nnetsauce

 21class AdaBoostClassifier(Boosting, ClassifierMixin):
 22    """AdaBoost Classification (SAMME) model class derived from class Boosting
 23
 24    Parameters:
 25
 26        obj: object
 27            any object containing a method fit (obj.fit()) and a method predict
 28            (obj.predict())
 29
 30        n_estimators: int
 31            number of boosting iterations
 32
 33        learning_rate: float
 34            learning rate of the boosting procedure
 35
 36        n_hidden_features: int
 37            number of nodes in the hidden layer
 38
 39        reg_lambda: float
 40            regularization parameter for weights
 41
 42        reg_alpha: float
 43            controls compromize between l1 and l2 norm of weights
 44
 45        activation_name: str
 46            activation function: 'relu', 'tanh', 'sigmoid', 'prelu' or 'elu'
 47
 48        a: float
 49            hyperparameter for 'prelu' or 'elu' activation function
 50
 51        nodes_sim: str
 52            type of simulation for the nodes: 'sobol', 'hammersley', 'halton',
 53            'uniform'
 54
 55        bias: boolean
 56            indicates if the hidden layer contains a bias term (True) or not
 57            (False)
 58
 59        dropout: float
 60            regularization parameter; (random) percentage of nodes dropped out
 61            of the training
 62
 63        direct_link: boolean
 64            indicates if the original predictors are included (True) in model's
 65            fitting or not (False)
 66
 67        n_clusters: int
 68            number of clusters for 'kmeans' or 'gmm' clustering (could be 0:
 69                no clustering)
 70
 71        cluster_encode: bool
 72            defines how the variable containing clusters is treated (default is one-hot)
 73            if `False`, then labels are used, without one-hot encoding
 74
 75        type_clust: str
 76            type of clustering method: currently k-means ('kmeans') or Gaussian
 77            Mixture Model ('gmm')
 78
 79        type_scaling: a tuple of 3 strings
 80            scaling methods for inputs, hidden layer, and clustering respectively
 81            (and when relevant).
 82            Currently available: standardization ('std') or MinMax scaling ('minmax')
 83
 84        col_sample: float
 85            percentage of covariates randomly chosen for training
 86
 87        row_sample: float
 88            percentage of rows chosen for training, by stratified bootstrapping
 89
 90        seed: int
 91            reproducibility seed for nodes_sim=='uniform'
 92
 93        verbose: int
 94            0 for no output, 1 for a progress bar (default is 1)
 95
 96        method: str
 97            type of Adaboost method, 'SAMME' (discrete) or 'SAMME.R' (real)
 98
 99        backend: str
100            "cpu" or "gpu" or "tpu"
101
102    Attributes:
103
104        alpha_: list
105            AdaBoost coefficients alpha_m
106
107        base_learners_: dict
108            a dictionary containing the base learners
109
110    Examples:
111
112    See also [https://github.com/Techtonique/nnetsauce/blob/master/examples/adaboost_classification.py](https://github.com/Techtonique/nnetsauce/blob/master/examples/adaboost_classification.py)
113
114    ```python
115    import nnetsauce as ns
116    import numpy as np
117    from sklearn.datasets import load_breast_cancer
118    from sklearn.linear_model import LogisticRegression
119    from sklearn.model_selection import train_test_split
120    from sklearn import metrics
121    from time import time
122
123    breast_cancer = load_breast_cancer()
124    Z = breast_cancer.data
125    t = breast_cancer.target
126    np.random.seed(123)
127    X_train, X_test, y_train, y_test = train_test_split(Z, t, test_size=0.2)
128
129    # SAMME.R
130    clf = LogisticRegression(solver='liblinear', multi_class = 'ovr',
131                            random_state=123)
132    fit_obj = ns.AdaBoostClassifier(clf,
133                                    n_hidden_features=int(11.22338867),
134                                    direct_link=True,
135                                    n_estimators=250, learning_rate=0.01126343,
136                                    col_sample=0.72684326, row_sample=0.86429443,
137                                    dropout=0.63078613, n_clusters=2,
138                                    type_clust="gmm",
139                                    verbose=1, seed = 123,
140                                    method="SAMME.R")
141
142    start = time()
143    fit_obj.fit(X_train, y_train)
144    print(f"Elapsed {time() - start}")
145
146    start = time()
147    print(fit_obj.score(X_test, y_test))
148    print(f"Elapsed {time() - start}")
149
150    preds = fit_obj.predict(X_test)
151
152    print(metrics.classification_report(preds, y_test))
153
154    ```
155
156    """
157
158    # construct the object -----
159    _estimator_type = "classifier"
160
161    def __init__(
162        self,
163        obj,
164        n_estimators=10,
165        learning_rate=0.1,
166        n_hidden_features=1,
167        reg_lambda=0,
168        reg_alpha=0.5,
169        activation_name="relu",
170        a=0.01,
171        nodes_sim="sobol",
172        bias=True,
173        dropout=0,
174        direct_link=False,
175        n_clusters=2,
176        cluster_encode=True,
177        type_clust="kmeans",
178        type_scaling=("std", "std", "std"),
179        col_sample=1,
180        row_sample=1,
181        seed=123,
182        verbose=1,
183        method="SAMME",
184        backend="cpu",
185    ):
186        self.type_fit = "classification"
187        self.verbose = verbose
188        self.method = method
189        self.reg_lambda = reg_lambda
190        self.reg_alpha = reg_alpha
191
192        super().__init__(
193            obj=obj,
194            n_estimators=n_estimators,
195            learning_rate=learning_rate,
196            n_hidden_features=n_hidden_features,
197            activation_name=activation_name,
198            a=a,
199            nodes_sim=nodes_sim,
200            bias=bias,
201            dropout=dropout,
202            direct_link=direct_link,
203            n_clusters=n_clusters,
204            cluster_encode=cluster_encode,
205            type_clust=type_clust,
206            type_scaling=type_scaling,
207            col_sample=col_sample,
208            row_sample=row_sample,
209            seed=seed,
210            backend=backend,
211        )
212
213        self.alpha_ = []
214        self.base_learners_ = dict.fromkeys(range(n_estimators))
215
216    def fit(self, X, y, sample_weight=None, **kwargs):
217        """Fit Boosting model to training data (X, y).
218
219        Parameters:
220
221            X: {array-like}, shape = [n_samples, n_features]
222                Training vectors, where n_samples is the number
223                of samples and n_features is the number of features.
224
225            y: array-like, shape = [n_samples]
226                Target values.
227
228            **kwargs: additional parameters to be passed to
229                    self.cook_training_set or self.obj.fit
230
231        Returns:
232
233             self: object
234        """
235
236        assert mx.is_factor(y), "y must contain only integers"
237
238        assert self.method in (
239            "SAMME",
240            "SAMME.R",
241        ), "`method` must be either 'SAMME' or 'SAMME.R'"
242
243        assert (self.reg_lambda <= 1) & (
244            self.reg_lambda >= 0
245        ), "must have self.reg_lambda <= 1 &  self.reg_lambda >= 0"
246
247        assert (self.reg_alpha <= 1) & (
248            self.reg_alpha >= 0
249        ), "must have self.reg_alpha <= 1 &  self.reg_alpha >= 0"
250
251        # training
252        n, p = X.shape
253        self.n_classes = len(np.unique(y))
254        self.classes_ = np.unique(y)  # for compatibility with sklearn
255        self.n_classes_ = len(self.classes_)  # for compatibility with sklearn
256
257        if sample_weight is None:
258            w_m = np.repeat(1.0 / n, n)
259        else:
260            w_m = np.asarray(sample_weight)
261
262        base_learner = CustomClassifier(
263            self.obj,
264            n_hidden_features=self.n_hidden_features,
265            activation_name=self.activation_name,
266            a=self.a,
267            nodes_sim=self.nodes_sim,
268            bias=self.bias,
269            dropout=self.dropout,
270            direct_link=self.direct_link,
271            n_clusters=self.n_clusters,
272            type_clust=self.type_clust,
273            type_scaling=self.type_scaling,
274            col_sample=self.col_sample,
275            row_sample=self.row_sample,
276            seed=self.seed,
277        )
278
279        if self.verbose == 1:
280            pbar = Progbar(self.n_estimators)
281
282        if self.method == "SAMME":
283            err_m = 1e6
284            err_bound = 1 - 1 / self.n_classes
285            self.alpha_.append(1.0)
286            x_range_n = range(n)
287
288            for m in range(self.n_estimators):
289                preds = base_learner.fit(
290                    X, y, sample_weight=w_m.ravel(), **kwargs
291                ).predict(X)
292
293                self.base_learners_.update({m: deepcopy(base_learner)})
294
295                cond = [y[i] != preds[i] for i in x_range_n]
296
297                err_m = max(
298                    sum([elt[0] * elt[1] for elt in zip(cond, w_m)]),
299                    2.220446049250313e-16,
300                )  # sum(w_m) == 1
301
302                if self.reg_lambda > 0:
303                    err_m += self.reg_lambda * (
304                        (1 - self.reg_alpha) * 0.5 * sum([x**2 for x in w_m])
305                        + self.reg_alpha * sum([abs(x) for x in w_m])
306                    )
307
308                err_m = min(err_m, err_bound)
309
310                alpha_m = self.learning_rate * log(
311                    (self.n_classes - 1) * (1 - err_m) / err_m
312                )
313
314                self.alpha_.append(alpha_m)
315
316                w_m_temp = [exp(alpha_m * cond[i]) for i in x_range_n]
317
318                sum_w_m = sum(w_m_temp)
319
320                w_m = np.asarray([w_m_temp[i] / sum_w_m for i in x_range_n])
321
322                base_learner.set_params(seed=self.seed + (m + 1) * 1000)
323
324                if self.verbose == 1:
325                    pbar.update(m)
326
327            if self.verbose == 1:
328                pbar.update(self.n_estimators)
329
330            self.n_estimators = len(self.base_learners_)
331            self.classes_ = np.unique(y)
332
333            return self
334
335        if self.method == "SAMME.R":
336            Y = mo.one_hot_encode2(y, self.n_classes)
337
338            if sample_weight is None:
339                w_m = np.repeat(1.0 / n, n)  # (N, 1)
340
341            else:
342                w_m = np.asarray(sample_weight)
343
344            for m in range(self.n_estimators):
345                probs = base_learner.fit(
346                    X, y, sample_weight=w_m.ravel(), **kwargs
347                ).predict_proba(X)
348
349                np.clip(
350                    a=probs, a_min=2.220446049250313e-16, a_max=1.0, out=probs
351                )
352
353                self.base_learners_.update({m: deepcopy(base_learner)})
354
355                w_m *= np.exp(
356                    -1.0
357                    * self.learning_rate
358                    * (1.0 - 1.0 / self.n_classes)
359                    * xlogy(Y, probs).sum(axis=1)
360                )
361
362                w_m /= np.sum(w_m)
363
364                base_learner.set_params(seed=self.seed + (m + 1) * 1000)
365
366                if self.verbose == 1:
367                    pbar.update(m)
368
369            if self.verbose == 1:
370                pbar.update(self.n_estimators)
371
372            self.n_estimators = len(self.base_learners_)
373            self.classes_ = np.unique(y)
374
375            return self
376
377    def predict(self, X, **kwargs):
378        """Predict test data X.
379
380        Parameters:
381
382            X: {array-like}, shape = [n_samples, n_features]
383                Training vectors, where n_samples is the number
384                of samples and n_features is the number of features.
385
386            **kwargs: additional parameters to be passed to
387                  self.cook_test_set
388
389        Returns:
390
391            model predictions: {array-like}
392        """
393        return self.predict_proba(X, **kwargs).argmax(axis=1)
394
395    def predict_proba(self, X, **kwargs):
396        """Predict probabilities for test data X.
397
398        Parameters:
399
400            X: {array-like}, shape = [n_samples, n_features]
401                Training vectors, where n_samples is the number
402                of samples and n_features is the number of features.
403
404            **kwargs: additional parameters to be passed to
405                  self.cook_test_set
406
407        Returns:
408
409            probability estimates for test data: {array-like}
410
411        """
412
413        n_iter = len(self.base_learners_)
414
415        if self.method == "SAMME":
416            ensemble_learner = np.zeros((X.shape[0], self.n_classes))
417
418            # if self.verbose == 1:
419            #    pbar = Progbar(n_iter)
420
421            for idx, base_learner in self.base_learners_.items():
422                preds = base_learner.predict(X, **kwargs)
423
424                ensemble_learner += self.alpha_[idx] * mo.one_hot_encode2(
425                    preds, self.n_classes
426                )
427
428                # if self.verbose == 1:
429                #    pbar.update(idx)
430
431            # if self.verbose == 1:
432            #    pbar.update(n_iter)
433
434            expit_ensemble_learner = expit(ensemble_learner)
435
436            sum_ensemble = expit_ensemble_learner.sum(axis=1)
437
438            return expit_ensemble_learner / sum_ensemble[:, None]
439
440        # if self.method == "SAMME.R":
441        ensemble_learner = 0
442
443        # if self.verbose == 1:
444        #    pbar = Progbar(n_iter)
445
446        for idx, base_learner in self.base_learners_.items():
447            probs = base_learner.predict_proba(X, **kwargs)
448
449            np.clip(a=probs, a_min=2.220446049250313e-16, a_max=1.0, out=probs)
450
451            log_preds_proba = np.log(probs)
452
453            ensemble_learner += (
454                log_preds_proba - log_preds_proba.mean(axis=1)[:, None]
455            )
456
457            # if self.verbose == 1:
458            #    pbar.update(idx)
459
460        ensemble_learner *= self.n_classes - 1
461
462        # if self.verbose == 1:
463        #    pbar.update(n_iter)
464
465        expit_ensemble_learner = expit(ensemble_learner)
466
467        sum_ensemble = expit_ensemble_learner.sum(axis=1)
468
469        return expit_ensemble_learner / sum_ensemble[:, None]
470
471    @property
472    def _estimator_type(self):
473        return "classifier"

  48class Base(BaseEstimator):
  49    """Base model from which all the other classes inherit.
  50
  51    This class contains the most important data preprocessing/feature engineering methods.
  52
  53    Parameters:
  54
  55        n_hidden_features: int
  56            number of nodes in the hidden layer
  57
  58        activation_name: str
  59            activation function: 'relu', 'tanh', 'sigmoid', 'prelu' or 'elu'
  60
  61        a: float
  62            hyperparameter for 'prelu' or 'elu' activation function
  63
  64        nodes_sim: str
  65            type of simulation for hidden layer nodes: 'sobol', 'hammersley', 'halton',
  66            'uniform'
  67
  68        bias: boolean
  69            indicates if the hidden layer contains a bias term (True) or
  70            not (False)
  71
  72        dropout: float
  73            regularization parameter; (random) percentage of nodes dropped out
  74            of the training
  75
  76        direct_link: boolean
  77            indicates if the original features are included (True) in model's
  78            fitting or not (False)
  79
  80        n_clusters: int
  81            number of clusters for type_clust='kmeans' or type_clust='gmm'
  82            clustering (could be 0: no clustering)
  83
  84        cluster_encode: bool
  85            defines how the variable containing clusters is treated (default is one-hot);
  86            if `False`, then labels are used, without one-hot encoding
  87
  88        type_clust: str
  89            type of clustering method: currently k-means ('kmeans') or Gaussian
  90            Mixture Model ('gmm')
  91
  92        type_scaling: a tuple of 3 strings
  93            scaling methods for inputs, hidden layer, and clustering respectively
  94            (and when relevant).
  95            Currently available: standardization ('std') or MinMax scaling ('minmax') or robust scaling ('robust') or  max absolute scaling ('maxabs')
  96
  97        col_sample: float
  98            percentage of features randomly chosen for training
  99
 100        row_sample: float
 101            percentage of rows chosen for training, by stratified bootstrapping
 102
 103        seed: int
 104            reproducibility seed for nodes_sim=='uniform', clustering and dropout
 105
 106        backend: str
 107            "cpu" or "gpu" or "tpu"
 108
 109    """
 110
 111    # construct the object -----
 112
 113    def __init__(
 114        self,
 115        n_hidden_features=5,
 116        activation_name="relu",
 117        a=0.01,
 118        nodes_sim="sobol",
 119        bias=True,
 120        dropout=0,
 121        direct_link=True,
 122        n_clusters=2,
 123        cluster_encode=True,
 124        type_clust="kmeans",
 125        type_scaling=("std", "std", "std"),
 126        col_sample=1,
 127        row_sample=1,
 128        seed=123,
 129        backend="cpu",
 130    ):
 131        if not JAX_AVAILABLE and backend != "cpu":
 132            raise RuntimeError(
 133                "JAX is required for this feature. Install with: pip install yourpackage[jax]"
 134            )
 135
 136        # input checks -----
 137
 138        sys_platform = platform.system()
 139
 140        if (sys_platform == "Windows") and (backend in ("gpu", "tpu")):
 141            warnings.warn(
 142                "No GPU/TPU computing on Windows yet, backend set to 'cpu'"
 143            )
 144            backend = "cpu"
 145
 146        assert activation_name in (
 147            "relu",
 148            "tanh",
 149            "sigmoid",
 150            "prelu",
 151            "elu",
 152        ), "'activation_name' must be in ('relu', 'tanh', 'sigmoid','prelu', 'elu')"
 153
 154        assert nodes_sim in (
 155            "sobol",
 156            "hammersley",
 157            "uniform",
 158            "halton",
 159        ), "'nodes_sim' must be in ('sobol', 'hammersley', 'uniform', 'halton')"
 160
 161        assert type_clust in (
 162            "kmeans",
 163            "gmm",
 164        ), "'type_clust' must be in ('kmeans', 'gmm')"
 165
 166        assert (len(type_scaling) == 3) & all(
 167            type_scaling[i] in ("minmax", "std", "robust", "maxabs")
 168            for i in range(len(type_scaling))
 169        ), "'type_scaling' must have length 3, and available scaling methods are 'minmax' scaling, standardization ('std'), robust scaling ('robust') and max absolute ('maxabs')"
 170
 171        assert (col_sample >= 0) & (
 172            col_sample <= 1
 173        ), "'col_sample' must be comprised between 0 and 1 (both included)"
 174
 175        assert backend in (
 176            "cpu",
 177            "gpu",
 178            "tpu",
 179        ), "must have 'backend' in ('cpu', 'gpu', 'tpu')"
 180
 181        self.n_hidden_features = n_hidden_features
 182        self.activation_name = activation_name
 183        self.a = a
 184        self.nodes_sim = nodes_sim
 185        self.bias = bias
 186        self.seed = seed
 187        self.backend = backend
 188        self.dropout = dropout
 189        self.direct_link = direct_link
 190        self.cluster_encode = cluster_encode
 191        self.type_clust = type_clust
 192        self.type_scaling = type_scaling
 193        self.col_sample = col_sample
 194        self.row_sample = row_sample
 195        self.n_clusters = n_clusters
 196        if isinstance(self, RegressorMixin):
 197            self.type_fit = "regression"
 198        elif isinstance(self, ClassifierMixin):
 199            self.type_fit = "classification"
 200        self.subsampler_ = None
 201        self.index_col_ = None
 202        self.index_row_ = True
 203        self.clustering_obj_ = None
 204        self.clustering_scaler_ = None
 205        self.nn_scaler_ = None
 206        self.scaler_ = None
 207        self.encoder_ = None
 208        self.W_ = None
 209        self.X_ = None
 210        self.y_ = None
 211        self.y_mean_ = None
 212        self.beta_ = None
 213
 214        # activation function -----
 215
 216        activation_options = {
 217            "relu": ac.relu if (self.backend == "cpu") else jnn.relu,
 218            "tanh": np.tanh if (self.backend == "cpu") else jnp.tanh,
 219            "sigmoid": (ac.sigmoid if (self.backend == "cpu") else jnn.sigmoid),
 220            "prelu": partial(ac.prelu, a=a),
 221            "elu": (
 222                partial(ac.elu, a=a)
 223                if (self.backend == "cpu")
 224                else partial(jnn.elu, a=a)
 225            ),
 226        }
 227
 228        self.activation_func = activation_options[activation_name]
 229
 230    # "preprocessing" methods to be inherited -----
 231
 232    def encode_clusters(self, X=None, predict=False, scaler=None, **kwargs):  #
 233        """Create new covariates with kmeans or GMM clustering
 234
 235        Parameters:
 236
 237            X: {array-like}, shape = [n_samples, n_features]
 238                Training vectors, where n_samples is the number
 239                of samples and n_features is the number of features.
 240
 241            predict: boolean
 242                is False on training set and True on test set
 243
 244            scaler: {object} of class StandardScaler, MinMaxScaler, RobustScaler or MaxAbsScaler
 245                if scaler has already been fitted on training data (online training), it can be passed here
 246
 247            **kwargs:
 248                additional parameters to be passed to the
 249                clustering method
 250
 251        Returns:
 252
 253            Clusters' matrix, one-hot encoded: {array-like}
 254
 255        """
 256
 257        np.random.seed(self.seed)
 258
 259        if X is None:
 260            X = self.X_
 261
 262        if isinstance(X, pd.DataFrame):
 263            X = copy.deepcopy(X.values.astype(float))
 264
 265        if len(X.shape) == 1:
 266            X = X.reshape(1, -1)
 267
 268        if predict is False:  # encode training set
 269            # scale input data before clustering
 270            self.clustering_scaler_, scaled_X = mo.scale_covariates(
 271                X, choice=self.type_scaling[2], scaler=self.clustering_scaler_
 272            )
 273
 274            self.clustering_obj_, X_clustered = mo.cluster_covariates(
 275                scaled_X,
 276                self.n_clusters,
 277                self.seed,
 278                type_clust=self.type_clust,
 279                **kwargs
 280            )
 281
 282            if self.cluster_encode:
 283                return mo.one_hot_encode(X_clustered, self.n_clusters).astype(
 284                    np.float16
 285                )
 286
 287            return X_clustered.astype(np.float16)
 288
 289        # if predict == True, encode test set
 290        X_clustered = self.clustering_obj_.predict(
 291            self.clustering_scaler_.transform(X)
 292        )
 293
 294        if self.cluster_encode == True:
 295            return mo.one_hot_encode(X_clustered, self.n_clusters).astype(
 296                np.float16
 297            )
 298
 299        return X_clustered.astype(np.float16)
 300
 301    def create_layer(self, scaled_X, W=None):
 302        """Create hidden layer.
 303
 304        Parameters:
 305
 306            scaled_X: {array-like}, shape = [n_samples, n_features]
 307                Training vectors, where n_samples is the number
 308                of samples and n_features is the number of features
 309
 310            W: {array-like}, shape = [n_features, hidden_features]
 311                if provided, constructs the hidden layer with W; otherwise computed internally
 312
 313        Returns:
 314
 315            Hidden layer matrix: {array-like}
 316
 317        """
 318
 319        n_features = scaled_X.shape[1]
 320
 321        # hash_sim = {
 322        #         "sobol": generate_sobol,
 323        #         "hammersley": generate_hammersley,
 324        #         "uniform": generate_uniform,
 325        #         "halton": generate_halton
 326        #     }
 327
 328        if self.bias is False:  # no bias term in the hidden layer
 329            if W is None:
 330                if self.nodes_sim == "sobol":
 331                    self.W_ = generate_sobol(
 332                        n_dims=n_features,
 333                        n_points=self.n_hidden_features,
 334                        seed=self.seed,
 335                    )
 336                elif self.nodes_sim == "hammersley":
 337                    self.W_ = generate_hammersley(
 338                        n_dims=n_features,
 339                        n_points=self.n_hidden_features,
 340                        seed=self.seed,
 341                    )
 342                elif self.nodes_sim == "uniform":
 343                    self.W_ = generate_uniform(
 344                        n_dims=n_features,
 345                        n_points=self.n_hidden_features,
 346                        seed=self.seed,
 347                    )
 348                else:
 349                    self.W_ = generate_halton(
 350                        n_dims=n_features,
 351                        n_points=self.n_hidden_features,
 352                        seed=self.seed,
 353                    )
 354
 355                assert (
 356                    scaled_X.shape[1] == self.W_.shape[0]
 357                ), "check dimensions of covariates X and matrix W"
 358
 359                return mo.dropout(
 360                    x=self.activation_func(
 361                        mo.safe_sparse_dot(
 362                            a=scaled_X, b=self.W_, backend=self.backend
 363                        )
 364                    ),
 365                    drop_prob=self.dropout,
 366                    seed=self.seed,
 367                )
 368
 369            # W is not none
 370            assert (
 371                scaled_X.shape[1] == W.shape[0]
 372            ), "check dimensions of covariates X and matrix W"
 373
 374            # self.W_ = W
 375            return mo.dropout(
 376                x=self.activation_func(
 377                    mo.safe_sparse_dot(a=scaled_X, b=W, backend=self.backend)
 378                ),
 379                drop_prob=self.dropout,
 380                seed=self.seed,
 381            )
 382
 383        # with bias term in the hidden layer
 384        if W is None:
 385            n_features_1 = n_features + 1
 386
 387            if self.nodes_sim == "sobol":
 388                self.W_ = generate_sobol(
 389                    n_dims=n_features_1,
 390                    n_points=self.n_hidden_features,
 391                    seed=self.seed,
 392                )
 393            elif self.nodes_sim == "hammersley":
 394                self.W_ = generate_hammersley(
 395                    n_dims=n_features_1,
 396                    n_points=self.n_hidden_features,
 397                    seed=self.seed,
 398                )
 399            elif self.nodes_sim == "uniform":
 400                self.W_ = generate_uniform(
 401                    n_dims=n_features_1,
 402                    n_points=self.n_hidden_features,
 403                    seed=self.seed,
 404                )
 405            else:
 406                self.W_ = generate_halton(
 407                    n_dims=n_features_1,
 408                    n_points=self.n_hidden_features,
 409                    seed=self.seed,
 410                )
 411
 412            # self.W_ = hash_sim[self.nodes_sim](
 413            #         n_dims=n_features_1,
 414            #         n_points=self.n_hidden_features,
 415            #         seed=self.seed,
 416            #     )
 417
 418            return mo.dropout(
 419                x=self.activation_func(
 420                    mo.safe_sparse_dot(
 421                        a=mo.cbind(
 422                            np.ones(scaled_X.shape[0]),
 423                            scaled_X,
 424                            backend=self.backend,
 425                        ),
 426                        b=self.W_,
 427                        backend=self.backend,
 428                    )
 429                ),
 430                drop_prob=self.dropout,
 431                seed=self.seed,
 432            )
 433
 434        # W is not None
 435        # self.W_ = W
 436        return mo.dropout(
 437            x=self.activation_func(
 438                mo.safe_sparse_dot(
 439                    a=mo.cbind(
 440                        np.ones(scaled_X.shape[0]),
 441                        scaled_X,
 442                        backend=self.backend,
 443                    ),
 444                    b=W,
 445                    backend=self.backend,
 446                )
 447            ),
 448            drop_prob=self.dropout,
 449            seed=self.seed,
 450        )
 451
 452    def _jax_create_layer(self, scaled_X, W=None):
 453        """JAX-compatible version of create_layer that exactly matches the original functionality."""
 454        key = jax.random.PRNGKey(self.seed)
 455        n_features = scaled_X.shape[1]
 456
 457        # Generate weights if not provided
 458        if W is None:
 459            if self.bias:
 460                n_features_1 = n_features + 1
 461                shape = (n_features_1, self.n_hidden_features)
 462            else:
 463                shape = (n_features, self.n_hidden_features)
 464
 465            # JAX-compatible weight generation matching original behavior
 466            if self.nodes_sim == "sobol":
 467                W_np = generate_sobol(
 468                    n_dims=n_features_1,
 469                    n_points=self.n_hidden_features,
 470                    seed=self.seed,
 471                )
 472                W = jnp.asarray(W_np)
 473            elif self.nodes_sim == "hammersley":
 474                W_np = generate_hammersley(
 475                    n_dims=n_features_1,
 476                    n_points=self.n_hidden_features,
 477                    seed=self.seed,
 478                )
 479                W = jnp.asarray(W_np)
 480            elif self.nodes_sim == "uniform":
 481                key, subkey = jax.random.split(key)
 482                W = jax.random.uniform(
 483                    subkey, shape=shape, minval=-1.0, maxval=1.0
 484                )
 485            else:  # halton
 486                W_np = generate_halton(
 487                    n_dims=n_features_1,
 488                    n_points=self.n_hidden_features,
 489                    seed=self.seed,
 490                )
 491                W = jnp.asarray(W_np)
 492
 493            self.W_ = np.array(W)  # Store as numpy for original methods
 494
 495        # Prepare input with bias if needed
 496        if self.bias:
 497            X_with_bias = jnp.hstack(
 498                [jnp.ones((scaled_X.shape[0], 1)), scaled_X]
 499            )
 500            print("X_with_bias shape:", X_with_bias.shape)
 501            print("W shape:", W.shape)
 502            linear_output = jnp.dot(X_with_bias, W)
 503        else:
 504            linear_output = jnp.dot(scaled_X, W)
 505
 506        # Apply activation function
 507        if self.activation_name == "relu":
 508            activated = jax.nn.relu(linear_output)
 509        elif self.activation_name == "tanh":
 510            activated = jnp.tanh(linear_output)
 511        elif self.activation_name == "sigmoid":
 512            activated = jax.nn.sigmoid(linear_output)
 513        else:  # leaky relu
 514            activated = jax.nn.leaky_relu(linear_output, negative_slope=self.a)
 515
 516        # Apply dropout
 517        if self.dropout > 0:
 518            key, subkey = jax.random.split(key)
 519            mask = jax.random.bernoulli(
 520                subkey, p=1 - self.dropout, shape=activated.shape
 521            )
 522            activated = jnp.where(mask, activated / (1 - self.dropout), 0)
 523
 524        return activated
 525
 526    def cook_training_set(self, y=None, X=None, W=None, **kwargs):
 527        """Create new hidden features for training set, with hidden layer, center the response.
 528
 529        Parameters:
 530
 531            y: array-like, shape = [n_samples]
 532                Target values
 533
 534            X: {array-like}, shape = [n_samples, n_features]
 535                Training vectors, where n_samples is the number
 536                of samples and n_features is the number of features
 537
 538            W: {array-like}, shape = [n_features, hidden_features]
 539                if provided, constructs the hidden layer via W
 540
 541        Returns:
 542
 543            (centered response, direct link + hidden layer matrix): {tuple}
 544
 545        """
 546
 547        # either X and y are stored or not
 548        # assert ((y is None) & (X is None)) | ((y is not None) & (X is not None))
 549        if self.n_hidden_features > 0:  # has a hidden layer
 550            assert (
 551                len(self.type_scaling) >= 2
 552            ), "must have len(self.type_scaling) >= 2 when self.n_hidden_features > 0"
 553
 554        if X is None:
 555            if self.col_sample == 1:
 556                input_X = self.X_
 557            else:
 558                n_features = self.X_.shape[1]
 559                new_n_features = int(np.ceil(n_features * self.col_sample))
 560                assert (
 561                    new_n_features >= 1
 562                ), "check class attribute 'col_sample' and the number of covariates provided for X"
 563                np.random.seed(self.seed)
 564                index_col = np.random.choice(
 565                    range(n_features), size=new_n_features, replace=False
 566                )
 567                self.index_col_ = index_col
 568                input_X = self.X_[:, self.index_col_]
 569
 570        else:  # X is not None # keep X vs self.X_
 571            if isinstance(X, pd.DataFrame):
 572                X = copy.deepcopy(X.values.astype(float))
 573
 574            if self.col_sample == 1:
 575                input_X = X
 576            else:
 577                n_features = X.shape[1]
 578                new_n_features = int(np.ceil(n_features * self.col_sample))
 579                assert (
 580                    new_n_features >= 1
 581                ), "check class attribute 'col_sample' and the number of covariates provided for X"
 582                np.random.seed(self.seed)
 583                index_col = np.random.choice(
 584                    range(n_features), size=new_n_features, replace=False
 585                )
 586                self.index_col_ = index_col
 587                input_X = X[:, self.index_col_]
 588
 589        if self.n_clusters <= 0:
 590            # data without any clustering: self.n_clusters is None -----
 591
 592            if self.n_hidden_features > 0:  # with hidden layer
 593                self.nn_scaler_, scaled_X = mo.scale_covariates(
 594                    input_X, choice=self.type_scaling[1], scaler=self.nn_scaler_
 595                )
 596                Phi_X = (
 597                    self.create_layer(scaled_X)
 598                    if W is None
 599                    else self.create_layer(scaled_X, W=W)
 600                )
 601                Z = (
 602                    mo.cbind(input_X, Phi_X, backend=self.backend)
 603                    if self.direct_link is True
 604                    else Phi_X
 605                )
 606                self.scaler_, scaled_Z = mo.scale_covariates(
 607                    Z, choice=self.type_scaling[0], scaler=self.scaler_
 608                )
 609            else:  # no hidden layer
 610                Z = input_X
 611                self.scaler_, scaled_Z = mo.scale_covariates(
 612                    Z, choice=self.type_scaling[0], scaler=self.scaler_
 613                )
 614
 615        else:
 616            # data with clustering: self.n_clusters is not None ----- # keep
 617
 618            augmented_X = mo.cbind(
 619                input_X,
 620                self.encode_clusters(input_X, **kwargs),
 621                backend=self.backend,
 622            )
 623
 624            if self.n_hidden_features > 0:  # with hidden layer
 625                self.nn_scaler_, scaled_X = mo.scale_covariates(
 626                    augmented_X,
 627                    choice=self.type_scaling[1],
 628                    scaler=self.nn_scaler_,
 629                )
 630                Phi_X = (
 631                    self.create_layer(scaled_X)
 632                    if W is None
 633                    else self.create_layer(scaled_X, W=W)
 634                )
 635                Z = (
 636                    mo.cbind(augmented_X, Phi_X, backend=self.backend)
 637                    if self.direct_link is True
 638                    else Phi_X
 639                )
 640                self.scaler_, scaled_Z = mo.scale_covariates(
 641                    Z, choice=self.type_scaling[0], scaler=self.scaler_
 642                )
 643            else:  # no hidden layer
 644                Z = augmented_X
 645                self.scaler_, scaled_Z = mo.scale_covariates(
 646                    Z, choice=self.type_scaling[0], scaler=self.scaler_
 647                )
 648
 649        # Returning model inputs -----
 650        if mx.is_factor(y) is False:  # regression
 651            # center y
 652            if y is None:
 653                self.y_mean_, centered_y = mo.center_response(self.y_)
 654            else:
 655                self.y_mean_, centered_y = mo.center_response(y)
 656
 657            # y is subsampled
 658            if self.row_sample < 1:
 659                n, p = Z.shape
 660
 661                self.subsampler_ = (
 662                    SubSampler(
 663                        y=self.y_, row_sample=self.row_sample, seed=self.seed
 664                    )
 665                    if y is None
 666                    else SubSampler(
 667                        y=y, row_sample=self.row_sample, seed=self.seed
 668                    )
 669                )
 670
 671                self.index_row_ = self.subsampler_.subsample()
 672
 673                n_row_sample = len(self.index_row_)
 674                # regression
 675                return (
 676                    centered_y[self.index_row_].reshape(n_row_sample),
 677                    self.scaler_.transform(
 678                        Z[self.index_row_, :].reshape(n_row_sample, p)
 679                    ),
 680                )
 681            # y is not subsampled
 682            # regression
 683            return (centered_y, self.scaler_.transform(Z))
 684
 685        # classification
 686        # y is subsampled
 687        if self.row_sample < 1:
 688            n, p = Z.shape
 689
 690            self.subsampler_ = (
 691                SubSampler(
 692                    y=self.y_, row_sample=self.row_sample, seed=self.seed
 693                )
 694                if y is None
 695                else SubSampler(y=y, row_sample=self.row_sample, seed=self.seed)
 696            )
 697
 698            self.index_row_ = self.subsampler_.subsample()
 699
 700            n_row_sample = len(self.index_row_)
 701            # classification
 702            return (
 703                y[self.index_row_].reshape(n_row_sample),
 704                self.scaler_.transform(
 705                    Z[self.index_row_, :].reshape(n_row_sample, p)
 706                ),
 707            )
 708        # y is not subsampled
 709        # classification
 710        return (y, self.scaler_.transform(Z))
 711
 712    def cook_test_set(self, X, **kwargs):
 713        """Transform data from test set, with hidden layer.
 714
 715        Parameters:
 716
 717            X: {array-like}, shape = [n_samples, n_features]
 718                Training vectors, where n_samples is the number
 719                of samples and n_features is the number of features
 720
 721            **kwargs: additional parameters to be passed to self.encode_cluster
 722
 723        Returns:
 724
 725            Transformed test set : {array-like}
 726        """
 727
 728        if isinstance(X, pd.DataFrame):
 729            X = copy.deepcopy(X.values.astype(float))
 730
 731        if len(X.shape) == 1:
 732            X = X.reshape(1, -1)
 733
 734        if (
 735            self.n_clusters == 0
 736        ):  # data without clustering: self.n_clusters is None -----
 737            if self.n_hidden_features > 0:
 738                # if hidden layer
 739                scaled_X = (
 740                    self.nn_scaler_.transform(X)
 741                    if (self.col_sample == 1)
 742                    else self.nn_scaler_.transform(X[:, self.index_col_])
 743                )
 744                Phi_X = self.create_layer(scaled_X, self.W_)
 745                if self.direct_link:
 746                    return self.scaler_.transform(
 747                        mo.cbind(scaled_X, Phi_X, backend=self.backend)
 748                    )
 749                # when self.direct_link == False
 750                return self.scaler_.transform(Phi_X)
 751            # if no hidden layer # self.n_hidden_features == 0
 752            return self.scaler_.transform(X)
 753
 754        # data with clustering: self.n_clusters > 0 -----
 755        if self.col_sample == 1:
 756            predicted_clusters = self.encode_clusters(
 757                X=X, predict=True, **kwargs
 758            )
 759            augmented_X = mo.cbind(X, predicted_clusters, backend=self.backend)
 760        else:
 761            predicted_clusters = self.encode_clusters(
 762                X=X[:, self.index_col_], predict=True, **kwargs
 763            )
 764            augmented_X = mo.cbind(
 765                X[:, self.index_col_], predicted_clusters, backend=self.backend
 766            )
 767
 768        if self.n_hidden_features > 0:  # if hidden layer
 769            scaled_X = self.nn_scaler_.transform(augmented_X)
 770            Phi_X = self.create_layer(scaled_X, self.W_)
 771            if self.direct_link:
 772                return self.scaler_.transform(
 773                    mo.cbind(augmented_X, Phi_X, backend=self.backend)
 774                )
 775            return self.scaler_.transform(Phi_X)
 776
 777        # if no hidden layer
 778        return self.scaler_.transform(augmented_X)
 779
 780    def cook_training_set_jax(self, y=None, X=None, W=None, **kwargs):
 781        """JAX-compatible version of cook_training_set that maintains side effects."""
 782        # Initialize random key
 783        key = jax.random.PRNGKey(self.seed)
 784
 785        # Convert inputs to JAX arrays
 786        X = jnp.asarray(X) if X is not None else jnp.asarray(self.X_)
 787        y = jnp.asarray(y) if y is not None else jnp.asarray(self.y_)
 788
 789        # Handle column sampling
 790        if self.col_sample < 1:
 791            n_features = X.shape[1]
 792            new_n_features = int(jnp.ceil(n_features * self.col_sample))
 793            assert new_n_features >= 1, "Invalid col_sample"
 794
 795            key, subkey = jax.random.split(key)
 796            index_col = jax.random.choice(
 797                subkey, n_features, shape=(new_n_features,), replace=False
 798            )
 799            self.index_col_ = np.array(
 800                index_col
 801            )  # Store as numpy for original methods
 802            input_X = X[:, index_col]
 803            n_features = (
 804                new_n_features  # Update n_features after column sampling
 805            )
 806        else:
 807            input_X = X
 808            n_features = X.shape[1]
 809
 810        augmented_X = input_X
 811
 812        # JAX-compatible scaling
 813        def jax_scale(data, mean=None, std=None):
 814            if mean is None:
 815                mean = jnp.mean(data, axis=0)
 816            if std is None:
 817                std = jnp.std(data, axis=0)
 818            return (data - mean) / (std + 1e-10), mean, std
 819
 820        # Hidden layer processing
 821        if self.n_hidden_features > 0:
 822            # Initialize weights if not provided
 823            if W is None:
 824                shape = (n_features, self.n_hidden_features)
 825
 826                # JAX-compatible weight generation
 827                if self.nodes_sim == "uniform":
 828                    key, subkey = jax.random.split(key)
 829                    W = jax.random.uniform(
 830                        subkey, shape=shape, minval=-1.0, maxval=1.0
 831                    ) * (1 / jnp.sqrt(n_features))
 832                else:
 833                    # For other sequences, use numpy generation then convert to JAX
 834                    if self.nodes_sim == "sobol":
 835                        W_np = generate_sobol(
 836                            n_dims=shape[0],
 837                            n_points=shape[1],
 838                            seed=self.seed,
 839                        )
 840                    elif self.nodes_sim == "hammersley":
 841                        W_np = generate_hammersley(
 842                            n_dims=shape[0],
 843                            n_points=shape[1],
 844                            seed=self.seed,
 845                        )
 846                    elif self.nodes_sim == "halton":
 847                        W_np = generate_halton(
 848                            n_dims=shape[0],
 849                            n_points=shape[1],
 850                            seed=self.seed,
 851                        )
 852                    else:  # default to uniform
 853                        key, subkey = jax.random.split(key)
 854                        W = jax.random.uniform(
 855                            subkey, shape=shape, minval=-1.0, maxval=1.0
 856                        ) * (1 / jnp.sqrt(n_features))
 857
 858                    if self.nodes_sim in ["sobol", "hammersley", "halton"]:
 859                        W = jnp.asarray(W_np) * (1 / jnp.sqrt(n_features))
 860
 861                self.W_ = np.array(W)  # Store as numpy for original methods
 862
 863            # Scale features
 864            scaled_X, self.nn_mean_, self.nn_std_ = jax_scale(
 865                augmented_X,
 866                getattr(self, "nn_mean_", None),
 867                getattr(self, "nn_std_", None),
 868            )
 869
 870            # Create hidden layer with proper bias handling
 871            linear_output = jnp.dot(scaled_X, W)
 872
 873            # Apply activation
 874            if self.activation_name == "relu":
 875                Phi_X = jax.nn.relu(linear_output)
 876            elif self.activation_name == "tanh":
 877                Phi_X = jnp.tanh(linear_output)
 878            elif self.activation_name == "sigmoid":
 879                Phi_X = jax.nn.sigmoid(linear_output)
 880            else:  # leaky relu
 881                Phi_X = jax.nn.leaky_relu(linear_output, negative_slope=self.a)
 882
 883            # Apply dropout
 884            if self.dropout > 0:
 885                key, subkey = jax.random.split(key)
 886                mask = jax.random.bernoulli(
 887                    subkey, p=1 - self.dropout, shape=Phi_X.shape
 888                )
 889                Phi_X = jnp.where(mask, Phi_X / (1 - self.dropout), 0)
 890
 891            Z = jnp.hstack([scaled_X, Phi_X]) if self.direct_link else Phi_X
 892        else:
 893            Z = augmented_X
 894
 895        # Final scaling
 896        scaled_Z, self.scale_mean_, self.scale_std_ = jax_scale(
 897            Z,
 898            getattr(self, "scale_mean_", None),
 899            getattr(self, "scale_std_", None),
 900        )
 901
 902        # Center response for regression
 903        if not hasattr(mx, "is_factor") or not mx.is_factor(
 904            y
 905        ):  # regression case
 906            self.y_mean_ = float(
 907                jnp.mean(y)
 908            )  # Convert to Python float for compatibility
 909            centered_y = y - self.y_mean_
 910        else:
 911            centered_y = y
 912
 913        # Handle row sampling
 914        if self.row_sample < 1:
 915            key, subkey = jax.random.split(key)
 916            n_samples = Z.shape[0]
 917            n_row_sample = int(jnp.ceil(n_samples * self.row_sample))
 918            index_row = jax.random.choice(
 919                subkey, n_samples, shape=(n_row_sample,), replace=False
 920            )
 921            self.index_row_ = np.array(
 922                index_row
 923            )  # Store as numpy for original methods
 924            return (centered_y[index_row], scaled_Z[index_row])
 925
 926        return (centered_y, scaled_Z)
 927
 928    def cook_test_set_jax(self, X, **kwargs):
 929        """JAX-compatible test set processing with matching dimension handling."""
 930        X = jnp.asarray(X)
 931
 932        if len(X.shape) == 1:
 933            X = X.reshape(1, -1)
 934
 935        # Handle column sampling
 936        input_X = (
 937            X if self.col_sample == 1 else X[:, jnp.asarray(self.index_col_)]
 938        )
 939
 940        augmented_X = input_X
 941
 942        # JAX-compatible scaling
 943        scaled_X = (augmented_X - self.nn_mean_) / (self.nn_std_ + 1e-10)
 944
 945        # Process hidden layer if needed
 946        if self.n_hidden_features > 0:
 947            Phi_X = self._jax_create_layer(scaled_X, jnp.asarray(self.W_))
 948            Z = jnp.hstack([scaled_X, Phi_X]) if self.direct_link else Phi_X
 949        else:
 950            Z = augmented_X
 951
 952        # Final scaling
 953        scaled_Z = (Z - self.scale_mean_) / (self.scale_std_ + 1e-10)
 954
 955        return scaled_Z
 956
 957    def _jax_create_layer(self, X, W):
 958        """JAX-compatible hidden layer creation."""
 959        # print("X", X.shape)
 960        # print("W", W.shape)
 961        # print("self.W_", self.W_.shape)
 962        linear_output = jnp.dot(X, W)
 963
 964        if self.activation_name == "relu":
 965            return jax.nn.relu(linear_output)
 966        elif self.activation_name == "tanh":
 967            return jnp.tanh(linear_output)
 968        elif self.activation_name == "sigmoid":
 969            return jax.nn.sigmoid(linear_output)
 970        else:  # leaky relu
 971            return jax.nn.leaky_relu(linear_output, negative_slope=self.a)
 972
 973    def cross_val_score(
 974        self,
 975        X,
 976        y,
 977        cv=5,
 978        scoring="accuracy",
 979        random_state=42,
 980        n_jobs=-1,
 981        epsilon=0.5,
 982        penalized=True,
 983        objective="abs",
 984        **kwargs
 985    ):
 986        """
 987        Penalized Cross-validation score for a model.
 988
 989        Parameters:
 990
 991            X: {array-like}, shape = [n_samples, n_features]
 992                Training vectors, where n_samples is the number
 993                of samples and n_features is the number of features
 994
 995            y: array-like, shape = [n_samples]
 996                Target values
 997
 998            X_test: {array-like}, shape = [n_samples, n_features]
 999                Test vectors, where n_samples is the number
1000                of samples and n_features is the number of features
1001
1002            y_test: array-like, shape = [n_samples]
1003                Target values
1004
1005            cv: int
1006                Number of folds
1007
1008            scoring: str
1009                Scoring metric
1010
1011            random_state: int
1012                Random state
1013
1014            n_jobs: int
1015                Number of jobs to run in parallel
1016
1017            epsilon: float
1018                Penalty parameter
1019
1020            penalized: bool
1021                Whether to obtain penalized cross-validation score or not
1022
1023            objective: str
1024                'abs': Minimize the absolute difference between cross-validation score and validation score
1025                'relative': Minimize the relative difference between cross-validation score and validation score
1026        Returns:
1027
1028            A namedtuple with the following fields:
1029                - cv_score: float
1030                    cross-validation score
1031                - val_score: float
1032                    validation score
1033                - penalized_score: float
1034                    penalized cross-validation score: cv_score / val_score + epsilon*(1/val_score + 1/cv_score)
1035                    If higher scoring metric is better, minimize the function result.
1036                    If lower scoring metric is better, maximize the function result.
1037        """
1038        if scoring == "accuracy":
1039            scoring_func = accuracy_score
1040        elif scoring == "balanced_accuracy":
1041            scoring_func = balanced_accuracy_score
1042        elif scoring == "f1":
1043            scoring_func = f1_score
1044        elif scoring == "roc_auc":
1045            scoring_func = roc_auc_score
1046        elif scoring == "r2":
1047            scoring_func = r2_score
1048        elif scoring == "mse":
1049            scoring_func = mean_squared_error
1050        elif scoring == "mae":
1051            scoring_func = mean_absolute_error
1052        elif scoring == "mape":
1053            scoring_func = mean_absolute_percentage_error
1054        elif scoring == "rmse":
1055
1056            def scoring_func(y_true, y_pred):
1057                return np.sqrt(mean_squared_error(y_true, y_pred))
1058
1059        X_train, X_val, y_train, y_val = train_test_split(
1060            X, y, test_size=0.2, random_state=random_state
1061        )
1062
1063        res = cross_val_score(
1064            self, X_train, y_train, cv=cv, scoring=scoring, n_jobs=n_jobs
1065        )  # cross-validation error
1066
1067        if penalized == False:
1068            return res
1069
1070        DescribeResult = namedtuple(
1071            "DescribeResult", ["cv_score", "val_score", "penalized_score"]
1072        )
1073
1074        numerator = res.mean()
1075
1076        # Evaluate on the (cv+1)-th fold
1077        preds_val = self.fit(X_train, y_train).predict(X_val)
1078        try:
1079            denominator = scoring(y_val, preds_val)  # validation error
1080        except Exception as e:
1081            denominator = scoring_func(y_val, preds_val)
1082
1083        # if higher is better
1084        if objective == "abs":
1085            penalized_score = np.abs(numerator - denominator) + epsilon * (
1086                1 / denominator + 1 / numerator
1087            )
1088        elif objective == "relative":
1089            ratio = numerator / denominator
1090            penalized_score = np.abs(ratio - 1) + epsilon * (
1091                1 / denominator + 1 / numerator
1092            )
1093
1094        return DescribeResult(
1095            cv_score=numerator,
1096            val_score=denominator,
1097            penalized_score=penalized_score,
1098        )