As we saw in Notebooks 01 and 02, the Feature-Weight Least-Squares regression provides an apparently stable solution when comparing models trained on both 15,000 data points and only 1,500 data points.
In this notebook, we're going to systematically investigate how stable our model is for a range of N values and for a range of N / p values, where N is the number of data points and p is the number of features (columns in our design matrix).
In [1]:
%matplotlib widget
import numpy as np
import matplotlib.pyplot as plt
from puffins.tuner import Tuner
from puffins.weight_functions import matern32
from puffins.data import TimeSeries,LinearModel
from puffins.uncertainties import UncertaintyEstimator
from puffins.basis_functions import basis_constant, basis_linear
np.random.seed(42) # to enforce reproducibility
RCOND = 1e-14 # numerical rounding for matrix conditioning
plotnum=1
You know the routine, unpack the data, simulate some more or less realistic uncertainties, and tune our models hyperparameters.
In [2]:
time, flux = np.loadtxt('../data/ugru.dat').T
flux_err = np.random.normal(0,0.005,len(flux))
period = 1.88045
n_harmonics = 100
feature_weighting_width = 0.5
In [3]:
data = TimeSeries(time, flux)
fwls = LinearModel('fw', basis_functions=[basis_constant,], feature_embedding='fourier',
feature_weighting_function=matern32, feature_weighting_width=feature_weighting_width,
period=period, n_harmonics=100, W=None)
In [4]:
joint_ = {'feature_weighting_width': [0.001,1,'uniform'], 'period': [1.87,1.89,'uniform']}
joint_tuner = Tuner(fwls, hyperpars=joint_, n_trials=200, direction='minimize')
joint_tuner.run_tune(data.predictors, data.targets)
[I 2025-02-07 15:54:29,140] A new study created in memory with name: no-name-2a757be3-de70-4105-97a6-0ea6285f3701
[I 2025-02-07 15:54:29,347] Trial 0 finished with value: 0.008064062002777194 and parameters: {'feature_weighting_width': 0.8188915978670656, 'period': 1.8836499392174317}. Best is trial 0 with value: 0.008064062002777194.
[I 2025-02-07 15:54:29,403] Trial 1 finished with value: 0.006373484494001758 and parameters: {'feature_weighting_width': 0.6591947691592918, 'period': 1.886552538503014}. Best is trial 1 with value: 0.006373484494001758.
[I 2025-02-07 15:54:29,460] Trial 2 finished with value: 0.0030271459246547804 and parameters: {'feature_weighting_width': 0.3942211613451906, 'period': 1.886370930953886}. Best is trial 2 with value: 0.0030271459246547804.
[I 2025-02-07 15:54:29,515] Trial 3 finished with value: 0.007942995277065419 and parameters: {'feature_weighting_width': 0.6925813740539578, 'period': 1.8887509003449023}. Best is trial 2 with value: 0.0030271459246547804.
[I 2025-02-07 15:54:29,560] Trial 4 finished with value: 0.0072043365185428705 and parameters: {'feature_weighting_width': 0.78505222247783, 'period': 1.8812838126941789}. Best is trial 2 with value: 0.0030271459246547804.
[I 2025-02-07 15:54:29,625] Trial 5 finished with value: 0.006105916522176777 and parameters: {'feature_weighting_width': 0.5802597733984258, 'period': 1.8728790955422987}. Best is trial 2 with value: 0.0030271459246547804.
[I 2025-02-07 15:54:29,671] Trial 6 finished with value: 0.002085723372299212 and parameters: {'feature_weighting_width': 0.34979333973718396, 'period': 1.8756127461479013}. Best is trial 6 with value: 0.002085723372299212.
[I 2025-02-07 15:54:29,729] Trial 7 finished with value: 0.008457142977786523 and parameters: {'feature_weighting_width': 0.83031583106121, 'period': 1.8846264462270432}. Best is trial 6 with value: 0.002085723372299212.
[I 2025-02-07 15:54:29,775] Trial 8 finished with value: 0.0029838007825030727 and parameters: {'feature_weighting_width': 0.45343384855235724, 'period': 1.8853498190347735}. Best is trial 6 with value: 0.002085723372299212.
[I 2025-02-07 15:54:29,827] Trial 9 finished with value: 0.00721814407101561 and parameters: {'feature_weighting_width': 0.6295556181846681, 'period': 1.8889335823753646}. Best is trial 6 with value: 0.002085723372299212.
[I 2025-02-07 15:54:29,890] Trial 10 finished with value: 0.00238085330777819 and parameters: {'feature_weighting_width': 0.11052847728838802, 'period': 1.8745175399639724}. Best is trial 6 with value: 0.002085723372299212.
[I 2025-02-07 15:54:29,962] Trial 11 finished with value: 0.0022312906004276416 and parameters: {'feature_weighting_width': 0.08823723748401532, 'period': 1.8747227229661367}. Best is trial 6 with value: 0.002085723372299212.
[I 2025-02-07 15:54:30,019] Trial 12 finished with value: 0.0010110101851516908 and parameters: {'feature_weighting_width': 0.025140606460268958, 'period': 1.8766882255482313}. Best is trial 12 with value: 0.0010110101851516908.
[I 2025-02-07 15:54:30,078] Trial 13 finished with value: 0.0005956661850664694 and parameters: {'feature_weighting_width': 0.24766836208996956, 'period': 1.8778514502526173}. Best is trial 13 with value: 0.0005956661850664694.
[I 2025-02-07 15:54:30,140] Trial 14 finished with value: 0.0004952171490117192 and parameters: {'feature_weighting_width': 0.20677834074298718, 'period': 1.8779628395401353}. Best is trial 14 with value: 0.0004952171490117192.
[I 2025-02-07 15:54:30,194] Trial 15 finished with value: 0.00023186695322567665 and parameters: {'feature_weighting_width': 0.24270391240490938, 'period': 1.8791454445545572}. Best is trial 15 with value: 0.00023186695322567665.
[I 2025-02-07 15:54:30,250] Trial 16 finished with value: 0.00012049650049861055 and parameters: {'feature_weighting_width': 0.23431961960735917, 'period': 1.8798351548782721}. Best is trial 16 with value: 0.00012049650049861055.
[I 2025-02-07 15:54:30,311] Trial 17 finished with value: 0.012841598627759989 and parameters: {'feature_weighting_width': 0.9921050674826919, 'period': 1.8701366367700898}. Best is trial 16 with value: 0.00012049650049861055.
[I 2025-02-07 15:54:30,373] Trial 18 finished with value: 0.00017609031491335443 and parameters: {'feature_weighting_width': 0.2582682503549413, 'period': 1.88112863371848}. Best is trial 16 with value: 0.00012049650049861055.
[I 2025-02-07 15:54:30,433] Trial 19 finished with value: 0.0006461838506978412 and parameters: {'feature_weighting_width': 0.3467326818476594, 'period': 1.881498777371936}. Best is trial 16 with value: 0.00012049650049861055.
[I 2025-02-07 15:54:30,494] Trial 20 finished with value: 0.0024754744628271465 and parameters: {'feature_weighting_width': 0.49905619030579446, 'period': 1.882278256549436}. Best is trial 16 with value: 0.00012049650049861055.
[I 2025-02-07 15:54:30,553] Trial 21 finished with value: 0.00019405120607973462 and parameters: {'feature_weighting_width': 0.24316647788926177, 'period': 1.8793737982028773}. Best is trial 16 with value: 0.00012049650049861055.
[I 2025-02-07 15:54:30,615] Trial 22 finished with value: 2.8792142984504802e-05 and parameters: {'feature_weighting_width': 0.17774263968774393, 'period': 1.8804324958569796}. Best is trial 22 with value: 2.8792142984504802e-05.
[I 2025-02-07 15:54:30,671] Trial 23 finished with value: 1.3956918651367865e-05 and parameters: {'feature_weighting_width': 0.1405184865517115, 'period': 1.8804333850358952}. Best is trial 23 with value: 1.3956918651367865e-05.
[I 2025-02-07 15:54:30,735] Trial 24 finished with value: 0.0005268476780639033 and parameters: {'feature_weighting_width': 0.13767451339655454, 'period': 1.8831571503802629}. Best is trial 23 with value: 1.3956918651367865e-05.
[I 2025-02-07 15:54:30,806] Trial 25 finished with value: 1.803849090081e-05 and parameters: {'feature_weighting_width': 0.03422658475933475, 'period': 1.8800721260263742}. Best is trial 23 with value: 1.3956918651367865e-05.
[I 2025-02-07 15:54:30,882] Trial 26 finished with value: 0.00048084505708285416 and parameters: {'feature_weighting_width': 0.04318976360358645, 'period': 1.8778954581979972}. Best is trial 23 with value: 1.3956918651367865e-05.
[I 2025-02-07 15:54:30,948] Trial 27 finished with value: 0.0004286729407925378 and parameters: {'feature_weighting_width': 0.1317022620124419, 'period': 1.8828852482694824}. Best is trial 23 with value: 1.3956918651367865e-05.
[I 2025-02-07 15:54:31,013] Trial 28 finished with value: 6.862860617488133e-06 and parameters: {'feature_weighting_width': 0.008241255894107902, 'period': 1.8804005746493018}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:31,084] Trial 29 finished with value: 0.0009024999150160435 and parameters: {'feature_weighting_width': 0.011269502589766283, 'period': 1.8840363180784037}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:31,143] Trial 30 finished with value: 0.0011955525531693446 and parameters: {'feature_weighting_width': 0.06958519553206857, 'period': 1.8763429575968584}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:31,209] Trial 31 finished with value: 2.388883665854922e-05 and parameters: {'feature_weighting_width': 0.16881125942957528, 'period': 1.8804682796921437}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:31,366] Trial 32 finished with value: 0.0002709370449161057 and parameters: {'feature_weighting_width': 0.16706710233748762, 'period': 1.8786068545996983}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:31,434] Trial 33 finished with value: 8.889126222161747e-06 and parameters: {'feature_weighting_width': 0.0054361968216724565, 'period': 1.880288233813678}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:31,506] Trial 34 finished with value: 0.00023453481597156026 and parameters: {'feature_weighting_width': 0.016432163427764705, 'period': 1.8822444443504007}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:31,989] Trial 35 finished with value: 1.1739037030153577e-05 and parameters: {'feature_weighting_width': 0.08358697633976851, 'period': 1.880228804112506}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,094] Trial 36 finished with value: 8.718681016906019e-05 and parameters: {'feature_weighting_width': 0.09700904584506992, 'period': 1.8815129138885898}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,172] Trial 37 finished with value: 0.00301650458878615 and parameters: {'feature_weighting_width': 0.31298811740985555, 'period': 1.8869964540721107}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,256] Trial 38 finished with value: 0.0015152301215815521 and parameters: {'feature_weighting_width': 0.0024585996976164786, 'period': 1.8851496522531876}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,336] Trial 39 finished with value: 0.0020198345234366376 and parameters: {'feature_weighting_width': 0.4232578549024719, 'period': 1.8769934005779987}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,416] Trial 40 finished with value: 0.000661609952078533 and parameters: {'feature_weighting_width': 0.08254311872784241, 'period': 1.883504986820158}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,513] Trial 41 finished with value: 1.3851292398733002e-05 and parameters: {'feature_weighting_width': 0.07944947774001773, 'period': 1.880171423878018}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,572] Trial 42 finished with value: 0.00022712410926682436 and parameters: {'feature_weighting_width': 0.12666547282864654, 'period': 1.87873591764255}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,649] Trial 43 finished with value: 2.5060792135609582e-05 and parameters: {'feature_weighting_width': 0.05704989960276523, 'period': 1.8809663319575043}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:32,889] Trial 44 finished with value: 0.00019390783474966197 and parameters: {'feature_weighting_width': 0.18825956905795754, 'period': 1.8819581074239893}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,222] Trial 45 finished with value: 4.235661972965558e-05 and parameters: {'feature_weighting_width': 0.06507850550519523, 'period': 1.879771924067094}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,489] Trial 46 finished with value: 0.0010383503035142625 and parameters: {'feature_weighting_width': 0.3157698274173394, 'period': 1.8773202053720268}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,572] Trial 47 finished with value: 0.007164353144339664 and parameters: {'feature_weighting_width': 0.7231314961671341, 'period': 1.8749782809965594}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,664] Trial 48 finished with value: 0.0034827275057009296 and parameters: {'feature_weighting_width': 0.5648985234785217, 'period': 1.8787443647865285}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,734] Trial 49 finished with value: 0.003144158808478662 and parameters: {'feature_weighting_width': 0.11484357008191493, 'period': 1.873534575774085}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,809] Trial 50 finished with value: 0.0014000296567981767 and parameters: {'feature_weighting_width': 0.14850036345479434, 'period': 1.875993033560351}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,866] Trial 51 finished with value: 7.669786393540319e-06 and parameters: {'feature_weighting_width': 0.042686795687090794, 'period': 1.8803530396516184}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,924] Trial 52 finished with value: 1.1052072632516963e-05 and parameters: {'feature_weighting_width': 0.07630431291802109, 'period': 1.8806927608559185}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:33,978] Trial 53 finished with value: 0.0052545565712945235 and parameters: {'feature_weighting_width': 0.004182690143954949, 'period': 1.8898133257170384}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,041] Trial 54 finished with value: 0.00030134833851473117 and parameters: {'feature_weighting_width': 0.07841505196794477, 'period': 1.882490270104716}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,100] Trial 55 finished with value: 7.420534391407847e-05 and parameters: {'feature_weighting_width': 0.05106513292221345, 'period': 1.8795057263521646}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,151] Trial 56 finished with value: 0.009112214060804381 and parameters: {'feature_weighting_width': 0.8981006203094288, 'period': 1.8810756751953654}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,214] Trial 57 finished with value: 0.00045366738990379934 and parameters: {'feature_weighting_width': 0.20898111337131678, 'period': 1.8780916080014107}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,296] Trial 58 finished with value: 0.00031196609000311797 and parameters: {'feature_weighting_width': 0.27877959201110675, 'period': 1.8816844962664911}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,366] Trial 59 finished with value: 0.001000729578261982 and parameters: {'feature_weighting_width': 0.09697281762125874, 'period': 1.884232676912549}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,423] Trial 60 finished with value: 1.4271073551601071e-05 and parameters: {'feature_weighting_width': 0.040708336003246956, 'period': 1.8807900807191809}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,484] Trial 61 finished with value: 1.4326416533090718e-05 and parameters: {'feature_weighting_width': 0.09805122438165914, 'period': 1.8801775057762595}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,543] Trial 62 finished with value: 5.0365004244204715e-05 and parameters: {'feature_weighting_width': 0.1380187606709059, 'period': 1.8797520864119797}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,616] Trial 63 finished with value: 6.950200565531377e-06 and parameters: {'feature_weighting_width': 0.04748397508658325, 'period': 1.8805149028129897}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,860] Trial 64 finished with value: 0.0001579920107223406 and parameters: {'feature_weighting_width': 0.0373736429478834, 'period': 1.8790238676798956}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:34,949] Trial 65 finished with value: 0.0003244708448796804 and parameters: {'feature_weighting_width': 0.003284137188691652, 'period': 1.8783680077726603}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:35,026] Trial 66 finished with value: 0.000704922503396296 and parameters: {'feature_weighting_width': 0.2026048696756398, 'period': 1.877407817077096}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:35,088] Trial 67 finished with value: 0.0005142944047975256 and parameters: {'feature_weighting_width': 0.05841723270414188, 'period': 1.8831345456893835}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:35,149] Trial 68 finished with value: 0.00011382266644827894 and parameters: {'feature_weighting_width': 0.08671999092145945, 'period': 1.8792577132324548}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:35,228] Trial 69 finished with value: 0.00011068994312285206 and parameters: {'feature_weighting_width': 0.15601054750664314, 'period': 1.881600503075556}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:35,291] Trial 70 finished with value: 0.00031607997171053753 and parameters: {'feature_weighting_width': 0.11602380579381194, 'period': 1.8825353855204203}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:35,361] Trial 71 finished with value: 7.79974777630573e-06 and parameters: {'feature_weighting_width': 0.029964959406708166, 'period': 1.8805973601891464}. Best is trial 28 with value: 6.862860617488133e-06.
[I 2025-02-07 15:54:35,426] Trial 72 finished with value: 6.567049932475663e-06 and parameters: {'feature_weighting_width': 0.029615401409264518, 'period': 1.880469603963969}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,479] Trial 73 finished with value: 1.3105301273477492e-05 and parameters: {'feature_weighting_width': 0.028911903379668664, 'period': 1.8807667852974308}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,540] Trial 74 finished with value: 6.567106468444795e-06 and parameters: {'feature_weighting_width': 0.02694215468082254, 'period': 1.8804537390600802}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,600] Trial 75 finished with value: 6.961831991707147e-05 and parameters: {'feature_weighting_width': 0.030140678480412842, 'period': 1.8813980715737628}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,668] Trial 76 finished with value: 0.00524303141428184 and parameters: {'feature_weighting_width': 0.005131086723929049, 'period': 1.8711604400014819}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,722] Trial 77 finished with value: 1.0743035283285539e-05 and parameters: {'feature_weighting_width': 0.051221796701380246, 'period': 1.8806986648596535}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,787] Trial 78 finished with value: 0.0001098586027905567 and parameters: {'feature_weighting_width': 0.03414637269643381, 'period': 1.8792765516417043}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,851] Trial 79 finished with value: 3.269789309004642e-05 and parameters: {'feature_weighting_width': 0.111615861335355, 'period': 1.8798989062217102}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,919] Trial 80 finished with value: 0.00018725696721821623 and parameters: {'feature_weighting_width': 0.049986126419698504, 'period': 1.882047482545702}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:35,976] Trial 81 finished with value: 3.45211628011264e-05 and parameters: {'feature_weighting_width': 0.06028890038011056, 'period': 1.8810825733659784}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,043] Trial 82 finished with value: 7.055408050439829e-06 and parameters: {'feature_weighting_width': 0.0016670157135253993, 'period': 1.8805520618229492}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,098] Trial 83 finished with value: 0.00036407806028203484 and parameters: {'feature_weighting_width': 0.019433791528220286, 'period': 1.8826989817675255}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,186] Trial 84 finished with value: 6.5914107385164494e-06 and parameters: {'feature_weighting_width': 0.02560837756678179, 'period': 1.8804432524417485}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,253] Trial 85 finished with value: 0.00013979146278613532 and parameters: {'feature_weighting_width': 0.0024494707768412116, 'period': 1.8818228230799638}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,312] Trial 86 finished with value: 0.00017722477025215342 and parameters: {'feature_weighting_width': 0.025057732422635103, 'period': 1.8789341162864173}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,377] Trial 87 finished with value: 4.1125383565383004e-05 and parameters: {'feature_weighting_width': 0.12006758536307817, 'period': 1.879814251537107}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,435] Trial 88 finished with value: 9.624142205936252e-06 and parameters: {'feature_weighting_width': 0.06648829788075328, 'period': 1.8802834886600273}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,492] Trial 89 finished with value: 0.0026812946025281453 and parameters: {'feature_weighting_width': 0.5055771071913453, 'period': 1.8781854417477843}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,553] Trial 90 finished with value: 7.777735823265033e-05 and parameters: {'feature_weighting_width': 0.09917454312340519, 'period': 1.879488750597042}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,614] Trial 91 finished with value: 7.76080263400674e-06 and parameters: {'feature_weighting_width': 0.07350161275904848, 'period': 1.8803887474407135}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,678] Trial 92 finished with value: 4.931864522913784e-05 and parameters: {'feature_weighting_width': 0.027004897581459072, 'period': 1.8812333850186396}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,736] Trial 93 finished with value: 7.1584627743964224e-06 and parameters: {'feature_weighting_width': 0.06632842154132279, 'period': 1.8804548465322617}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,795] Trial 94 finished with value: 0.00017799335989568746 and parameters: {'feature_weighting_width': 0.07330163364434443, 'period': 1.8820052001697387}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,853] Trial 95 finished with value: 1.5589792019905528e-05 and parameters: {'feature_weighting_width': 0.1466558615508035, 'period': 1.8805062319440142}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,919] Trial 96 finished with value: 9.60972993777275e-05 and parameters: {'feature_weighting_width': 0.17535411324073422, 'period': 1.8814477448647937}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:36,986] Trial 97 finished with value: 5.920779224287027e-05 and parameters: {'feature_weighting_width': 0.04734048796290022, 'period': 1.879619449652347}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,044] Trial 98 finished with value: 0.0002283545319975106 and parameters: {'feature_weighting_width': 0.09155585792630053, 'period': 1.8787200328929738}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,117] Trial 99 finished with value: 0.005219250615721393 and parameters: {'feature_weighting_width': 0.6732508613105528, 'period': 1.8810921583521176}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,210] Trial 100 finished with value: 0.0009114583737671798 and parameters: {'feature_weighting_width': 0.3856728647664163, 'period': 1.880178946425833}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,281] Trial 101 finished with value: 9.068413668898905e-06 and parameters: {'feature_weighting_width': 0.023244938031555383, 'period': 1.8806534878245038}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,344] Trial 102 finished with value: 3.079443034389387e-05 and parameters: {'feature_weighting_width': 0.061930759643827535, 'period': 1.879896828201906}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,409] Trial 103 finished with value: 0.00011227060427297643 and parameters: {'feature_weighting_width': 0.0020323570690341693, 'period': 1.8792625139766554}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,463] Trial 104 finished with value: 6.958243939874426e-06 and parameters: {'feature_weighting_width': 0.038334846496395895, 'period': 1.8804026343079348}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,537] Trial 105 finished with value: 0.0002530959268370042 and parameters: {'feature_weighting_width': 0.10507456341108708, 'period': 1.8823117524967519}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,604] Trial 106 finished with value: 0.0005743493668547534 and parameters: {'feature_weighting_width': 0.040869687201582426, 'period': 1.8832912610925183}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,670] Trial 107 finished with value: 0.0005830444614310508 and parameters: {'feature_weighting_width': 0.07535025025278061, 'period': 1.877626970107295}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,744] Trial 108 finished with value: 0.0002917503770212161 and parameters: {'feature_weighting_width': 0.12192169434575933, 'period': 1.8784895462571114}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,816] Trial 109 finished with value: 6.6091239923994884e-06 and parameters: {'feature_weighting_width': 0.020823827410016444, 'period': 1.8804989171936322}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,873] Trial 110 finished with value: 5.68191453529028e-05 and parameters: {'feature_weighting_width': 0.04767933009577095, 'period': 1.8812968785538642}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,926] Trial 111 finished with value: 6.740423275180199e-06 and parameters: {'feature_weighting_width': 0.018720722337801525, 'period': 1.8805205378731744}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:37,998] Trial 112 finished with value: 1.7153829233339828e-05 and parameters: {'feature_weighting_width': 0.020580661560896378, 'period': 1.8800866846101607}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,062] Trial 113 finished with value: 2.6521306023430286e-05 and parameters: {'feature_weighting_width': 0.0799015137644487, 'period': 1.8809799633098412}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,129] Trial 114 finished with value: 6.037366828342422e-05 and parameters: {'feature_weighting_width': 0.05730528375698884, 'period': 1.8796110871329692}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,525] Trial 115 finished with value: 0.0001133249699970813 and parameters: {'feature_weighting_width': 0.0010313871314010029, 'period': 1.881679926183328}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,603] Trial 116 finished with value: 8.142859403928873e-06 and parameters: {'feature_weighting_width': 0.09473917980100698, 'period': 1.8804274901907756}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,693] Trial 117 finished with value: 0.00016337874021092182 and parameters: {'feature_weighting_width': 0.020870662901464762, 'period': 1.8789980910051125}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,752] Trial 118 finished with value: 1.6906124953768287e-05 and parameters: {'feature_weighting_width': 0.044292426971100377, 'period': 1.8808410383311303}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,814] Trial 119 finished with value: 0.008137878099068194 and parameters: {'feature_weighting_width': 0.8399197467165274, 'period': 1.8801009706424658}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,864] Trial 120 finished with value: 6.657128464579186e-05 and parameters: {'feature_weighting_width': 0.06891762981866237, 'period': 1.8813722567268651}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,933] Trial 121 finished with value: 8.32287705836982e-06 and parameters: {'feature_weighting_width': 0.02889084555833154, 'period': 1.880622774549822}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:38,981] Trial 122 finished with value: 8.391576360332654e-05 and parameters: {'feature_weighting_width': 0.035349308894513695, 'period': 1.879437655302927}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,064] Trial 123 finished with value: 7.093997133054524e-06 and parameters: {'feature_weighting_width': 0.02010281944103126, 'period': 1.8803803692651344}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,114] Trial 124 finished with value: 0.0027097075782735176 and parameters: {'feature_weighting_width': 0.0010122473019684962, 'period': 1.8868693212943195}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,175] Trial 125 finished with value: 0.00016910753603414718 and parameters: {'feature_weighting_width': 0.06077104937654136, 'period': 1.8819649958684248}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,235] Trial 126 finished with value: 3.0179935456451437e-05 and parameters: {'feature_weighting_width': 0.08508151909062368, 'period': 1.8799108900402068}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,298] Trial 127 finished with value: 0.004178863857743535 and parameters: {'feature_weighting_width': 0.614675484785809, 'period': 1.880330315744757}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,348] Trial 128 finished with value: 4.0216354150850135e-05 and parameters: {'feature_weighting_width': 0.1320812648032172, 'period': 1.8810921520587218}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,401] Trial 129 finished with value: 0.000107859717904703 and parameters: {'feature_weighting_width': 0.016465273607867002, 'period': 1.881648314392276}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,457] Trial 130 finished with value: 0.0004121985648021591 and parameters: {'feature_weighting_width': 0.0466767334985947, 'period': 1.8828466385216902}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,525] Trial 131 finished with value: 7.0897110194279764e-06 and parameters: {'feature_weighting_width': 0.02187385513701896, 'period': 1.8805543897524566}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,585] Trial 132 finished with value: 6.834027924146657e-06 and parameters: {'feature_weighting_width': 0.018404508796711624, 'period': 1.8805315136499376}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,661] Trial 133 finished with value: 2.2178897623111206e-05 and parameters: {'feature_weighting_width': 0.02302084148589882, 'period': 1.880930220872941}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:39,936] Trial 134 finished with value: 0.010630469238991698 and parameters: {'feature_weighting_width': 0.9905037498119194, 'period': 1.8790640743259512}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,032] Trial 135 finished with value: 5.941795734920949e-05 and parameters: {'feature_weighting_width': 0.043025719538026266, 'period': 1.8796173699685805}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,126] Trial 136 finished with value: 2.502205018552143e-05 and parameters: {'feature_weighting_width': 0.011457909382991873, 'period': 1.8799648310191701}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,173] Trial 137 finished with value: 1.3596368078188373e-05 and parameters: {'feature_weighting_width': 0.10525887549196987, 'period': 1.8807286510210706}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,241] Trial 138 finished with value: 5.0628577024945116e-05 and parameters: {'feature_weighting_width': 0.06181023143818557, 'period': 1.8812420908025205}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,311] Trial 139 finished with value: 0.00026479792318884595 and parameters: {'feature_weighting_width': 0.0013077354440671693, 'period': 1.8823600000459484}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,384] Trial 140 finished with value: 6.9600954082386235e-06 and parameters: {'feature_weighting_width': 0.031533341382223, 'period': 1.8803955467942612}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,441] Trial 141 finished with value: 6.7627856359905554e-06 and parameters: {'feature_weighting_width': 0.034233754898526696, 'period': 1.8805143457860483}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,489] Trial 142 finished with value: 6.708171026210416e-06 and parameters: {'feature_weighting_width': 0.03122237964516545, 'period': 1.8804253896647003}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,550] Trial 143 finished with value: 3.977475983310455e-05 and parameters: {'feature_weighting_width': 0.02765411832885406, 'period': 1.8797933331003318}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,608] Trial 144 finished with value: 0.0001006944998642536 and parameters: {'feature_weighting_width': 0.020496143118782686, 'period': 1.879330727551221}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,661] Trial 145 finished with value: 2.023383089674715e-05 and parameters: {'feature_weighting_width': 0.04312987120794025, 'period': 1.880898098041517}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,723] Trial 146 finished with value: 1.3138286676340005e-05 and parameters: {'feature_weighting_width': 0.08520992216715093, 'period': 1.8801927985615658}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,777] Trial 147 finished with value: 0.00010247245461389124 and parameters: {'feature_weighting_width': 0.0011229918502323431, 'period': 1.881616323570437}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,832] Trial 148 finished with value: 0.006290009022717868 and parameters: {'feature_weighting_width': 0.7342159517685257, 'period': 1.8804950956212458}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,889] Trial 149 finished with value: 5.2198651928249215e-05 and parameters: {'feature_weighting_width': 0.0364163060795147, 'period': 1.8812584619425416}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:40,954] Trial 150 finished with value: 5.8618461307682226e-05 and parameters: {'feature_weighting_width': 0.05712866412525813, 'period': 1.8796252891220238}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,010] Trial 151 finished with value: 7.2924097022502445e-06 and parameters: {'feature_weighting_width': 0.06741179344561818, 'period': 1.8805090034326106}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,075] Trial 152 finished with value: 1.8121209910732058e-05 and parameters: {'feature_weighting_width': 0.03171611702511484, 'period': 1.8808650524354547}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,152] Trial 153 finished with value: 1.4255120926914475e-05 and parameters: {'feature_weighting_width': 0.018326777905444302, 'period': 1.8801428136762839}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,209] Trial 154 finished with value: 2.483517680384988e-05 and parameters: {'feature_weighting_width': 0.04768508403729268, 'period': 1.879970374468807}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,266] Trial 155 finished with value: 0.00014161815744715892 and parameters: {'feature_weighting_width': 0.07964900222804108, 'period': 1.8818300318498715}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,319] Trial 156 finished with value: 6.928898529196537e-06 and parameters: {'feature_weighting_width': 0.018202731572719646, 'period': 1.8805409730916967}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,378] Trial 157 finished with value: 0.00018882771845258505 and parameters: {'feature_weighting_width': 0.016431415141021723, 'period': 1.878882416246397}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,429] Trial 158 finished with value: 1.2181133035845326e-05 and parameters: {'feature_weighting_width': 0.040786761873266825, 'period': 1.8807420774811516}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,493] Trial 159 finished with value: 6.534038424129223e-05 and parameters: {'feature_weighting_width': 0.017258201901797963, 'period': 1.8813659575507138}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,540] Trial 160 finished with value: 8.457121473224387e-05 and parameters: {'feature_weighting_width': 0.05644781954337176, 'period': 1.8794345459853667}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,596] Trial 161 finished with value: 7.115996277857852e-06 and parameters: {'feature_weighting_width': 0.03143867565712856, 'period': 1.8803819747117638}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,654] Trial 162 finished with value: 1.0728198452591054e-05 and parameters: {'feature_weighting_width': 0.03036879778912036, 'period': 1.880229257641139}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,709] Trial 163 finished with value: 2.856618547236273e-05 and parameters: {'feature_weighting_width': 0.0015001523669131989, 'period': 1.8810168171942354}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,760] Trial 164 finished with value: 3.624599357236557e-05 and parameters: {'feature_weighting_width': 0.047398019496023555, 'period': 1.8798321098537418}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,827] Trial 165 finished with value: 6.719524428289703e-06 and parameters: {'feature_weighting_width': 0.017726727862910328, 'period': 1.880517842792238}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,883] Trial 166 finished with value: 1.0662034477323112e-05 and parameters: {'feature_weighting_width': 0.017328613507340822, 'period': 1.880705159968819}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:41,950] Trial 167 finished with value: 7.29092494223879e-05 and parameters: {'feature_weighting_width': 0.07058129684143338, 'period': 1.8814192455807064}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,009] Trial 168 finished with value: 0.00012445176923458071 and parameters: {'feature_weighting_width': 0.09206945822743949, 'period': 1.879199304967126}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,064] Trial 169 finished with value: 2.4586525228715665e-05 and parameters: {'feature_weighting_width': 0.055072650859550695, 'period': 1.879975482304911}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,129] Trial 170 finished with value: 0.0023627974156798966 and parameters: {'feature_weighting_width': 0.49413982720766914, 'period': 1.882042507285122}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,199] Trial 171 finished with value: 6.722757020281946e-06 and parameters: {'feature_weighting_width': 0.029105982785593638, 'period': 1.8804210152691758}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,253] Trial 172 finished with value: 6.5828969108696726e-06 and parameters: {'feature_weighting_width': 0.0038948327291780382, 'period': 1.8804935458922591}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,319] Trial 173 finished with value: 2.593847850966743e-05 and parameters: {'feature_weighting_width': 0.0015946340956330407, 'period': 1.8809829791006614}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,370] Trial 174 finished with value: 6.819564123966146e-06 and parameters: {'feature_weighting_width': 0.03537110637445699, 'period': 1.88052056477033}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,439] Trial 175 finished with value: 6.511884654902958e-05 and parameters: {'feature_weighting_width': 0.04391716630297342, 'period': 1.8795725162999752}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,503] Trial 176 finished with value: 3.132684818233623e-05 and parameters: {'feature_weighting_width': 0.0359555556636987, 'period': 1.8810495193786194}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,560] Trial 177 finished with value: 1.8278267431442436e-05 and parameters: {'feature_weighting_width': 0.07623313449030322, 'period': 1.8800806916850752}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,613] Trial 178 finished with value: 9.499529278521139e-06 and parameters: {'feature_weighting_width': 0.058468616637492976, 'period': 1.880653387214627}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,672] Trial 179 finished with value: 9.370794619814833e-05 and parameters: {'feature_weighting_width': 0.0013788399195566806, 'period': 1.8815623194236466}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,728] Trial 180 finished with value: 1.3695726682725092e-05 and parameters: {'feature_weighting_width': 0.10602642234091558, 'period': 1.8802063180573048}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,791] Trial 181 finished with value: 6.857030417744738e-06 and parameters: {'feature_weighting_width': 0.01772642908716727, 'period': 1.880533965717506}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,852] Trial 182 finished with value: 1.0772026610234305e-05 and parameters: {'feature_weighting_width': 0.022568825525049116, 'period': 1.8807081650680202}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,908] Trial 183 finished with value: 4.177890857184264e-05 and parameters: {'feature_weighting_width': 0.03988510397645817, 'period': 1.8797740414489903}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:42,964] Trial 184 finished with value: 3.5409519583715116e-05 and parameters: {'feature_weighting_width': 0.01877442390160451, 'period': 1.8810964867599225}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,031] Trial 185 finished with value: 7.64542871756608e-06 and parameters: {'feature_weighting_width': 0.05596098720945125, 'period': 1.8803694561197115}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,081] Trial 186 finished with value: 2.9594856863348696e-05 and parameters: {'feature_weighting_width': 0.03742466162275986, 'period': 1.8799070094858163}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,146] Trial 187 finished with value: 5.148946445144624e-05 and parameters: {'feature_weighting_width': 0.001811497504940085, 'period': 1.8812527258630674}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,435] Trial 188 finished with value: 7.492602407265556e-06 and parameters: {'feature_weighting_width': 0.020427342751772576, 'period': 1.880581907882163}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,499] Trial 189 finished with value: 0.00010210931360940024 and parameters: {'feature_weighting_width': 0.0697738855900236, 'period': 1.8793244266068359}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,561] Trial 190 finished with value: 9.574954575036898e-06 and parameters: {'feature_weighting_width': 0.03822442239522984, 'period': 1.8802675324198954}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,644] Trial 191 finished with value: 1.540660027761826e-05 and parameters: {'feature_weighting_width': 0.01866320765021054, 'period': 1.8808159404961273}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,731] Trial 192 finished with value: 7.2017070349509214e-06 and parameters: {'feature_weighting_width': 0.025365865876608742, 'period': 1.8805622215841882}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,792] Trial 193 finished with value: 4.965599048075361e-05 and parameters: {'feature_weighting_width': 0.003226808978895518, 'period': 1.8796992510265476}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,856] Trial 194 finished with value: 1.3324682103273025e-05 and parameters: {'feature_weighting_width': 0.052426798868330016, 'period': 1.8801703645531442}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,914] Trial 195 finished with value: 2.1781318102632272e-05 and parameters: {'feature_weighting_width': 0.02989701799618119, 'period': 1.88092396122092}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:43,976] Trial 196 finished with value: 7.699633421407557e-05 and parameters: {'feature_weighting_width': 0.00105778723935308, 'period': 1.8814513227596517}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:44,036] Trial 197 finished with value: 0.003413298136603899 and parameters: {'feature_weighting_width': 0.05419705892054592, 'period': 1.8877455756552162}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:44,103] Trial 198 finished with value: 7.689750611472777e-06 and parameters: {'feature_weighting_width': 0.08567658328140851, 'period': 1.880491149402599}. Best is trial 72 with value: 6.567049932475663e-06.
[I 2025-02-07 15:54:44,161] Trial 199 finished with value: 3.73125711729922e-05 and parameters: {'feature_weighting_width': 0.03365497696268553, 'period': 1.881116484684637}. Best is trial 72 with value: 6.567049932475663e-06.
In [5]:
print(joint_tuner)
fwls.set_X_kwargs(update=True, **joint_tuner.best_hyperpars)
fwls.set_X_train(data.predictors)
fwls.train(data.targets)
Tuner: feature_weighting_width: 0.029615401409264518 period: 1.880469603963969
Great, now we have our model that was tuned to 100% of the data.
First, at fixed p = 2 * n_harmonics + 1 = 201, we'll explore how the regression coefficients behave for decreasing N, in 5% increments.
In [6]:
n = len(time)
coefficients_i = []
means_i = []
vars_i = []
step_size = int(n * 0.05)
estimator = UncertaintyEstimator(data, fwls)
for step in range(step_size, n - step_size + 1, step_size):
ddjk_i = estimator.run_delete_d_jackknife_sampling(n_groups=500, n_delete=step)
coefficients_i.append(ddjk_i['sampled_coefs'])
means_i.append(ddjk_i['coefs_mean'])
vars_i.append(ddjk_i['coefs_var'])
Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:33<00:00, 15.10it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:27<00:00, 18.14it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:23<00:00, 21.41it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:24<00:00, 20.27it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:21<00:00, 23.45it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:20<00:00, 24.96it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:19<00:00, 25.37it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:18<00:00, 26.62it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:17<00:00, 29.36it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:17<00:00, 28.43it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:13<00:00, 36.67it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:13<00:00, 38.19it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:13<00:00, 38.10it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:14<00:00, 35.14it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:10<00:00, 46.44it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:10<00:00, 49.97it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:09<00:00, 50.20it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:05<00:00, 83.41it/s] Delete-d Jackkinfe Sampling: 100%|██████████| 500/500 [00:04<00:00, 100.31it/s]
In [7]:
coefficients_i = np.array(coefficients_i)
print(np.shape(coefficients_i[:,:,1]))
print(np.shape([step for step in range(step_size, n - step_size + 1, step_size)]))
(19, 500) (19,)
In [8]:
fig, ax = plt.subplots(4,1, figsize=(12,8))
# First harmonic cosine term
ax[0].boxplot( coefficients_i[:,:,1].T, positions=[step for step in range(step_size, n - step_size + 1, step_size)], widths=500)
ax[0].violinplot( coefficients_i[:,:,1].T, positions=[step for step in range(step_size, n - step_size + 1, step_size)], widths=500)
# Fifth harmonic cosine term
ax[1].boxplot( coefficients_i[:,:,11].T, positions=[step for step in range(step_size, n - step_size + 1, step_size)], widths=400)
# Tenth harmonic cosine term
ax[2].boxplot( coefficients_i[:,:,21].T, positions=[step for step in range(step_size, n - step_size + 1, step_size)], widths=500)
# 50th harmonic cosine term
ax[3].boxplot( coefficients_i[:,:,101].T, positions=[step for step in range(step_size, n - step_size + 1, step_size)], widths=500)
fig.subplots_adjust(hspace=0.5)
The x-axis represents the number of points removed from the data set before fitting the regression model. Incredibly, we can see that the feature-weighted regression solution is highly stable, even awhen we have just 10% of the data (750 points) remaining.
Why is this important? Well, it means that we have a roughly uniform basis against which we can compare the data with fairly different data sources (e.g. Kepler vs. Gaia).