
% Store variables in case warp needs to be undone
optimState_old = optimState;
gp_old = gp;
hypstruct_old = hypstruct;
elbo_old = elbo;
elbo_sd_old = elbo_sd;
% Compute input warping
[trinfo_warp,optimState,warp_action] = warp_input_vbmc(vp_tmp,optimState,stats.gp(idx_best),options);
% Update GP hyperparameters and variational posterior
[vp,hypstruct.hyp] = warp_gpandvp_vbmc(trinfo_warp,vp,gp);
if isempty(action); action = warp_action; else; action = [action ', ' warp_action]; end
timer.warping = timer.warping + toc(t);
if options.WarpUndoCheck
% Train GP
t = tic;
[gp,hypstruct,~,optimState] = ...
gptrain_vbmc(hypstruct,optimState,stats,options);
timer.gpTrain = timer.gpTrain + toc(t);
% Optimize variational parameters
t = tic;
if ~vp.optimize_mu % Variational components fixed to training inputs
vp.mu = gp.X';
Knew = size(vp.mu,2);
else
% Update number of variational mixture components
Knew = vp.K;
end
% Decide number of fast/slow optimizations
Nfastopts = ceil(evaloption_vbmc(options.NSelbo,Knew));
Nslowopts = options.ElboStarts; % Full optimizations
% Run optimization of variational parameters
vp = vpoptimize_vbmc(Nfastopts,Nslowopts,vp,gp,Knew,optimState,options,prnt);
optimState.vpK = vp.K;
optimState.H = vp.stats.entropy; % Save current entropy
% Compute ELBO from real variational posterior (might differ from training posterior)
vp_real = vptrain2real(vp,0,options);
elbo = vp_real.stats.elbo;
elbo_sd = vp_real.stats.elbo_sd;
timer.variationalFit = timer.variationalFit + toc(t);
% Compute symmetrized KL-divergence between old and new posteriors
%Nkl = 1e5;
%sKL = max(0,0.5*sum(vbmc_kldiv(vp,vp_old,Nkl,options.KLgauss)))
%[elbo elbo_old]
%[elbo_sd elbo_sd_old]
% Keep warping only if it substantially improves ELBO
% and uncertainty does not blow up too much
if (elbo < (elbo_old + options.WarpTolImprovement)) || ...
(elbo_sd > (elbo_sd_old*options.WarpTolSDMultiplier + options.WarpTolSDBase))
% Undo input warping
vp = vp_old;
gp = gp_old;
optimState = optimState_old;
hypstruct = hypstruct_old;
% Still keep track of failed warping (failed warp counts twice)
optimState.WarpingCount = optimState.WarpingCount + 2;
optimState.LastWarping = optimState.iter;
if isempty(action); action = 'undo'; else; action = [action ', undo']; end
end
end
end
%% Actively sample new points into the training set
t = tic;
optimState.trinfo = vp.trinfo;
if iter == 1; new_funevals = options.FunEvalStart; else; new_funevals = options.FunEvalsPerIter; end
if optimState.Xn > 0
optimState.ymax = max(optimState.y(optimState.X_flag));
end
if optimState.SkipActiveSampling
optimState.SkipActiveSampling = false;
else
if ~isempty(gp) && options.SeparateSearchGP && ~options.VarActiveSample
% Train a distinct GP for active sampling
if mod(iter,2) == 0
meantemp = optimState.gpMeanfun;
optimState.gpMeanfun = 'const';
[gp_search,hypstruct_search] = gptrain_vbmc(hypstruct_search,optimState,stats,options);
optimState.gpMeanfun = meantemp;
else
gp_search = gp;
end
else
gp_search = gp;
end
% Performe active sampling
if options.VarActiveSample % Unused
% FIX TIMER HERE IF USING THIS
[optimState,vp,t_active,t_func] = ...
variationalactivesample_vbmc(optimState,new_funevals,funwrapper,vp,vp_old,gp_search,options);
else
optimState.hypstruct = hypstruct;
[optimState,vp,gp,timer] = ...
activesample_vbmc(optimState,new_funevals,funwrapper,vp,vp_old,gp_search,stats,timer,options);
hypstruct = optimState.hypstruct;
end
end
optimState.N = optimState.Xn; % Number of training inputs
optimState.Neff = sum(optimState.nevals(optimState.X_flag));
%% Train GP
t = tic;
[gp,hypstruct,Ns_gp,optimState] = ...
gptrain_vbmc(hypstruct,optimState,stats,options);
timer.gpTrain = timer.gpTrain + toc(t);
% Check if reached stable sampling regime
if Ns_gp == options.StableGPSamples && optimState.StopSampling == 0
optimState.StopSampling = optimState.N;
end
% if ~exist('wsabi_hyp','var'); wsabi_hyp = zeros(1,D+1); end
% priorMu = (optimState.PLB + optimState.PUB)/2;
% priorVar = diag(optimState.PUB - optimState.PLB);
% kernelVar = diag(exp(wsabi_hyp(2:end)));
% lambda = exp(wsabi_hyp(1));
% hypVar = [1e4,4*ones(1,D)];
% [log_mu,log_Var,~,~,~,wsabi_hyp] = wsabi_oneshot(...
% 'L',priorMu,priorVar,kernelVar,lambda,0.8,gp.X,gp.y,hypVar);
% log_mu
%% Optimize variational parameters
t = tic;
if ~vp.optimize_mu % Variational components fixed to training inputs
vp.mu = gp.X';
Knew = size(vp.mu,2);
else
% Update number of variational mixture components
Knew = updateK(optimState,stats,options);
end
% Decide number of fast/slow optimizations
Nfastopts = ceil(evaloption_vbmc(options.NSelbo,K));
if optimState.RecomputeVarPost || options.AlwaysRefitVarPost
Nslowopts = options.ElboStarts; % Full optimizations
optimState.RecomputeVarPost = false;
else
% Only incremental change from previous iteration
Nfastopts = ceil(Nfastopts * options.NSelboIncr);
Nslowopts = 1;
end
% Run optimization of variational parameters
if optimState.Warmup && options.BOWarmup
vp_fields = {'elbo','elbo_sd','G','H','varG','varH'};
for i = 1:numel(vp_fields); vp.stats.(vp_fields{i}) = NaN; end
varss = NaN;
pruned = 0;
% elseif Knew == vp.K && ~optimState.Warmup && vp.K >= 10
% [vp,varss] = vpoptimizeweights_vbmc(vp,gp,optimState,options,prnt);
% pruned = 0;
else
[vp,varss,pruned] = ...
vpoptimize_vbmc(Nfastopts,Nslowopts,vp,gp,Knew,optimState,options,prnt);
optimState.vp_repo{end+1} = get_vptheta(vp);
end
optimState.vpK = vp.K;
optimState.H = vp.stats.entropy; % Save current entropy
% Get real variational posterior (might differ from training posterior)
vp_real = vptrain2real(vp,0,options);
elbo = vp_real.stats.elbo;
elbo_sd = vp_real.stats.elbo_sd;
timer.variationalFit = timer.variationalFit + toc(t);
%% Plot current iteration (to be improved)
if options.Plot
vbmc_iterplot(vp,gp,optimState,stats,elbo);
end
%hh = [gp.post.hyp];
%exp(hh(gp.Ncov+gp.Nnoise+2:end,:))
%mubar
%Sigma
%----------------------------------------------------------------------
%% Finalize iteration
t = tic;
% Compute symmetrized KL-divergence between old and new posteriors
Nkl = 1e5;
sKL = max(0,0.5*sum(vbmc_kldiv(vp,vp_old,Nkl,options.KLgauss)));
% mtv = vbmc_mtv(vp,vp_old,Nkl)
% Evaluate max LCB of GP prediction on all training inputs
[~,~,fmu,fs2] = gplite_pred(gp,gp.X,gp.y,gp.s2);
optimState.lcbmax = max(fmu - options.ELCBOImproWeight*sqrt(fs2));
if options.AdaptiveEntropyAlpha
% Evaluate deterministic entropy
Hl = entlb_vbmc(vp,0,0);
Hu = entub_vbmc(vp,0,0);
optimState.entropy_alpha = max(0,min(1,(vp.stats.entropy - Hl)/(Hu - Hl)));
optimState.entropy_alpha
end
% Compare variational posterior's moments with ground truth
if ~isempty(options.TrueMean) && ~isempty(options.TrueCov) ...
&& all(isfinite(options.TrueMean(:))) ...
&& all(isfinite(options.TrueCov(:)))
[mubar_orig,Sigma_orig] = vbmc_moments(vp_real,1,1e6);
[kl(1),kl(2)] = mvnkl(mubar_orig,Sigma_orig,options.TrueMean,options.TrueCov);
sKL_true = 0.5*sum(kl)
else
sKL_true = [];
end
% Record moments in transformed space
[mubar,Sigma] = vbmc_moments(vp,0);
if isempty(optimState.RunMean) || isempty(optimState.RunCov)
optimState.RunMean = mubar(:);
optimState.RunCov = Sigma;
optimState.LastRunAvg = optimState.N;
% optimState.RunCorrection = 1;
else
Nnew = optimState.N - optimState.LastRunAvg;
wRun = options.MomentsRunWeight^Nnew;
optimState.RunMean = wRun*optimState.RunMean + (1-wRun)*mubar(:);
optimState.RunCov = wRun*optimState.RunCov + (1-wRun)*Sigma;
optimState.LastRunAvg = optimState.N;
% optimState.RunT = optimState.RunT + 1;
end
% t_fits(iter) = toc(timer_fits);
% dt = (t_active(iter)+t_fits(iter))/new_funevals;
timer.finalize = toc(t);
timer.totalruntime = NaN; % Update at the end of iteration
% timer
% Record all useful stats
stats = savestats(stats, ...
optimState,vp,elbo,elbo_sd,varss,sKL,sKL_true,gp,hypstruct.full,...
Ns_gp,pruned,timer,options.Diagnostics);
%----------------------------------------------------------------------
%% Check termination conditions and warmup
[optimState,stats,isFinished_flag,exitflag,action,msg] = ...
vbmc_termination(optimState,action,stats,options);
vp.stats.stable = stats.stable(optimState.iter); % Save stability
% Check if we are still warming-up
if optimState.Warmup && iter > 1
if options.RecomputeLCBmax
optimState.lcbmax_vec = recompute_lcbmax(gp,optimState,stats,options)';
end
[optimState,action,trim_flag] = vbmc_warmup(optimState,stats,action,options);
if trim_flag % Re-update GP after trimming
gp = gpreupdate(gp,optimState,options);
end
if ~optimState.Warmup
vp.optimize_mu = logical(options.VariableMeans);
vp.optimize_weights = logical(options.VariableWeights);
if options.BOWarmup
optimState.gpMeanfun = options.gpMeanFun;
hypstruct.hyp = [];
end
% Switch to main algorithm options
options = options_main;
hypstruct.runcov = []; % Reset GP hyperparameter covariance
optimState.vp_repo = []; % Reset VP repository
optimState.acqInfo = getAcqInfo(options.SearchAcqFcn); % Re-get acq info
end
end
stats.warmup(iter) = optimState.Warmup;
% Check and update fitness shaping / output warping threshold
if ~isempty(optimState.OutwarpDelta) && optimState.R < options.WarpTolReliability
Xrnd = vbmc_rnd(vp,2e4,0);
ymu = gplite_pred(gp,Xrnd,[],[],0,1);
ydelta = max([0,optimState.ymax-quantile(ymu,1e-3)])
if (ydelta > optimState.OutwarpDelta*options.OutwarpThreshTol) && (optimState.R < 1)
optimState.OutwarpDelta = optimState.OutwarpDelta*options.OutwarpThreshMult;
end
end
if options.AcqHedge % Update hedge values
optimState.hedge = acqhedge_vbmc('upd',optimState.hedge,stats,options);
end
%% Write iteration output
% vp.w
% Stopped GP sampling this iteration?
if Ns_gp == options.StableGPSamples && ...
stats.gpNsamples(max(1,iter-1)) > options.StableGPSamples
if Ns_gp == 0
if isempty(action); action = 'switch to GP opt'; else; action = [action ', switch to GP opt']; end
else
if isempty(action); action = 'stable GP sampling'; else; action = [action ', stable GP sampling']; end
end
end
if prnt > 2
if options.BOWarmup && optimState.Warmup
fprintf(displayFormat_warmup,iter,optimState.funccount,max(optimState.y_orig),action);
else
if optimState.Cache.active
fprintf(displayFormat,iter,optimState.funccount,optimState.cachecount,elbo,elbo_sd,sKL,vp.K,optimState.R,action);
elseif optimState.UncertaintyHandlingLevel > 0 && options.MaxRepeatedObservations > 0
fprintf(displayFormat,iter,optimState.funccount,optimState.N,elbo,elbo_sd,sKL,vp.K,optimState.R,action);
else
fprintf(displayFormat,iter,optimState.funccount,elbo,elbo_sd,sKL,vp.K,optimState.R,action);
end
end
end
stats.timer(iter).totalruntime = toc(t0);
end
vp_old = vp;
% Pick "best" variational solution to return (and real vp, if train vp differs)
[vp,elbo,elbo_sd,idx_best] = ...
best_vbmc(stats,iter,options.BestSafeSD,options.BestFracBack,options.RankCriterion,0);
new_final_vp_flag = idx_best ~= iter;
gp = stats.gp(idx_best);
vp.gp = gp; % Add GP to variational posterior
% Last variational optimization with large number of components
[vp,elbo,elbo_sd,changedflag] = finalboost_vbmc(vp,idx_best,optimState,stats,options);
if changedflag; new_final_vp_flag = true; end
if new_final_vp_flag && prnt > 2
% Recompute symmetrized KL-divergence
sKL = max(0,0.5*sum(vbmc_kldiv(vp,vp_old,Nkl,options.KLgauss)));
end
% Convert training variational posterior to real variational posterior
vp_train = vp;
vp = vptrain2real(vp_train,1);
elbo = vp.stats.elbo;
elbo_sd = vp.stats.elbo_sd;
if new_final_vp_flag && prnt > 2
if optimState.UncertaintyHandlingLevel > 0 && options.MaxRepeatedObservations > 0
fprintf(displayFormat,Inf,optimState.funccount,optimState.N,elbo,elbo_sd,sKL,vp.K,stats.rindex(idx_best),'finalize');
else
fprintf(displayFormat,Inf,optimState.funccount,elbo,elbo_sd,sKL,vp.K,stats.rindex(idx_best),'finalize');
end
end
% Set EXITFLAG based on stability (might check other things in the future)
switch exitflag
case 0
if vp.stats.stable; exitflag = 1; end
case 1
if ~vp.stats.stable; exitflag = 0; end
end
% Print final message
if prnt > 1
fprintf('\n%s\n', msg);
fprintf('Estimated ELBO: %.3f +/- %.3f.\n', elbo, elbo_sd);
if exitflag < 1
fprintf('Caution: Returned variational solution may have not converged.\n');
end
fprintf('\n');
end
if nargout > 4
output = vbmc_output(vp,optimState,msg,stats,idx_best,vbmc_version);
% Compute total running time and fractional overhead
optimState.totaltime = toc(t0);
output.overhead = optimState.totaltime / optimState.totalfunevaltime - 1;
end
if nargout > 5
% Prepare SAMPLES struct
idx = 1:optimState.Xn;
samples.X = optimState.X_orig(idx,:);
if isfield(optimState,'temperature') && ~isempty(optimState.temperature)
T = optimState.temperature;
else
T = 1;
end
samples.y = optimState.y_orig(idx,:)*T;
if isfield(optimState,'S') && ~isempty(optimState.S)
samples.y_sd = optimState.S(idx,:)*T;
end
samples.active_flag = optimState.X_flag(idx,:);
samples.nevals = optimState.nevals(idx,:);
end
if nargout > 7
% Remove GP from stats struct unless diagnostic run
if ~options.Diagnostics
stats = rmfield(stats,'gp');
stats = rmfield(stats,'gpHypFull');
stats.timer(iter).totalruntime = toc(t0);
end
end
if exitflag < 1 && options.RetryMaxFunEvals > 0
% Rerun VBMC with better initialization if first try did not work
if prnt > 0
fprintf('First attempt did not converge. Trying to rerun variational optimization.\n');
end
% Get better VBMC parameters and initialization from current run
vp0 = stats.vp(idx_best);
[x0,LB,UB,PLB,PUB,Xvp] = initFromVP(vp0,LB,UB,PLB,PUB,0);
Ninit = max(options.FunEvalStart,ceil(options.RetryMaxFunEvals/10));
x0 = [x0; robustSampleFromVP(vp0,Ninit-1,Xvp)];
options.FunEvalStart = Ninit;
options.MaxFunEvals = options.RetryMaxFunEvals;
options.RetryMaxFunEvals = 0; % Avoid infinite loop
options.SGDStepSize = 0.2*options.SGDStepSize; % Increase stability
options.ActiveSampleGPUpdate = true;
options.ActiveSampleVPUpdate = true;
try
[vp,elbo,elbo_sd,exitflag,output2,samples2,optimState2,stats] = vbmc(fun,x0,LB,UB,PLB,PUB,options,varargin{:});
if nargout > 4
optimState2.totaltime = toc(t0);
output2.overhead = optimState.totaltime / (optimState.totalfunevaltime + optimState2.totalfunevaltime) - 1;
output2.iterations = output2.iterations + output.iterations;
output2.funccount = output2.funccount + output.funccount;
output2.retried = 'yes';
samples = samples2;
output = output2;
optimState = optimState2;
end
catch retryException