Puffins

NB 03 - Tuning hyper-parameters

Now that we've seen how powerful this feature weighted regression model can be, we have some house-keeping to do. While the model is as simple as it can be, there are still some parameters that we can tune. In the case of a Ridge Regression, you have the penalty term λ, and in the case of the feature weighted model you have the width, S, of the weighting term, which effectively acts as a kernel in our case.

In addition to this, both the period of the periodic signal and the number of harmonics in our Fourier basis can technically be optimised as hyper-parameters. While the number of harmonics is less important because of the feature weighting which naturally suppresses high frequency harmonics, the period is something that can benefit from being tuned as a hyperparameter. Furthermore, this cleverly allows us to avoid including this in the regression as a feature since the embedding depends on the period in a non-linear fashion!

There are several well-known methods for determining the optimal values of hyper-parameters in a model. In the case of U Gru, we're dealing with highly correlated data, and we're not exactly looking to predict or forecast the data into the future, so we can use tuning methods that don't explicitly test the time-series nature of the data. However, we can imagine scenarios in which we might want to, so we'll compare the outcomes for hyper-parameters tuned on our data ignoring and accounting for the time-series behaviour of our data. Additionally, there will be times where we work with non-uniformly sampled time-series data, so we'll also try using a K-Folds cross-validation routine inside our tuning loop.

%matplotlib widget
import numpy as np
import matplotlib.pyplot as plt

from puffins.weight_functions import matern32
from puffins.basis_functions import basis_constant, basis_linear

from puffins.data import TimeSeries,LinearModel
from puffins.tuner import Tuner


np.random.seed(42) # to enforce reproducibility
RCOND = 1e-14 # numerical rounding for matrix conditioning
plotnum=1

Let's download / unpack the data

time, flux = np.loadtxt('../data/ugru.dat').T
period = 1.88045
n_harmonics = 100
feature_weighting_width = 0.5

Un-tuned model

Now we're going to establish our "un-tuned" model and save it for later comparison.

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)

fwls.set_X_train(data.predictors)
fwls.train(data.targets)
untuned_model = fwls.trained_model
untuned_mse = fwls.trained_mse

Tuning our model's hyperparameters

In this next step, we'll see how to tune the hyper-parameters of our model with a wrapper around optuna.

First, we need to make a dictionary of our hyperparameters, their ranges, and their distributions. Next, we instantiate our Tuner class, and then run the tuning!

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 15:51:11,831] A new study created in memory with name: no-name-8894b544-d16c-44bb-a22c-b67b9dbb56d4
[I 2025-02-07 15:51:11,941] Trial 0 finished with value: 0.005010285255168618 and parameters: {'feature_weighting_width': 0.6588756353417918, 'period': 1.881716524400105}. Best is trial 0 with value: 0.005010285255168618.
[I 2025-02-07 15:51:11,999] Trial 1 finished with value: 0.004418631909825303 and parameters: {'feature_weighting_width': 0.47395014160346277, 'period': 1.873586290528734}. Best is trial 1 with value: 0.004418631909825303.
[I 2025-02-07 15:51:12,053] Trial 2 finished with value: 0.0007580263993759587 and parameters: {'feature_weighting_width': 0.2450525158376507, 'period': 1.883525801042138}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,107] Trial 3 finished with value: 0.0053011437199111805 and parameters: {'feature_weighting_width': 0.5585641633580463, 'period': 1.873764169075811}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,160] Trial 4 finished with value: 0.004339810191286182 and parameters: {'feature_weighting_width': 0.5271346619248998, 'period': 1.886235120756511}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,211] Trial 5 finished with value: 0.003415456000695661 and parameters: {'feature_weighting_width': 0.36360711490416003, 'period': 1.8872212602658074}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,284] Trial 6 finished with value: 0.005695834965996821 and parameters: {'feature_weighting_width': 0.6477465411305688, 'period': 1.8756756245682245}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,344] Trial 7 finished with value: 0.005600415777676053 and parameters: {'feature_weighting_width': 0.6174912681044865, 'period': 1.8747840836999623}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,409] Trial 8 finished with value: 0.002399673595880299 and parameters: {'feature_weighting_width': 0.46454098122203136, 'period': 1.8772580946335968}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,478] Trial 9 finished with value: 0.004598016737935171 and parameters: {'feature_weighting_width': 0.6308831381951795, 'period': 1.8823127567798048}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,889] Trial 10 finished with value: 0.0047522356280118114 and parameters: {'feature_weighting_width': 0.016805541070915142, 'period': 1.8892712564395688}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:12,976] Trial 11 finished with value: 0.010506975841516707 and parameters: {'feature_weighting_width': 0.9827585903909319, 'period': 1.8791162175140306}. Best is trial 2 with value: 0.0007580263993759587.
[I 2025-02-07 15:51:13,044] Trial 12 finished with value: 0.0003444822734747181 and parameters: {'feature_weighting_width': 0.20253546626366592, 'period': 1.8784240353779718}. Best is trial 12 with value: 0.0003444822734747181.
[I 2025-02-07 15:51:13,101] Trial 13 finished with value: 0.0009324755304296257 and parameters: {'feature_weighting_width': 0.12815511639180735, 'period': 1.884093120024342}. Best is trial 12 with value: 0.0003444822734747181.
[I 2025-02-07 15:51:13,178] Trial 14 finished with value: 0.00019926204346387444 and parameters: {'feature_weighting_width': 0.24358007391108322, 'period': 1.8793459467231557}. Best is trial 14 with value: 0.00019926204346387444.
[I 2025-02-07 15:51:13,356] Trial 15 finished with value: 0.005825319840050308 and parameters: {'feature_weighting_width': 0.24587535538005814, 'period': 1.8705760934633802}. Best is trial 14 with value: 0.00019926204346387444.
[I 2025-02-07 15:51:13,434] Trial 16 finished with value: 0.00021209699583044761 and parameters: {'feature_weighting_width': 0.2656998885864332, 'period': 1.8796669824915049}. Best is trial 14 with value: 0.00019926204346387444.
[I 2025-02-07 15:51:13,506] Trial 17 finished with value: 0.000713029135751708 and parameters: {'feature_weighting_width': 0.36404282349824063, 'period': 1.8805529568370214}. Best is trial 14 with value: 0.00019926204346387444.
[I 2025-02-07 15:51:13,568] Trial 18 finished with value: 0.0005586740840297779 and parameters: {'feature_weighting_width': 0.02996998134978257, 'period': 1.877688184770356}. Best is trial 14 with value: 0.00019926204346387444.
[I 2025-02-07 15:51:13,641] Trial 19 finished with value: 0.006019899714739338 and parameters: {'feature_weighting_width': 0.3656042767303346, 'period': 1.8706287519666276}. Best is trial 14 with value: 0.00019926204346387444.
[I 2025-02-07 15:51:13,711] Trial 20 finished with value: 1.460038473692133e-05 and parameters: {'feature_weighting_width': 0.13562339768771184, 'period': 1.8803087822973314}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:13,799] Trial 21 finished with value: 1.5274788346787146e-05 and parameters: {'feature_weighting_width': 0.145632172813007, 'period': 1.8804355225861493}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:13,858] Trial 22 finished with value: 2.399193139987679e-05 and parameters: {'feature_weighting_width': 0.11738560472616152, 'period': 1.8809102868437684}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:13,928] Trial 23 finished with value: 0.0013177363054688045 and parameters: {'feature_weighting_width': 0.13307930986690855, 'period': 1.8848134131682026}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:13,986] Trial 24 finished with value: 5.822543853471928e-05 and parameters: {'feature_weighting_width': 0.10162175130581518, 'period': 1.8812971346093834}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,056] Trial 25 finished with value: 0.008004851182574746 and parameters: {'feature_weighting_width': 0.8068639008438738, 'period': 1.8767375821871597}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,353] Trial 26 finished with value: 0.0004678800202355344 and parameters: {'feature_weighting_width': 0.07385444600805377, 'period': 1.8830071609170143}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,475] Trial 27 finished with value: 2.8610897156043587e-05 and parameters: {'feature_weighting_width': 0.16992212317288657, 'period': 1.880709333608398}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,551] Trial 28 finished with value: 0.002259971301690777 and parameters: {'feature_weighting_width': 0.3159095368437609, 'period': 1.8859037870637119}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,646] Trial 29 finished with value: 0.00021849094918631055 and parameters: {'feature_weighting_width': 0.006757403772269854, 'period': 1.88218014583913}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,704] Trial 30 finished with value: 0.00651475630383186 and parameters: {'feature_weighting_width': 0.7458766739381268, 'period': 1.8812463695869386}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,772] Trial 31 finished with value: 2.499169669643828e-05 and parameters: {'feature_weighting_width': 0.17098920399955292, 'period': 1.8804838447641554}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,856] Trial 32 finished with value: 4.363615184234919e-05 and parameters: {'feature_weighting_width': 0.19006255848612486, 'period': 1.8801663204938905}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,918] Trial 33 finished with value: 0.0004349171230589346 and parameters: {'feature_weighting_width': 0.07981315226292707, 'period': 1.8780260691912227}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:14,970] Trial 34 finished with value: 0.0018896818917233764 and parameters: {'feature_weighting_width': 0.4476817241324168, 'period': 1.8827321130082444}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,025] Trial 35 finished with value: 0.0011090514009888528 and parameters: {'feature_weighting_width': 0.17617036460108573, 'period': 1.8844183493016065}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,084] Trial 36 finished with value: 0.001145431026471205 and parameters: {'feature_weighting_width': 0.06599089710365282, 'period': 1.876434321016085}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,145] Trial 37 finished with value: 0.0004337529297676043 and parameters: {'feature_weighting_width': 0.28925695443875166, 'period': 1.8788383870993688}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,206] Trial 38 finished with value: 0.0012574409977070158 and parameters: {'feature_weighting_width': 0.4107390595086019, 'period': 1.8817309802207671}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,268] Trial 39 finished with value: 0.0023849807164452257 and parameters: {'feature_weighting_width': 0.32073140500225616, 'period': 1.874892415263558}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,322] Trial 40 finished with value: 0.0006523609577404625 and parameters: {'feature_weighting_width': 0.14300589444178397, 'period': 1.8834721153408136}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,382] Trial 41 finished with value: 2.795249486331676e-05 and parameters: {'feature_weighting_width': 0.15780148370398503, 'period': 1.8808175505280849}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,448] Trial 42 finished with value: 8.764334010924975e-05 and parameters: {'feature_weighting_width': 0.20981857682110636, 'period': 1.8798022109547574}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,518] Trial 43 finished with value: 7.664914084595091e-05 and parameters: {'feature_weighting_width': 0.11828313469707621, 'period': 1.881428595011104}. Best is trial 20 with value: 1.460038473692133e-05.
[I 2025-02-07 15:51:15,581] Trial 44 finished with value: 8.203400974090368e-06 and parameters: {'feature_weighting_width': 0.06785950751949396, 'period': 1.880586485162367}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:15,672] Trial 45 finished with value: 0.0018106637808397816 and parameters: {'feature_weighting_width': 0.05517152649907954, 'period': 1.8856144388402334}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:15,737] Trial 46 finished with value: 0.0003208817308782962 and parameters: {'feature_weighting_width': 0.22528000378731958, 'period': 1.878608940003716}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:15,791] Trial 47 finished with value: 0.00286083347474886 and parameters: {'feature_weighting_width': 0.10400193323242947, 'period': 1.8870631878725759}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:15,860] Trial 48 finished with value: 0.003195391044306777 and parameters: {'feature_weighting_width': 0.5556712734961706, 'period': 1.8800233132023272}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:15,922] Trial 49 finished with value: 0.000248375588582206 and parameters: {'feature_weighting_width': 0.001085590890464061, 'period': 1.882298164960726}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,000] Trial 50 finished with value: 0.0008052172600062633 and parameters: {'feature_weighting_width': 0.043316362841338926, 'period': 1.8771099462626162}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,068] Trial 51 finished with value: 2.2155474239358237e-05 and parameters: {'feature_weighting_width': 0.15808344518785328, 'period': 1.8806685574023505}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,146] Trial 52 finished with value: 0.0001629835626050691 and parameters: {'feature_weighting_width': 0.20538594468686217, 'period': 1.8792152334254968}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,206] Trial 53 finished with value: 0.0008667577999991854 and parameters: {'feature_weighting_width': 0.2644156982179492, 'period': 1.883680034045385}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,271] Trial 54 finished with value: 9.468496062631956e-06 and parameters: {'feature_weighting_width': 0.10665424599972956, 'period': 1.8803701285220473}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,343] Trial 55 finished with value: 0.0004178675707674503 and parameters: {'feature_weighting_width': 0.1059385860240041, 'period': 1.878078347491133}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,408] Trial 56 finished with value: 8.184995570561222e-05 and parameters: {'feature_weighting_width': 0.0477846764173729, 'period': 1.8794522100634714}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,471] Trial 57 finished with value: 0.009919107130026717 and parameters: {'feature_weighting_width': 0.9466908668821713, 'period': 1.8816339153385484}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,527] Trial 58 finished with value: 0.00048709481998478844 and parameters: {'feature_weighting_width': 0.14400685580094919, 'period': 1.883045889553528}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,586] Trial 59 finished with value: 0.0002050839716108016 and parameters: {'feature_weighting_width': 0.08100101953404829, 'period': 1.8821230880843258}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,650] Trial 60 finished with value: 0.00012743879722991678 and parameters: {'feature_weighting_width': 0.24427168978795594, 'period': 1.8809409298433335}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,711] Trial 61 finished with value: 1.075012872780982e-05 and parameters: {'feature_weighting_width': 0.1243115852468122, 'period': 1.88048091531546}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,776] Trial 62 finished with value: 2.8035180608119723e-05 and parameters: {'feature_weighting_width': 0.12921117149519937, 'period': 1.8799907315377518}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,846] Trial 63 finished with value: 0.00018125528035096934 and parameters: {'feature_weighting_width': 0.03314129453487341, 'period': 1.8789160298055771}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,917] Trial 64 finished with value: 8.664579511980216e-06 and parameters: {'feature_weighting_width': 0.103254526556808, 'period': 1.880512364879754}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:16,978] Trial 65 finished with value: 0.004016646805753115 and parameters: {'feature_weighting_width': 0.0755264092582021, 'period': 1.8725053751223815}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:17,044] Trial 66 finished with value: 0.0005766059733607719 and parameters: {'feature_weighting_width': 0.16315084873468877, 'period': 1.8776693293745677}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:17,114] Trial 67 finished with value: 0.004792911230275172 and parameters: {'feature_weighting_width': 0.19344805747016525, 'period': 1.8893077256163777}. Best is trial 44 with value: 8.203400974090368e-06.
[I 2025-02-07 15:51:17,174] Trial 68 finished with value: 8.016559551068104e-06 and parameters: {'feature_weighting_width': 0.09270598174214399, 'period': 1.8805028480987052}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,243] Trial 69 finished with value: 0.0013962675598758918 and parameters: {'feature_weighting_width': 0.023209878100698772, 'period': 1.8759921808137316}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,311] Trial 70 finished with value: 7.780146750932105e-05 and parameters: {'feature_weighting_width': 0.08752521331324059, 'period': 1.8794850686337758}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,379] Trial 71 finished with value: 1.1230047707632789e-05 and parameters: {'feature_weighting_width': 0.12671839732183623, 'period': 1.8805086117096548}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,445] Trial 72 finished with value: 1.567144430647011e-05 and parameters: {'feature_weighting_width': 0.11047882857905075, 'period': 1.8801670688702234}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,500] Trial 73 finished with value: 0.00022309614206523007 and parameters: {'feature_weighting_width': 0.22082073552997644, 'period': 1.8819402124877993}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,563] Trial 74 finished with value: 0.000355635397683182 and parameters: {'feature_weighting_width': 0.05824746363820405, 'period': 1.8782665618626242}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,623] Trial 75 finished with value: 4.046449138265416e-05 and parameters: {'feature_weighting_width': 0.132451430931028, 'period': 1.8810941317197263}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,746] Trial 76 finished with value: 0.0005715691159189003 and parameters: {'feature_weighting_width': 0.28882184917706244, 'period': 1.8826465632569698}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,808] Trial 77 finished with value: 7.818134150060902e-05 and parameters: {'feature_weighting_width': 0.10107347093130058, 'period': 1.8814498828589188}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,871] Trial 78 finished with value: 2.9703231289210433e-05 and parameters: {'feature_weighting_width': 0.1776086017731475, 'period': 1.8803458261238184}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,939] Trial 79 finished with value: 0.0001416254113413237 and parameters: {'feature_weighting_width': 0.030339330871157255, 'period': 1.8791045511690128}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:17,996] Trial 80 finished with value: 0.0002693177052935019 and parameters: {'feature_weighting_width': 0.08490314890750636, 'period': 1.8785626012874612}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,063] Trial 81 finished with value: 1.2553538166207695e-05 and parameters: {'feature_weighting_width': 0.11997119174082913, 'period': 1.880285490615452}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,130] Trial 82 finished with value: 5.858988846404124e-05 and parameters: {'feature_weighting_width': 0.14323569850050513, 'period': 1.8796874939777235}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,184] Trial 83 finished with value: 0.005950883476002961 and parameters: {'feature_weighting_width': 0.7151333954177352, 'period': 1.8804959347458643}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,258] Trial 84 finished with value: 0.0001443720760448351 and parameters: {'feature_weighting_width': 0.18614494338215326, 'period': 1.881710472809363}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,326] Trial 85 finished with value: 4.814606840411787e-05 and parameters: {'feature_weighting_width': 0.06295994250305861, 'period': 1.88121950366869}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,386] Trial 86 finished with value: 4.0650366173379865e-05 and parameters: {'feature_weighting_width': 0.12269010119388758, 'period': 1.8798230066282227}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,446] Trial 87 finished with value: 0.000348649249859133 and parameters: {'feature_weighting_width': 0.018155184222897025, 'period': 1.8826496041115661}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,504] Trial 88 finished with value: 1.7447249817257353e-05 and parameters: {'feature_weighting_width': 0.15179455457779914, 'period': 1.88054221917224}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,561] Trial 89 finished with value: 0.00016590859951885653 and parameters: {'feature_weighting_width': 0.10796314018158823, 'period': 1.8789937168490423}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,629] Trial 90 finished with value: 0.0028669519480190335 and parameters: {'feature_weighting_width': 0.5073219342507836, 'period': 1.8775919981988052}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,683] Trial 91 finished with value: 1.4856999493464313e-05 and parameters: {'feature_weighting_width': 0.09525040226907178, 'period': 1.8801618573578287}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,747] Trial 92 finished with value: 2.1762609101091528e-05 and parameters: {'feature_weighting_width': 0.05681091857052381, 'period': 1.8809186415092942}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,803] Trial 93 finished with value: 1.2762002150197427e-05 and parameters: {'feature_weighting_width': 0.09301531507359953, 'period': 1.8802104207273513}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,862] Trial 94 finished with value: 6.147521175400866e-05 and parameters: {'feature_weighting_width': 0.07865087414363145, 'period': 1.879605336629379}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:18,933] Trial 95 finished with value: 1.7152622184560987e-05 and parameters: {'feature_weighting_width': 0.09071274600132266, 'period': 1.88011000535108}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,013] Trial 96 finished with value: 0.00014570558457589273 and parameters: {'feature_weighting_width': 0.1219930862907378, 'period': 1.8818378584625628}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,078] Trial 97 finished with value: 4.862503476782986e-05 and parameters: {'feature_weighting_width': 0.045086164632360516, 'period': 1.8812260331817143}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,128] Trial 98 finished with value: 8.058405715532413e-05 and parameters: {'feature_weighting_width': 0.004496391255649032, 'period': 1.8794599220159933}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,183] Trial 99 finished with value: 0.0003100242044314952 and parameters: {'feature_weighting_width': 0.2099249129447469, 'period': 1.8785755427248998}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,260] Trial 100 finished with value: 2.9943818769845117e-05 and parameters: {'feature_weighting_width': 0.1735281490650081, 'period': 1.8806933257139296}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,320] Trial 101 finished with value: 2.5715194570247386e-05 and parameters: {'feature_weighting_width': 0.14478857778417423, 'period': 1.880082646325743}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,386] Trial 102 finished with value: 8.800115666439253e-06 and parameters: {'feature_weighting_width': 0.09578394624977199, 'period': 1.8803681482054733}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,443] Trial 103 finished with value: 0.00013677679532478535 and parameters: {'feature_weighting_width': 0.09642198426331189, 'period': 1.879134565048338}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,507] Trial 104 finished with value: 2.484568064639545e-05 and parameters: {'feature_weighting_width': 0.06635393236402276, 'period': 1.8809610905457534}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,642] Trial 105 finished with value: 1.0548993881909626e-05 and parameters: {'feature_weighting_width': 0.1230117216240023, 'period': 1.8804703124291196}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,704] Trial 106 finished with value: 0.000317741088275575 and parameters: {'feature_weighting_width': 0.23185707984524298, 'period': 1.8822792029729076}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,809] Trial 107 finished with value: 8.213571321405487e-05 and parameters: {'feature_weighting_width': 0.1198872972452259, 'period': 1.881466096761213}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,876] Trial 108 finished with value: 0.0005716072907929256 and parameters: {'feature_weighting_width': 0.03838833790367034, 'period': 1.8832843001535235}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:19,934] Trial 109 finished with value: 1.8648876120366558e-05 and parameters: {'feature_weighting_width': 0.1548401349342695, 'period': 1.8805569994816047}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,013] Trial 110 finished with value: 0.0042231740116062885 and parameters: {'feature_weighting_width': 0.19197626571160759, 'period': 1.8886763896361798}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,078] Trial 111 finished with value: 1.765522587212924e-05 and parameters: {'feature_weighting_width': 0.10098553614251284, 'period': 1.880110448983656}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,141] Trial 112 finished with value: 5.2123277465931086e-05 and parameters: {'feature_weighting_width': 0.07503818910954049, 'period': 1.8796829067338798}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,205] Trial 113 finished with value: 0.00011454352748669654 and parameters: {'feature_weighting_width': 0.12987289133274674, 'period': 1.8792745937902053}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,265] Trial 114 finished with value: 2.616713598598046e-05 and parameters: {'feature_weighting_width': 0.16905712190273095, 'period': 1.8802954018634463}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,327] Trial 115 finished with value: 0.0011425313377593147 and parameters: {'feature_weighting_width': 0.40770993388828836, 'period': 1.8809438742386286}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,385] Trial 116 finished with value: 0.0002026199727631571 and parameters: {'feature_weighting_width': 0.04685513596312347, 'period': 1.8788233164793067}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,454] Trial 117 finished with value: 0.003791013531734883 and parameters: {'feature_weighting_width': 0.5895581884720662, 'period': 1.8814726312647}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,523] Trial 118 finished with value: 0.0083475796944651 and parameters: {'feature_weighting_width': 0.848628793469964, 'period': 1.8820734344138141}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,589] Trial 119 finished with value: 4.5052350379631716e-05 and parameters: {'feature_weighting_width': 0.09141668472256129, 'period': 1.8797523564697873}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,651] Trial 120 finished with value: 0.00043943453577907903 and parameters: {'feature_weighting_width': 0.021748415019932757, 'period': 1.8780120444334212}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,736] Trial 121 finished with value: 1.262743581292658e-05 and parameters: {'feature_weighting_width': 0.13404877009899172, 'period': 1.8805195155848082}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,794] Trial 122 finished with value: 1.3471564230511112e-05 and parameters: {'feature_weighting_width': 0.13724559686690718, 'period': 1.8803976550604642}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,865] Trial 123 finished with value: 1.4215255000267542e-05 and parameters: {'feature_weighting_width': 0.1362208188646226, 'period': 1.8806035708410231}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,925] Trial 124 finished with value: 1.4300544062297827e-05 and parameters: {'feature_weighting_width': 0.11983228100661769, 'period': 1.8807082585888948}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:20,989] Trial 125 finished with value: 5.517642299896077e-05 and parameters: {'feature_weighting_width': 0.14248467524046476, 'period': 1.8812200951404745}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,046] Trial 126 finished with value: 0.00015551539597857602 and parameters: {'feature_weighting_width': 0.16604465102131705, 'period': 1.8818300642717796}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,108] Trial 127 finished with value: 4.7145741987660193e-05 and parameters: {'feature_weighting_width': 0.19837703287073152, 'period': 1.880675515029723}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,176] Trial 128 finished with value: 3.499888062019113e-05 and parameters: {'feature_weighting_width': 0.06798271029305322, 'period': 1.8798495159156077}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,235] Trial 129 finished with value: 9.98953526960732e-06 and parameters: {'feature_weighting_width': 0.11439378936878032, 'period': 1.8803845368438694}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,300] Trial 130 finished with value: 9.509853699580758e-05 and parameters: {'feature_weighting_width': 0.1199460484111526, 'period': 1.8793843477738994}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,362] Trial 131 finished with value: 1.3173168967197426e-05 and parameters: {'feature_weighting_width': 0.13451333181709074, 'period': 1.8803739658186691}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,426] Trial 132 finished with value: 3.556096439862934e-05 and parameters: {'feature_weighting_width': 0.11060355029621322, 'period': 1.881072132286364}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,483] Trial 133 finished with value: 2.053210528786035e-05 and parameters: {'feature_weighting_width': 0.156557476324652, 'period': 1.8803088806972459}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,541] Trial 134 finished with value: 3.512232106376083e-05 and parameters: {'feature_weighting_width': 0.08142078365402919, 'period': 1.8798515899323127}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,601] Trial 135 finished with value: 9.372260395445761e-05 and parameters: {'feature_weighting_width': 0.055276374265496156, 'period': 1.881561339061982}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,660] Trial 136 finished with value: 9.672210136700289e-06 and parameters: {'feature_weighting_width': 0.10472911471953425, 'period': 1.880348000049087}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,722] Trial 137 finished with value: 0.00011818768541509176 and parameters: {'feature_weighting_width': 0.10504175928166573, 'period': 1.879237748507009}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,781] Trial 138 finished with value: 2.868949218746213e-05 and parameters: {'feature_weighting_width': 0.07154025341931988, 'period': 1.8810108061651993}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,847] Trial 139 finished with value: 0.00021822704069668683 and parameters: {'feature_weighting_width': 0.09232060150957581, 'period': 1.8787610484459112}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,899] Trial 140 finished with value: 2.743945122230524e-05 and parameters: {'feature_weighting_width': 0.03766034137743492, 'period': 1.8799340332294998}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:21,956] Trial 141 finished with value: 1.3160964457062553e-05 and parameters: {'feature_weighting_width': 0.13389667750685705, 'period': 1.8805702778939015}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,011] Trial 142 finished with value: 2.989924204473717e-05 and parameters: {'feature_weighting_width': 0.17878862619289532, 'period': 1.880379361009027}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,075] Trial 143 finished with value: 5.9371791347030505e-05 and parameters: {'feature_weighting_width': 0.11560797135528393, 'period': 1.881297146563234}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,127] Trial 144 finished with value: 0.0003166285123188962 and parameters: {'feature_weighting_width': 0.15270735153717482, 'period': 1.8825151061346683}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,183] Trial 145 finished with value: 2.0620430478638493e-05 and parameters: {'feature_weighting_width': 0.1310574625893358, 'period': 1.8808159975493681}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,243] Trial 146 finished with value: 7.360565758694784e-05 and parameters: {'feature_weighting_width': 0.09114543708498526, 'period': 1.8795159506484043}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,308] Trial 147 finished with value: 1.8424760664786715e-05 and parameters: {'feature_weighting_width': 0.06434185360758246, 'period': 1.8800735589542337}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,380] Trial 148 finished with value: 0.00010422647493785352 and parameters: {'feature_weighting_width': 0.11238087714643949, 'period': 1.8816141992053776}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,438] Trial 149 finished with value: 3.299198665096172e-05 and parameters: {'feature_weighting_width': 0.1838269275808127, 'period': 1.8805464184712066}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,521] Trial 150 finished with value: 4.7896912509517665e-05 and parameters: {'feature_weighting_width': 0.1594256644184589, 'period': 1.881093037704123}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,580] Trial 151 finished with value: 1.4849185637169825e-05 and parameters: {'feature_weighting_width': 0.1353327321430145, 'period': 1.8802958785226143}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,657] Trial 152 finished with value: 6.043799088194904e-05 and parameters: {'feature_weighting_width': 0.1350225676423546, 'period': 1.879655119599203}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,718] Trial 153 finished with value: 8.735803530312871e-06 and parameters: {'feature_weighting_width': 0.09972761232420145, 'period': 1.8803900499276658}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,784] Trial 154 finished with value: 1.6515105401208517e-05 and parameters: {'feature_weighting_width': 0.07889700215916869, 'period': 1.8808211694342927}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,842] Trial 155 finished with value: 3.496121058686187e-05 and parameters: {'feature_weighting_width': 0.09913726213672194, 'period': 1.8798614957311315}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,899] Trial 156 finished with value: 0.00013539117755176854 and parameters: {'feature_weighting_width': 0.05042123232189578, 'period': 1.8791370964619598}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:22,963] Trial 157 finished with value: 1.698094892933132e-05 and parameters: {'feature_weighting_width': 0.10693657846579885, 'period': 1.88013220495873}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:23,022] Trial 158 finished with value: 6.663968088782823e-05 and parameters: {'feature_weighting_width': 0.025553044969746253, 'period': 1.8813758221038281}. Best is trial 68 with value: 8.016559551068104e-06.
[I 2025-02-07 15:51:23,115] Trial 159 finished with value: 7.823722523191651e-06 and parameters: {'feature_weighting_width': 0.07837689718236332, 'period': 1.8805416211569161}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,183] Trial 160 finished with value: 0.00014381753824231267 and parameters: {'feature_weighting_width': 0.08091407939041959, 'period': 1.8818410814190427}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,243] Trial 161 finished with value: 1.1289512513222247e-05 and parameters: {'feature_weighting_width': 0.11979097291747809, 'period': 1.8805954554470912}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,303] Trial 162 finished with value: 1.4767779174667888e-05 and parameters: {'feature_weighting_width': 0.061669278613245046, 'period': 1.8807933196326714}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,368] Trial 163 finished with value: 8.478571220128183e-05 and parameters: {'feature_weighting_width': 0.11203079840581984, 'period': 1.8794466707369215}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,457] Trial 164 finished with value: 4.531513821398526e-05 and parameters: {'feature_weighting_width': 0.09267452585306826, 'period': 1.8811859049255029}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,530] Trial 165 finished with value: 0.005188878654142474 and parameters: {'feature_weighting_width': 0.6722787574093088, 'period': 1.8805751616154158}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,617] Trial 166 finished with value: 3.796850959436566e-05 and parameters: {'feature_weighting_width': 0.15502070948855404, 'period': 1.879944245354354}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,714] Trial 167 finished with value: 2.117171340512535e-05 and parameters: {'feature_weighting_width': 0.12154757968468255, 'period': 1.880854623343974}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,785] Trial 168 finished with value: 0.00021506196746327047 and parameters: {'feature_weighting_width': 0.07949943372357038, 'period': 1.8821648055269689}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,858] Trial 169 finished with value: 1.1426552533706423e-05 and parameters: {'feature_weighting_width': 0.041058691846938375, 'period': 1.8802129314699498}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,927] Trial 170 finished with value: 5.29775740910004e-05 and parameters: {'feature_weighting_width': 0.04292460603799423, 'period': 1.879671119602156}. Best is trial 159 with value: 7.823722523191651e-06.
[I 2025-02-07 15:51:23,997] Trial 171 finished with value: 6.582923384676726e-06 and parameters: {'feature_weighting_width': 0.0025196240495124547, 'period': 1.8804417078825764}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,074] Trial 172 finished with value: 1.5246912477554303e-05 and parameters: {'feature_weighting_width': 0.005856024424750486, 'period': 1.8801225423270498}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,146] Trial 173 finished with value: 8.196089006009493e-06 and parameters: {'feature_weighting_width': 0.026536108045533857, 'period': 1.8803177062821392}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,210] Trial 174 finished with value: 3.529887176767838e-05 and parameters: {'feature_weighting_width': 0.022923438567217375, 'period': 1.8810952410160944}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,277] Trial 175 finished with value: 6.788835826951413e-06 and parameters: {'feature_weighting_width': 0.011174813055496113, 'period': 1.8804086024700855}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,391] Trial 176 finished with value: 7.624660805692977e-05 and parameters: {'feature_weighting_width': 0.012185730386375689, 'period': 1.8794899889165932}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,447] Trial 177 finished with value: 0.004513389042384002 and parameters: {'feature_weighting_width': 0.002833241494689699, 'period': 1.871949539860696}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,507] Trial 178 finished with value: 8.596137585691653e-05 and parameters: {'feature_weighting_width': 0.03421733567873113, 'period': 1.8815121417371188}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,571] Trial 179 finished with value: 1.0126890824766444e-05 and parameters: {'feature_weighting_width': 0.0460860937960728, 'period': 1.8802530666435222}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,623] Trial 180 finished with value: 2.1448860125667425e-05 and parameters: {'feature_weighting_width': 0.052520361191097764, 'period': 1.880020694452455}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,679] Trial 181 finished with value: 7.49600178316074e-06 and parameters: {'feature_weighting_width': 0.033688507690256275, 'period': 1.8803568383031077}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,732] Trial 182 finished with value: 1.5536223351191063e-05 and parameters: {'feature_weighting_width': 0.02268857197203194, 'period': 1.880818396144059}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,792] Trial 183 finished with value: 7.024093577802224e-06 and parameters: {'feature_weighting_width': 0.03879693516292976, 'period': 1.8803966063642237}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,866] Trial 184 finished with value: 7.0501064779699215e-06 and parameters: {'feature_weighting_width': 0.06158440665731979, 'period': 1.8804697535475752}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,937] Trial 185 finished with value: 0.00015828709415778642 and parameters: {'feature_weighting_width': 0.05871631494033418, 'period': 1.8790230958800889}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:24,989] Trial 186 finished with value: 4.403973201963451e-05 and parameters: {'feature_weighting_width': 0.018446514767917886, 'period': 1.8797511482252462}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,047] Trial 187 finished with value: 2.316491153037644e-05 and parameters: {'feature_weighting_width': 0.0038770220338229175, 'period': 1.8809446807114567}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,114] Trial 188 finished with value: 6.677819932973349e-06 and parameters: {'feature_weighting_width': 0.037362980342415406, 'period': 1.8804441040764257}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,177] Trial 189 finished with value: 5.774273346721912e-05 and parameters: {'feature_weighting_width': 0.0361412370954531, 'period': 1.8813053380018736}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,244] Trial 190 finished with value: 8.721239122459455e-06 and parameters: {'feature_weighting_width': 0.06312359788587135, 'period': 1.8803177322288362}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,302] Trial 191 finished with value: 8.102738749203488e-06 and parameters: {'feature_weighting_width': 0.0621033511461807, 'period': 1.880348171435801}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,369] Trial 192 finished with value: 2.5164189242723493e-05 and parameters: {'feature_weighting_width': 0.06018079916279543, 'period': 1.8799687239069771}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,431] Trial 193 finished with value: 6.797017366215383e-06 and parameters: {'feature_weighting_width': 0.030371412830049946, 'period': 1.8804121293337026}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,487] Trial 194 finished with value: 1.0045033052067376e-05 and parameters: {'feature_weighting_width': 0.03340001689659003, 'period': 1.8802504536369444}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,554] Trial 195 finished with value: 7.514443372702708e-05 and parameters: {'feature_weighting_width': 0.07089828656940962, 'period': 1.8795010437081203}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,611] Trial 196 finished with value: 2.228789098070029e-05 and parameters: {'feature_weighting_width': 0.02674396814954208, 'period': 1.8809317003629933}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,681] Trial 197 finished with value: 3.0682347436542436e-05 and parameters: {'feature_weighting_width': 0.030683960721944535, 'period': 1.8798932700169697}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,740] Trial 198 finished with value: 7.833659614766022e-06 and parameters: {'feature_weighting_width': 0.053557486382977776, 'period': 1.8805811275750108}. Best is trial 171 with value: 6.582923384676726e-06.
[I 2025-02-07 15:51:25,830] Trial 199 finished with value: 1.026778838071238e-05 and parameters: {'feature_weighting_width': 0.060618409468920116, 'period': 1.8806785837639821}. Best is trial 171 with value: 6.582923384676726e-06.

print(joint_tuner)

Tuner:
 feature_weighting_width: 0.0025196240495124547
period: 1.8804417078825764

Updating the model

As we can see above, we've found the "optimal" values for the period and feature weighting width parameters in our model. Now, we need to update the model to use these "optimal" values, and retrain our model with these values.

fwls.set_X_kwargs(update=True, **joint_tuner.best_hyperpars)
fwls.set_X_train(data.predictors)
fwls.train(data.targets)

Model comparison

Now that we've gone through the trouble of tuning our hyper-parameters, we should take a look at the models to see if they're really that much better.

plotnum += 1
fig_, ax_ = plt.subplots(num=plotnum)
ph_untuned = data.predictors / period % 1
ph_tuned = data.predictors / fwls.X_kwargs['period'] % 1
ax_.plot(ph_tuned, data.targets, 'o', color='grey', alpha=0.01)
ax_.plot(ph_untuned, untuned_model, '+', ms=1.5, color='darkorange', alpha=0.85)
ax_.plot(ph_tuned, fwls.trained_model, 'x', ms=1.5, color='dodgerblue')
ax_.set_xlabel('Time')
ax_.set_ylabel('(Predicted) Flux')

Text(0, 0.5, '(Predicted) Flux')

Figure

Clearly, the tuning was worthwhile! As a note on treating the period of the seasonal trend as a hyper-parameter, I'd like to point out that we used a fairly narrow range over which we tuned the value. In some other tests, it does a good job of finding the optimal value over a much larger range, but this is not a general behaviour. Specifically, in cases where the range encompases the first harmonic of the period (=1/2 * period), then the model can bifurcate between these values. As a rule of thumb, you'll often have a pretty decent idea of what the period is with some small uncertainty range, so I would suggest keeping the tuning range as small as you can reasonably manage.

Other notes

Although we jointly tuned the period and feature_weighting_width values, in some cases it may be beneficial to tune each individually. In these cases, you can easily do this by declaring indiviaul tuners and updating the LinearModel inbetween tuning runs, e.g.:

period_ = {'period': [1.87,1.89,'uniform']} width_ = {'feature_weighting_width': [0.001,1.,'uniform']}

period_tuner = Tuner( fwls, hyperpars=period_, n_trials=200, direction='minimize') period_tuner.run_tune(time, flux) print(period_tuner.best_hyperpars) fwls.set_X_kwargs(update=True, period=period_tuner.best_hyperpars['period'])

width_tuner = Tuner( fwls, hyperpars=width_, n_trials=50, direction='minimize') width_tuner.run_tune(time, flux)

fwls.set_X_kwargs(update=True, feature_weighting_width=width_tuner.best_hyperpars['feature_weighting_width'])

fwls.set_X_train(data.predictors) fwls.train(data.targets)