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The model presented here is a frequentist – conformalized – version of the Bayesian one presented last week in #152. The model is implemented in learningmachine, both in Python and R. Model explanations are given as sensitivity analyses.

0 - install packages

For R

utils::install.packages(c("rmarkdown", "reticulate", "remotes"))

Installing packages into '/cloud/lib/x86_64-pc-linux-gnu-library/4.4'
(as 'lib' is unspecified)

remotes::install_github("thierrymoudiki/bayesianrvfl")

Skipping install of 'bayesianrvfl' from a github remote, the SHA1 (a8e9e78a) has not changed since last install.
  Use `force = TRUE` to force installationSkipping install of 'learningmachine' from a github remote, the SHA1 (6b930284) has not changed since last install.
  Use `force = TRUE` to force installation

library("learningmachine")

Loading required package: randtoolboxLoading required package: rngWELLThis is randtoolbox. For an overview, type 'help("randtoolbox")'.Loading required package: tseriesRegistered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo Loading required package: memoiseLoading required package: foreachLoading required package: skimrLoading required package: snowLoading required package: doSNOWLoading required package: iterators

For Python

pip install matplotlib

Defaulting to user installation because normal site-packages is not writeable
Requirement already satisfied: matplotlib in /cloud/python/lib/python3.8/site-packages (3.7.5)
Requirement already satisfied: pyparsing>=2.3.1 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (3.1.2)
Requirement already satisfied: packaging>=20.0 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (24.1)
Requirement already satisfied: kiwisolver>=1.0.1 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (1.4.5)
Requirement already satisfied: importlib-resources>=3.2.0 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (6.4.3)
Requirement already satisfied: numpy<2,>=1.20 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (1.24.4)
Requirement already satisfied: pillow>=6.2.0 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (10.4.0)
Requirement already satisfied: cycler>=0.10 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (0.12.1)
Requirement already satisfied: python-dateutil>=2.7 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (2.9.0.post0)
Requirement already satisfied: fonttools>=4.22.0 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (4.53.1)
Requirement already satisfied: contourpy>=1.0.1 in /cloud/python/lib/python3.8/site-packages (from matplotlib) (1.1.1)
Requirement already satisfied: zipp>=3.1.0 in /cloud/python/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib) (3.20.0)
Requirement already satisfied: six>=1.5 in /cloud/python/lib/python3.8/site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)

[notice] A new release of pip is available: 23.0.1 -> 24.2
[notice] To update, run: /opt/python/3.8.17/bin/python3.8 -m pip install --upgrade pip

pip install git+https://github.com/Techtonique/learningmachine_python.git

Defaulting to user installation because normal site-packages is not writeable
Collecting git+https://github.com/Techtonique/learningmachine_python.git
  Cloning https://github.com/Techtonique/learningmachine_python.git to /tmp/pip-req-build-37h1oa6g
  Running command git clone --filter=blob:none --quiet https://github.com/Techtonique/learningmachine_python.git /tmp/pip-req-build-37h1oa6g
  Resolved https://github.com/Techtonique/learningmachine_python.git to commit 3ec7ca96df71add6218d55db9ef5d8eb40275877
  Preparing metadata (setup.py): started
  Preparing metadata (setup.py): finished with status 'done'
Requirement already satisfied: numpy in /cloud/python/lib/python3.8/site-packages (from learningmachine==2.2.2) (1.24.4)
Requirement already satisfied: pandas in /cloud/python/lib/python3.8/site-packages (from learningmachine==2.2.2) (2.0.3)
Requirement already satisfied: rpy2>=3.4.5 in /cloud/python/lib/python3.8/site-packages (from learningmachine==2.2.2) (3.5.16)
Requirement already satisfied: scikit-learn in /cloud/python/lib/python3.8/site-packages (from learningmachine==2.2.2) (1.3.2)
Requirement already satisfied: scipy in /cloud/python/lib/python3.8/site-packages (from learningmachine==2.2.2) (1.10.1)
Requirement already satisfied: jinja2 in /cloud/python/lib/python3.8/site-packages (from rpy2>=3.4.5->learningmachine==2.2.2) (3.1.4)
Requirement already satisfied: tzlocal in /cloud/python/lib/python3.8/site-packages (from rpy2>=3.4.5->learningmachine==2.2.2) (5.2)
Requirement already satisfied: backports.zoneinfo in /cloud/python/lib/python3.8/site-packages (from rpy2>=3.4.5->learningmachine==2.2.2) (0.2.1)
Requirement already satisfied: cffi>=1.15.1 in /cloud/python/lib/python3.8/site-packages (from rpy2>=3.4.5->learningmachine==2.2.2) (1.17.0)
Requirement already satisfied: tzdata>=2022.1 in /cloud/python/lib/python3.8/site-packages (from pandas->learningmachine==2.2.2) (2024.1)
Requirement already satisfied: python-dateutil>=2.8.2 in /cloud/python/lib/python3.8/site-packages (from pandas->learningmachine==2.2.2) (2.9.0.post0)
Requirement already satisfied: pytz>=2020.1 in /cloud/python/lib/python3.8/site-packages (from pandas->learningmachine==2.2.2) (2024.1)
Requirement already satisfied: threadpoolctl>=2.0.0 in /cloud/python/lib/python3.8/site-packages (from scikit-learn->learningmachine==2.2.2) (3.5.0)
Requirement already satisfied: joblib>=1.1.1 in /cloud/python/lib/python3.8/site-packages (from scikit-learn->learningmachine==2.2.2) (1.4.2)
Requirement already satisfied: pycparser in /cloud/python/lib/python3.8/site-packages (from cffi>=1.15.1->rpy2>=3.4.5->learningmachine==2.2.2) (2.22)
Requirement already satisfied: six>=1.5 in /cloud/python/lib/python3.8/site-packages (from python-dateutil>=2.8.2->pandas->learningmachine==2.2.2) (1.16.0)
Requirement already satisfied: MarkupSafe>=2.0 in /cloud/python/lib/python3.8/site-packages (from jinja2->rpy2>=3.4.5->learningmachine==2.2.2) (2.1.5)

[notice] A new release of pip is available: 23.0.1 -> 24.2
[notice] To update, run: /opt/python/3.8.17/bin/python3.8 -m pip install --upgrade pip

1 - Python code version

import packages

import numpy as np 
import warnings 
import learningmachine as lm

/cloud/python/lib/python3.8/site-packages/rpy2/rinterface_lib/embedded.py:276: UserWarning: R was initialized outside of rpy2 (R_NilValue != NULL). Trying to use it nevertheless.
  warnings.warn(msg)
R was initialized outside of rpy2 (R_NilValue != NULL). Trying to use it nevertheless.

plotting function

warnings.filterwarnings('ignore')

split_color = 'green'
split_color2 = 'orange'
local_color = 'gray'

def plot_func(x,
              y,
              y_u=None,
              y_l=None,
              pred=None,
              shade_color=split_color,
              method_name="",
              title=""):

    fig = plt.figure()

    plt.plot(x, y, 'k.', alpha=.3, markersize=10,
             fillstyle='full', label=u'Test set observations')

    if (y_u is not None) and (y_l is not None):
        plt.fill(np.concatenate([x, x[::-1]]),
                 np.concatenate([y_u, y_l[::-1]]),
                 alpha=.3, fc=shade_color, ec='None',
                 label = method_name + ' Prediction interval')

    if pred is not None:
        plt.plot(x, pred, 'k--', lw=2, alpha=0.9,
                 label=u'Predicted value')

    #plt.ylim([-2.5, 7])
    plt.xlabel('$X$')
    plt.ylabel('$Y$')
    plt.legend(loc='upper right')
    plt.title(title)

    plt.show()

fit_obj = lm.Regressor(method="rvfl",
pi_method = "kdejackknifeplus",
nb_hidden = 3)

data = fetch_california_housing()

X, y = data.data[:600], data.target[:600]

X = pd.DataFrame(X, columns=data.feature_names)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2,
random_state=123)

start = time()

fit_obj.fit(X_train, y_train, reg_lambda=1)

Regressor(method='rvfl', nb_hidden=3, pi_method='kdejackknifeplus')Elapsed time:  11.298886775970459preds: DescribeResult(preds=array([2.49357776, 1.43407668, 1.5975387 , 1.12443032, 2.82375138,
       2.4580493 , 3.54353746, 1.8909777 , 2.05285337, 3.77584837,
       1.83513261, 1.07393557, 1.94194497, 0.92784638, 1.05871262,
       2.22243527, 1.65294959, 1.91187611, 1.77770079, 1.25768064,
       1.87622468, 1.74061527, 2.92453382, 1.66174853, 1.6614039 ,
       1.77202212, 5.07081658, 2.38262843, 2.53746616, 1.363203  ,
       3.20583396, 1.86606062, 1.70192252, 1.07269937, 1.31627684,
       2.03799042, 3.26290966, 3.97461689, 1.13406842, 2.47295003,
       1.5368609 , 1.09332542, 1.4092314 , 2.60417043, 5.89174275,
       1.50619443, 2.4628304 , 2.19871466, 2.1841939 , 1.48221595,
       1.87870123, 0.77989849, 1.44449574, 2.38624907, 1.29244221,
       0.78829802, 1.41881675, 1.74509957, 1.11005633, 4.01926467,
       2.05504522, 1.71159601, 3.2461924 , 2.83470994, 2.19983398,
       1.59497106, 1.70886701, 1.90077656, 1.45410688, 1.66886891,
       1.75110881, 3.05357402, 3.6834588 , 1.08916238, 1.84916719,
       1.80851509, 2.15596533, 1.97719052, 1.92875913, 3.38678466,
       1.32564179, 1.81436977, 1.63403928, 1.18568231, 1.7315052 ,
       0.8090071 , 2.47389329, 1.19407051, 2.23409297, 2.30256486,
       5.37829418, 1.38890835, 2.00637569, 1.99204335, 1.85314134,
       2.86190699, 1.91334581, 1.24205971, 3.20558421, 4.26259962,
       2.01732404, 3.95679516, 1.39072672, 1.65839735, 2.30550471,
       2.3517598 , 2.13887703, 1.25020289, 1.88503591, 1.16169133,
       2.00430928, 3.26703677, 1.3242707 , 2.01948611, 2.43700375,
       1.69810225, 1.69708568, 2.18234363, 2.12271321, 0.94102412]), sims=array([[2.52197294, 2.65764086, 2.40986397, ..., 2.78250935, 2.00710776,
        2.45581687],
       [1.73158936, 1.64068277, 1.30405511, ..., 1.5192879 , 1.7531569 ,
        1.96604158],
       [1.9742429 , 1.39726812, 1.32734606, ..., 1.22639871, 1.46987265,
        1.40392566],
       ...,
       [2.0119616 , 2.40848185, 2.09426227, ..., 2.62052065, 2.51099616,
        2.36614074],
       [1.35463496, 2.3932347 , 2.05260157, ..., 2.40050845, 1.99334353,
        1.87698499],
       [0.48279083, 0.94856269, 0.97790733, ..., 1.0927788 , 1.23311912,
        0.40108719]]), lower=array([ 1.93689669e+00,  6.14177968e-01,  1.04195634e+00,  3.75503359e-01,
        2.02144872e+00,  1.82276306e+00,  2.64944272e+00,  1.34667642e+00,
        1.29086670e+00,  3.05297704e+00,  1.17765182e+00,  4.30461766e-01,
        1.37895403e+00,  2.98779763e-01,  4.40822194e-01,  1.55654853e+00,
        9.38628380e-01,  1.21829098e+00,  9.84558834e-01,  6.49532691e-01,
        9.01772850e-01,  1.19276603e+00,  2.17680551e+00,  1.09038146e+00,
        1.16893453e+00,  9.31502331e-01,  4.18264443e+00,  1.49607918e+00,
        1.57691294e+00,  3.28849227e-01,  2.39003022e+00,  1.07840109e+00,
        8.10677053e-01,  5.57945108e-01,  5.89483726e-01,  1.40646500e+00,
        2.38769699e+00,  3.33592642e+00,  4.92576112e-01,  1.64897773e+00,
        8.70602613e-01,  3.28203503e-01,  5.98006128e-01,  1.85519350e+00,
        5.28848929e+00,  8.98852307e-01,  1.62711360e+00,  1.55280346e+00,
        1.49136612e+00,  8.73686102e-01,  1.36286310e+00, -1.81572146e-01,
        7.77535746e-01,  1.55053396e+00,  7.13006914e-01,  4.64261897e-03,
        8.01311589e-01,  7.48462573e-01,  4.37894150e-01,  3.20953201e+00,
        1.01569966e+00,  1.04846962e+00,  2.60967933e+00,  1.88654294e+00,
        1.14477050e+00,  1.14136267e+00,  1.18280741e+00,  1.25494957e+00,
        8.98454204e-01,  2.10925704e-01,  1.05478650e+00,  2.35858707e+00,
        2.94164760e+00,  1.67571043e-01,  1.33878742e+00,  1.25839350e+00,
        1.53951656e+00,  9.05624320e-01,  1.17061173e+00,  2.54655499e+00,
        6.47466317e-01,  1.20289748e+00,  1.13571370e+00,  4.64266018e-01,
        1.14215867e+00,  1.49252246e-01,  1.82103747e+00, -2.49955629e-01,
        1.61755751e+00,  1.65686043e+00,  4.78967402e+00,  4.81742186e-01,
        1.44596520e+00,  1.32448131e+00,  8.89972080e-01,  2.34075771e+00,
        1.24303256e+00,  7.03972518e-01,  2.60285187e+00,  3.53153738e+00,
        1.35196678e+00,  3.50221519e+00,  4.47336205e-01,  9.67171390e-01,
        1.76976985e+00,  1.59672116e+00,  1.28269514e+00,  6.40395915e-01,
        1.29953005e+00,  5.27235568e-01,  1.46471898e+00,  1.66067091e+00,
        4.41349172e-01,  1.39726429e+00,  1.80795176e+00,  1.07103425e+00,
        5.76820176e-01,  1.21573235e+00,  1.34041046e+00,  1.73301081e-01]), upper=array([2.99397933, 1.96132754, 1.9741853 , 1.56915801, 3.40435554,
       2.91464536, 4.17157769, 2.35189282, 2.54248989, 4.34702931,
       2.28681813, 1.58798973, 2.46838793, 1.4842451 , 1.52209298,
       2.75057218, 2.25719594, 2.41607558, 2.30447366, 1.71324602,
       2.33541568, 2.24194145, 3.37712022, 2.16161502, 2.16743013,
       2.32044303, 5.7525094 , 2.95770978, 3.05001003, 1.96251894,
       3.65612204, 2.41472665, 2.15530985, 1.58579045, 1.84162227,
       2.53564354, 3.82321955, 4.44042528, 1.60388757, 2.96240096,
       2.12835682, 1.5469312 , 1.86880196, 3.16319094, 6.30956862,
       1.96174807, 2.99380439, 2.88775395, 2.60191973, 1.93653757,
       2.19505169, 1.30622414, 1.85682241, 2.95891228, 1.79928438,
       1.29625491, 2.09220303, 2.36290631, 1.53658861, 4.7506125 ,
       2.67337766, 2.17030365, 3.75023808, 3.35541687, 2.77520135,
       2.08450402, 2.16371497, 2.38837026, 1.87832477, 2.16419849,
       2.36599111, 3.50414737, 4.29523451, 1.53640485, 2.2309006 ,
       2.33145818, 2.66451633, 2.49759326, 2.43879385, 3.90232458,
       1.84661217, 2.27974655, 2.06887939, 1.71836616, 2.15279379,
       1.31422259, 2.90745441, 1.76813   , 2.71020272, 2.81272411,
       5.92280218, 1.86562672, 2.5298048 , 2.51531422, 2.39877546,
       3.36143692, 2.46371693, 1.76912589, 3.67435993, 4.72940884,
       2.48373427, 4.37798834, 2.15801521, 2.11703737, 3.27506479,
       2.88194859, 2.6982464 , 1.80432322, 2.45259713, 1.66864527,
       2.49172073, 3.85706896, 1.95383092, 2.49247639, 2.9572688 ,
       2.24464142, 2.27349167, 2.61578328, 2.64429111, 1.49723436]))coverage rate: 0.8

plot_func(x = range(len(y_test)),
          y = y_test,
          y_u=preds.upper,
          y_l=preds.lower,
          pred=preds.preds,
          method_name="before update",
          title="")

xxx

# update
fit_obj.update(X_test.iloc[0,:], y_test[0])

Regressor(method='rvfl', nb_hidden=3, pi_method='kdejackknifeplus')coverage rate: 0.8067226890756303

plot_func(x = range(len(y_test[:-1])),
          y = y_test[:-1],
          y_u=preds.upper,
          y_l=preds.lower,
          pred=preds.preds,
          method_name="after update",
          title="")

xxx

2 - R code version

X <- as.matrix(mtcars[,-1])
y <- mtcars$mpg

set.seed(123)
(index_train <- base::sample.int(n = nrow(X),
                                 size = floor(0.7*nrow(X)),
                                 replace = FALSE))

 [1] 31 15 19 14  3 10 18 22 11  5 20 29 23 30  9 28  8 27  7 32 26 17[1] 22 10[1] 10 10

obj <- learningmachine::Regressor$new(method = "rvfl",
nb_hidden = 50L, pi_method = "splitconformal")

obj$get_type()

[1] "regression"[1] "Regressor"

t0 <- proc.time()[3]
obj$fit(X_train, y_train, reg_lambda = 0.01)
cat("Elapsed: ", proc.time()[3] - t0, "s n")

Elapsed:  0.01 s n

print(obj$predict(X_test))

$preds
          Mazda RX4       Mazda RX4 Wag      Hornet 4 Drive             Valiant 
          21.350888           19.789387           13.106761            9.695310 
         Merc 450SE          Merc 450SL Lincoln Continental       Toyota Corona 
          11.131161           12.568682            2.044672           19.289805 
         Camaro Z28    Pontiac Firebird 
          14.847878           12.282272 

$lower
          Mazda RX4       Mazda RX4 Wag      Hornet 4 Drive             Valiant 
         12.3508879          10.7893873           4.1067608           0.6953102 
         Merc 450SE          Merc 450SL Lincoln Continental       Toyota Corona 
          2.1311611           3.5686817          -6.9553279          10.2898053 
         Camaro Z28    Pontiac Firebird 
          5.8478777           3.2822719 

$upper
          Mazda RX4       Mazda RX4 Wag      Hornet 4 Drive             Valiant 
           30.35089            28.78939            22.10676            18.69531 
         Merc 450SE          Merc 450SL Lincoln Continental       Toyota Corona 
           20.13116            21.56868            11.04467            28.28981 
         Camaro Z28    Pontiac Firebird 
           23.84788            21.28227 

obj$summary(X_test, y=y_test, show_progress=FALSE)

$R_squared
[1] -1.505856

$R_squared_adj
[1] 23.55271

$Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -1.548   1.461   5.000   4.349   7.949   8.405 

$Coverage_rate
[1] 100

$ttests
        estimate       lower        upper      p-value signif
cyl   137.649985   39.777048  235.5229227 1.115728e-02      *
disp   -2.406399   -4.650678   -0.1621204 3.825959e-02      *
hp     -0.527573   -1.402043    0.3468975 2.054686e-01       
drat  707.372951  246.095138 1168.6507638 7.059500e-03     **
wt   -500.429007 -565.047979 -435.8100352 2.910469e-08    ***
qsec  -89.930939 -124.899691  -54.9621860 2.537870e-04    ***
vs    234.198406 -127.886990  596.2838006 1.774484e-01       
am   -235.789718 -512.422513   40.8430776 8.592503e-02      .
gear   52.646721   -6.640614  111.9340567 7.547657e-02      .
carb  -17.100561  -87.819649   53.6185270 5.976705e-01       

$effects
── Data Summary ────────────────────────
                           Values 
Name                       effects
Number of rows             10     
Number of columns          10     
_______________________           
Column type frequency:            
  numeric                  10     
________________________          
Group variables            None   

── Variable type: numeric ──────────────────────────────────────────────────────
   skim_variable     mean     sd      p0      p25      p50       p75     p100
 1 cyl            138.    137.     -8.40   75.8     91.1     98.6     394.   
 2 disp            -2.41    3.14   -8.46   -1.32    -1.08    -0.775    -0.300
 3 hp              -0.528   1.22   -3.40   -0.695   -0.188    0.0137    0.893
 4 drat           707.    645.     55.7   388.     482.     563.     1939.   
 5 wt            -500.     90.3  -698.   -538.    -500.    -458.     -377.   
 6 qsec           -89.9    48.9  -145.   -128.    -102.     -64.0       2.67 
 7 vs             234.    506.   -121.    -13.2     36.8     53.2    1269.   
 8 am            -236.    387.   -653.   -450.    -397.    -168.      519.   
 9 gear            52.6    82.9  -107.     -4.69    66.2    112.      170.   
10 carb           -17.1    98.9  -117.    -64.6    -60.6    -17.5     171.   
   hist 
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 9 ▂▅▅▅▇
10 ▇▂▁▁▂

t0 <- proc.time()[3]
obj$fit(X_train, y_train)
cat("Elapsed: ", proc.time()[3] - t0, "s n")

Elapsed:  0.128 s n

xxx

[1] 1

update RVFL model

previous_coefs <- drop(obj$model$coef)

newx <- X_test[1, ]

newy <- y_test[1]

new_X_test <- X_test[-1, ]

new_y_test <- y_test[-1]

t0 <- proc.time()[3]
obj$update(newx, newy)
cat("Elapsed: ", proc.time()[3] - t0, "s n")

Elapsed:  0.242 s n

summary(previous_coefs)

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.68212 -0.26567 -0.05157  0.00700  0.21046  2.19222      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-0.030666 -0.002610  0.004189  0.002917  0.011386  0.025243 

xxx

obj$summary(new_X_test, y=new_y_test, show_progress=FALSE)

$R_squared
[1] -1.809339

$R_squared_adj
[1] 12.23735

$Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -1.168   2.513   5.541   5.058   8.185   8.703 

$Coverage_rate
[1] 100

$ttests
         estimate       lower        upper      p-value signif
cyl   111.6701473   17.076928  206.2633669 2.615518e-02      *
disp   -1.7983224   -3.876380    0.2797349 8.106884e-02      .
hp     -0.4167545   -1.501658    0.6681495 4.015523e-01       
drat  569.9102780  148.862037  990.9585186 1.420088e-02      *
wt   -504.1496696 -583.757006 -424.5423330 4.741273e-07    ***
qsec -107.9102921 -138.571336  -77.2492482 3.936777e-05    ***
vs    145.0280002 -173.164419  463.2204193 3.239468e-01       
am   -319.6910568 -566.618653  -72.7634604 1.745263e-02      *
gear   57.7630332  -18.934712  134.4607782 1.206459e-01       
carb  -42.9572292 -108.690903   22.7764447 1.702409e-01       

$effects
── Data Summary ────────────────────────
                           Values 
Name                       effects
Number of rows             9      
Number of columns          10     
_______________________           
Column type frequency:            
  numeric                  10     
________________________          
Group variables            None   

── Variable type: numeric ──────────────────────────────────────────────────────
   skim_variable     mean     sd      p0      p25       p50       p75     p100
 1 cyl            112.    123.    -13.5    64.5     93.6      93.9     426.   
 2 disp            -1.80    2.70   -8.94   -1.41    -0.805    -0.689    -0.361
 3 hp              -0.417   1.41   -3.54   -0.679   -0.0942   -0.0556    1.19 
 4 drat           570.    548.     36.8   371.     439.      501.     1972.   
 5 wt            -504.    104.   -742.   -523.    -497.     -461.     -382.   
 6 qsec          -108.     39.9  -152.   -143.    -115.      -93.0     -35.9  
 7 vs             145.    414.   -116.    -23.9     51.1      81.2    1231.   
 8 am            -320.    321.   -575.   -479.    -395.     -368.      465.   
 9 gear            57.8    99.8  -113.      1.22    35.2     130.      196.   
10 carb           -43.0    85.5  -129.    -79.6    -77.9     -22.5     165.   
   hist 
 1 ▅▇▁▁▂
 2 ▁▁▁▁▇
 3 ▂▁▂▇▃
 4 ▅▇▁▁▂
 5 ▂▁▂▇▃
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 7 ▇▁▁▁▁
 8 ▇▁▁▁▁
 9 ▃▇▇▇▇
10 ▇▅▁▁▂

res <- obj$predict(X = new_X_test)

new_y_train <- c(y_train, newy)

plot(c(new_y_train, res$preds), type='l',
main="",
ylab="",
ylim = c(min(c(res$upper, res$lower, y)),
max(c(res$upper, res$lower, y))))
lines(c(new_y_train, res$upper), col="gray60")
lines(c(new_y_train, res$lower), col="gray60")
lines(c(new_y_train, res$preds), col = "red")
lines(c(new_y_train, new_y_test), col = "blue")
abline(v = length(y_train), lty=2, col="black")

xxx

[1] 1

update RVFL model (Pt.2)

newx <- X_test[2, ]

newy <- y_test[2]

new_X_test <- X_test[-c(1, 2), ]

new_y_test <- y_test[-c(1, 2)]

t0 <- proc.time()[3]
obj$update(newx, newy)
cat("Elapsed: ", proc.time()[3] - t0, "s n")

Elapsed:  0.077 s n

obj$summary(new_X_test, y=new_y_test, show_progress=FALSE)

$R_squared
[1] -3.356623

$R_squared_adj
[1] 11.16545

$Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -1.950   5.030   6.374   6.369   8.774  11.528 

$Coverage_rate
[1] 75

$ttests
         estimate       lower        upper      p-value signif
cyl    40.8981137    6.878148   74.9180798 2.494779e-02      *
disp   -0.7335494   -1.206939   -0.2601595 8.026181e-03     **
hp     -0.8233606   -2.198927    0.5522055 1.998737e-01       
drat  549.7206897  416.053783  683.3875968 2.570765e-05    ***
wt   -469.9351032 -535.877454 -403.9927527 6.344763e-07    ***
qsec -116.6183871 -156.767393  -76.4693814 2.380078e-04    ***
vs   -194.4213942 -288.046178 -100.7966103 1.732503e-03     **
am   -395.7216847 -562.762331 -228.6810387 8.143911e-04    ***
gear   53.0732573  -59.833653  165.9801679 3.030574e-01       
carb  -25.9448064  -63.759959   11.8703467 1.487567e-01       

$effects
── Data Summary ────────────────────────
                           Values 
Name                       effects
Number of rows             8      
Number of columns          10     
_______________________           
Column type frequency:            
  numeric                  10     
________________________          
Group variables            None   

── Variable type: numeric ──────────────────────────────────────────────────────
   skim_variable     mean      sd      p0     p25      p50      p75     p100
 1 cyl             40.9    40.7    -40.5    23.9    56.3     69.9     77.8  
 2 disp            -0.734   0.566   -1.64   -1.03   -0.571   -0.372   -0.139
 3 hp              -0.823   1.65    -3.99   -1.18   -0.974   -0.196    1.25 
 4 drat           550.    160.     170.    549.    606.     642.     643.   
 5 wt            -470.     78.9   -543.   -537.   -489.    -437.    -336.   
 6 qsec          -117.     48.0   -179.   -143.   -131.     -99.1    -29.9  
 7 vs            -194.    112.    -377.   -283.   -162.    -120.     -46.3  
 8 am            -396.    200.    -719.   -481.   -357.    -319.     -67.7  
 9 gear            53.1   135.    -143.    -23.9    16.5    172.     231.   
10 carb           -25.9    45.2   -101.    -48.8   -23.8     -9.36    45.7  
   hist 
 1 ▂▂▂▁▇
 2 ▅▁▂▇▅
 3 ▂▁▇▂▃
 4 ▁▁▁▁▇
 5 ▇▅▂▁▅
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 7 ▂▅▂▇▂
 8 ▃▁▇▂▂
 9 ▂▅▅▁▇
10 ▂▅▇▁▅

res <- obj$predict(X = new_X_test)

new_y_train <- c(y_train, y_test[c(1, 2)])

plot(c(new_y_train, res$preds), type='l',
main="",
ylab="",
ylim = c(min(c(res$upper, res$lower, y)),
max(c(res$upper, res$lower, y))))
lines(c(new_y_train, res$upper), col="gray60")
lines(c(new_y_train, res$lower), col="gray60")
lines(c(new_y_train, res$preds), col = "red")
lines(c(new_y_train, new_y_test), col = "blue")
abline(v = length(y_train), lty=2, col="black")

xxx

[1] 0.75

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Citation

For attribution, please cite this work as:

T. Moudiki (2024-08-19). Conformalized adaptive (online/streaming) learning using learningmachine in Python and R. Retrieved from https://thierrymoudiki.github.io/blog/2024/08/19/r/python/code-conformal-adaptive-RVFL

BibTeX citation (remove empty spaces)
@misc{ tmoudiki20240819, author = { T. Moudiki }, title = { Conformalized adaptive (online/streaming) learning using learningmachine in Python and R }, url = { https://thierrymoudiki.github.io/blog/2024/08/19/r/python/code-conformal-adaptive-RVFL }, year = { 2024 } }

Under License Creative Commons Attribution 4.0 International

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nnetsauce version 0.5.0, randomized neural networks on GPU Jul 17, 2020

Maximizing your tip as a waiter (Part 2) Jul 10, 2020

New version of mlsauce, with Gradient Boosted randomized networks and stump decision trees Jul 3, 2020

Announcements Jun 26, 2020

Parallel AdaOpt classification Jun 19, 2020

Comments section and other news Jun 12, 2020

Maximizing your tip as a waiter Jun 5, 2020

AdaOpt classification on MNIST handwritten digits (without preprocessing) May 29, 2020

AdaOpt (a probabilistic classifier based on a mix of multivariable optimization and nearest neighbors) for R May 22, 2020

AdaOpt May 15, 2020

Custom errors for cross-validation using crossval::crossval_ml May 8, 2020

Documentation+Pypi for the `teller`, a model-agnostic tool for Machine Learning explainability May 1, 2020

Encoding your categorical variables based on the response variable and correlations Apr 24, 2020

Linear model, xgboost and randomForest cross-validation using crossval::crossval_ml Apr 17, 2020

Grid search cross-validation using crossval Apr 10, 2020

Documentation for the querier, a query language for Data Frames Apr 3, 2020

Time series cross-validation using crossval Mar 27, 2020

On model specification, identification, degrees of freedom and regularization Mar 20, 2020

Import data into the querier (now on Pypi), a query language for Data Frames Mar 13, 2020

R notebooks for nnetsauce Mar 6, 2020

Version 0.4.0 of nnetsauce, with fruits and breast cancer classification Feb 28, 2020

Create a specific feed in your Jekyll blog Feb 21, 2020

Git/Github for contributing to package development Feb 14, 2020

Feedback forms for contributing Feb 7, 2020

nnetsauce for R Jan 31, 2020

A new version of nnetsauce (v0.3.1) Jan 24, 2020

ESGtoolkit, a tool for Monte Carlo simulation (v0.2.0) Jan 17, 2020

Search bar, new year 2020 Jan 10, 2020

2019 Recap, the nnetsauce, the teller and the querier Dec 20, 2019

Understanding model interactions with the `teller` Dec 13, 2019

Using the `teller` on a classifier Dec 6, 2019

Benchmarking the querier's verbs Nov 29, 2019

Composing the querier's verbs for data wrangling Nov 22, 2019

Comparing and explaining model predictions with the teller Nov 15, 2019

Tests for the significance of marginal effects in the teller Nov 8, 2019

Introducing the teller Nov 1, 2019

Introducing the querier Oct 25, 2019

Prediction intervals for nnetsauce models Oct 18, 2019

Using R in Python for statistical learning/data science Oct 11, 2019

Model calibration with `crossval` Oct 4, 2019

Bagging in the nnetsauce Sep 25, 2019

Adaboost learning with nnetsauce Sep 18, 2019

Change in blog's presentation Sep 4, 2019

nnetsauce on Pypi Jun 5, 2019

More nnetsauce (examples of use) May 9, 2019

nnetsauce Mar 13, 2019

crossval Mar 13, 2019

test Mar 10, 2019