# Born's Classifier

from bornrule import BornClassifier


Bases: ClassifierMixin, BaseEstimator

Scikit-learn implementation of Born's Classifier

This class is compatible with the scikit-learn ecosystem. It supports both dense and sparse input and GPU-accelerated computing via CuPy. This classifier is suitable for classification with non-negative feature vectors. The data X are treated as unnormalized probability distributions.

Parameters:

Name Type Description Default
a float

Amplitude. Must be strictly positive.

0.5
b float

Balance. Must be non-negative.

1.0
h float

Entropy. Must be non-negative.

1.0

Attributes:

Name Type Description
gpu_ bool

Whether the model was fitted on GPU.

corpus_ array-like of shape (n_features_in_, n_classes)

Fitted corpus.

classes_ ndarray of shape (n_classes,)

Unique classes labels.

n_features_in_ int

Number of features seen during fit.

Source code in bornrule/born.py
  16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 class BornClassifier(ClassifierMixin, BaseEstimator): """Scikit-learn implementation of Born's Classifier This class is compatible with the [scikit-learn](https://scikit-learn.org) ecosystem. It supports both dense and sparse input and GPU-accelerated computing via [CuPy](https://cupy.dev). This classifier is suitable for classification with non-negative feature vectors. The data X are treated as unnormalized probability distributions. Parameters ---------- a : float Amplitude. Must be strictly positive. b : float Balance. Must be non-negative. h : float Entropy. Must be non-negative. Attributes ---------- gpu_ : bool Whether the model was fitted on GPU. corpus_ : array-like of shape (n_features_in_, n_classes) Fitted corpus. classes_ : ndarray of shape (n_classes,) Unique classes labels. n_features_in_ : int Number of features seen during fit. """ def __init__(self, a=0.5, b=1., h=1.): self.a = a self.b = b self.h = h def fit(self, X, y, sample_weight=None): """Fit the classifier according to the training data X, y. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where n_samples is the number of samples and n_features is the number of features. y : array-like of shape (n_samples,) or (n_samples, n_classes) Target values. If 2d array, this is the probability distribution over the n_classes for each of the n_samples. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- self : object Returns the instance itself. """ attrs = [ "gpu_", "corpus_", "classes_", "n_features_in_" ] for attr in attrs: if hasattr(self, attr): delattr(self, attr) return self.partial_fit(X, y, classes=y, sample_weight=sample_weight) def partial_fit(self, X, y, classes=None, sample_weight=None): """Incremental fit on a batch of samples. This method is expected to be called several times consecutively on different chunks of a dataset so as to implement out-of-core or online learning. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where n_samples is the number of samples and n_features is the number of features. y : array-like of shape (n_samples,) or (n_samples, n_classes) Target values. If 2d array, this is the probability distribution over the n_classes for each of the n_samples. classes : array-like of shape (n_classes,) List of all the classes that can possibly appear in the y vector. Must be provided at the first call to partial_fit, can be omitted in subsequent calls. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- self : object Returns the instance itself. """ X, y = self._sanitize(X, y) first_call = self._check_partial_fit_first_call(classes) if first_call: self.corpus_ = 0 self.n_features_in_ = X.shape[1] if not self._check_encoded(y): y = self._one_hot_encoding(y) if sample_weight is not None: sample_weight = self._check_sample_weight(sample_weight, X) y = self._multiply(y, sample_weight.reshape(-1, 1)) self.corpus_ += X.T @ self._multiply(y, self._power(self._sum(X, axis=1), -1)) return self def predict(self, X): """Perform classification on the test data X. Parameters ---------- X : array-like of shape (n_samples, n_features) Test data, where n_samples is the number of samples and n_features is the number of features. Returns ------- y : ndarray of shape (n_samples,) Predicted target classes for X. """ proba = self.predict_proba(X) idx = self._dense().argmax(proba, axis=1) return self.classes_[idx] def predict_proba(self, X): """Return probability estimates for the test data X. Parameters ---------- X : array-like of shape (n_samples, n_features) Test data, where n_samples is the number of samples and n_features is the number of features. Returns ------- y : ndarray of shape (n_samples, n_classes) Returns the probability of the samples for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_. """ self._check_fitted() X = self._sanitize(X) u = self._power(self._power(X, self.a) @ self._weights(), 1. / self.a) y = self._normalize(u, axis=1) if self._sparse().issparse(y): y = y.todense() return self._dense().asarray(y) def explain(self, X=None, sample_weight=None): r"""Global and local explanation For each test vector $x$, the $a$-th power of the unnormalized probability for the $k$-th class is given by the matrix product: math u_k^a = \sum_j W_{jk}x_j^a  where $W$ is a matrix of non-negative weights that generally depends on the model's hyper-parameters ($a$, $b$, $h$). The classification probabilities are obtained by normalizing $u$ such that it sums up to $1$. This method returns global or local feature importance weights, depending on X: - When X is not provided, this method returns the global weights $W$. - When X is a single sample, this method returns a matrix of entries $(j,k)$ where each entry is given by $W_{jk}x_j^a$. - When X contains multiple samples, then the values above are computed for each sample and this method returns their weighted sum. By default, each sample is given unit weight. Parameters ---------- X : array-like of shape (n_samples, n_features) Test data, where n_samples is the number of samples and n_features is the number of features. If not provided, then global weights are returned. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- E : array-like of shape (n_features, n_classes) Returns the feature importance for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_. """ self._check_fitted() if X is None: return self._weights() X = self._sanitize(X) X = self._normalize(X, axis=1) X = self._power(X, self.a) if sample_weight is not None: sample_weight = self._check_sample_weight(sample_weight, X) X = self._multiply(X, sample_weight.reshape(-1, 1)) return self._multiply(self._weights(), self._sum(X, axis=0).T) # X = self._sanitize(X) # if sample_weight is not None: # sample_weight = self._check_sample_weight(sample_weight, X) # # W_jk = self._weights() # X_nj = self._power(X, self.a) # X_nk = X_nj @ W_jk # # if self.gpu_ and self._sparse().issparse(X_nj): # X_nj = X_nj.tocsc() # # E_jk = 0 # for n in range(X.shape[0]): # # X_j, X_k = X_nj[n:n+1].T, X_nk[n:n+1] # X_jk = self._multiply(W_jk, X_j) # # U_k = self._power(X_k, 1. / self.a) # Y_k = self._normalize(U_k, axis=1) # # if self._sparse().issparse(X_j): # Z_j = X_j != 0 # X_k = Z_j @ X_k # Y_k = Z_j @ Y_k # # U_jk = self._power(X_k - X_jk, 1. / self.a) # Y_jk = self._normalize(U_jk, axis=1) # # D_jk = Y_k - Y_jk # if sample_weight is not None: # D_jk = sample_weight[n] * D_jk # # E_jk += D_jk # # return E_jk if sample_weight is not None else E_jk / X.shape[0] def _dense(self): return cupy if self.gpu_ else numpy def _sparse(self): return cupy.sparse if self.gpu_ else scipy.sparse def _weights(self): P_jk = self.corpus_ if self.b != 0: P_jk = self._multiply(P_jk, self._power(self._sum(self.corpus_, axis=0), -self.b)) if self.b != 1: P_jk = self._multiply(P_jk, self._power(self._sum(self.corpus_, axis=1), self.b-1)) W_jk = self._power(P_jk, self.a) if self.h != 0 and len(self.classes_) > 1: P_jk = self._normalize(P_jk, axis=1) H_j = 1 + self._sum(self._multiply(P_jk, self._log(P_jk)), axis=1) / self._dense().log(P_jk.shape[1]) W_jk = self._multiply(W_jk, self._power(H_j, self.h)) return W_jk def _sum(self, x, axis): if self._sparse().issparse(x): return x.sum(axis=axis) return self._dense().asarray(x).sum(axis=axis, keepdims=True) def _multiply(self, x, y): if self._sparse().issparse(x): return x.multiply(y).tocsr() if self._sparse().issparse(y): return y.multiply(x).tocsr() return self._dense().multiply(x, y) def _power(self, x, p): x = x.copy() if self._sparse().issparse(x): x.data = self._dense().power(x.data, p) else: nz = self._dense().nonzero(x) x[nz] = self._dense().power(x[nz], p) return x def _log(self, x): x = x.copy() if self._sparse().issparse(x): x.data = self._dense().log(x.data) else: nz = self._dense().nonzero(x) x[nz] = self._dense().log(x[nz]) return x def _normalize(self, x, axis, p=1.): s = self._sum(x, axis) n = self._power(s, -p) return self._multiply(x, n) def _sanitize(self, X, y="no_validation"): only_X = isinstance(y, str) and y == "no_validation" gpu = self._check_gpu(X=X, y=y if not only_X else None) if getattr(self, "gpu_", None) is None: self.gpu_ = gpu elif self.gpu_ != gpu: raise ValueError( "X is not on the same device (CPU/GPU) as on last call " "to partial_fit, was: %r" % (self.gpu_, )) if not self.gpu_: kwargs = { "accept_sparse": "csr", "reset": False, "dtype": (numpy.float32, numpy.float64) } if only_X: X = super()._validate_data(X=X, **kwargs) else: X, y = super()._validate_data(X=X, y=y, multi_output=self._check_encoded(y), **kwargs) if not self._check_non_negative(X): raise ValueError("X must contain non-negative values") return X if only_X else (X, y) def _unique_labels(self, y): if self._check_encoded(y): return self._dense().arange(0, y.shape[1]) elif self.gpu_: return self._dense().unique(y) else: return unique_labels(y) def _one_hot_encoding(self, y): classes = self.classes_ n, m = len(y), len(classes) if self.gpu_: y = y.get() classes = classes.get() unseen = set(y) - set(classes) if unseen: raise ValueError( "classes=%r were not allowed on first call " "to partial_fit" % (unseen, )) idx = {c: i for i, c in enumerate(classes)} col = self._dense().array([idx[c] for c in y]) row = self._dense().array(range(0, n)) val = self._dense().ones(n) return self._sparse().csr_matrix((val, (row, col)), shape=(n, m)) def _check_encoded(self, y): return self._sparse().issparse(y) or (getattr(y, "ndim", 0) == 2 and y.shape[1] > 1) def _check_non_negative(self, X): if self._sparse().issparse(X): if self._dense().any(X.data < 0): return False elif self._dense().any(X < 0): return False return True def _check_sample_weight(self, sample_weight, X): if self.gpu_: return sample_weight return _check_sample_weight(sample_weight=sample_weight, X=X) def _check_partial_fit_first_call(self, classes): if getattr(self, "classes_", None) is None and classes is None: raise ValueError("classes must be passed on the first call to partial_fit") elif classes is not None: classes = self._unique_labels(classes) if getattr(self, "classes_", None) is not None: if not self._dense().array_equal(self.classes_, classes): raise ValueError( "classes=%r is not the same as on last call " "to partial_fit, was: %r" % (classes, self.classes_)) else: self.classes_ = classes return True return False def _check_gpu(self, X, y=None): if not gpu_support: return False cp_X = cupy.get_array_module(X).__name__ == "cupy" if y is None: return cp_X cp_y = cupy.get_array_module(y).__name__ == "cupy" if cp_X == cp_y: return cp_X elif cp_X and not cp_y: raise ValueError("X is on GPU, but y is not") elif not cp_X and cp_y: raise ValueError("y is on GPU, but X is not") def _check_fitted(self): if getattr(self, "corpus_", None) is None: raise NotFittedError( f"This {self.__class__.__name__} instance is not fitted yet. " "Call 'fit' with appropriate arguments before using this estimator") def _more_tags(self): return { 'requires_y': True, 'requires_positive_X': True, 'X_types': ['2darray', 'sparse'], '_xfail_checks': { 'check_classifiers_classes': 'This is a pathological data set for BornClassifier. ' 'For some specific cases, it predicts less classes than expected', 'check_classifiers_train': 'Test fails because of negative values in X' } } 

## fit(X, y, sample_weight=None)

Fit the classifier according to the training data X, y.

Parameters:

Name Type Description Default
X array-like of shape (n_samples, n_features)

Training data, where n_samples is the number of samples and n_features is the number of features.

required
y array-like of shape (n_samples,) or (n_samples, n_classes)

Target values. If 2d array, this is the probability distribution over the n_classes for each of the n_samples.

required
sample_weight array-like of shape (n_samples,)

Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.

None

Returns:

Name Type Description
self object

Returns the instance itself.

Source code in bornrule/born.py
 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 def fit(self, X, y, sample_weight=None): """Fit the classifier according to the training data X, y. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where n_samples is the number of samples and n_features is the number of features. y : array-like of shape (n_samples,) or (n_samples, n_classes) Target values. If 2d array, this is the probability distribution over the n_classes for each of the n_samples. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- self : object Returns the instance itself. """ attrs = [ "gpu_", "corpus_", "classes_", "n_features_in_" ] for attr in attrs: if hasattr(self, attr): delattr(self, attr) return self.partial_fit(X, y, classes=y, sample_weight=sample_weight) 

## partial_fit(X, y, classes=None, sample_weight=None)

Incremental fit on a batch of samples.

This method is expected to be called several times consecutively on different chunks of a dataset so as to implement out-of-core or online learning.

Parameters:

Name Type Description Default
X array-like of shape (n_samples, n_features)

Training data, where n_samples is the number of samples and n_features is the number of features.

required
y array-like of shape (n_samples,) or (n_samples, n_classes)

Target values. If 2d array, this is the probability distribution over the n_classes for each of the n_samples.

required
classes array-like of shape (n_classes,)

List of all the classes that can possibly appear in the y vector. Must be provided at the first call to partial_fit, can be omitted in subsequent calls.

None
sample_weight array-like of shape (n_samples,)

Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.

None

Returns:

Name Type Description
self object

Returns the instance itself.

Source code in bornrule/born.py
  85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 def partial_fit(self, X, y, classes=None, sample_weight=None): """Incremental fit on a batch of samples. This method is expected to be called several times consecutively on different chunks of a dataset so as to implement out-of-core or online learning. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where n_samples is the number of samples and n_features is the number of features. y : array-like of shape (n_samples,) or (n_samples, n_classes) Target values. If 2d array, this is the probability distribution over the n_classes for each of the n_samples. classes : array-like of shape (n_classes,) List of all the classes that can possibly appear in the y vector. Must be provided at the first call to partial_fit, can be omitted in subsequent calls. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- self : object Returns the instance itself. """ X, y = self._sanitize(X, y) first_call = self._check_partial_fit_first_call(classes) if first_call: self.corpus_ = 0 self.n_features_in_ = X.shape[1] if not self._check_encoded(y): y = self._one_hot_encoding(y) if sample_weight is not None: sample_weight = self._check_sample_weight(sample_weight, X) y = self._multiply(y, sample_weight.reshape(-1, 1)) self.corpus_ += X.T @ self._multiply(y, self._power(self._sum(X, axis=1), -1)) return self 

## predict(X)

Perform classification on the test data X.

Parameters:

Name Type Description Default
X array-like of shape (n_samples, n_features)

Test data, where n_samples is the number of samples and n_features is the number of features.

required

Returns:

Name Type Description
y ndarray of shape (n_samples,)

Predicted target classes for X.

Source code in bornrule/born.py
 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 def predict(self, X): """Perform classification on the test data X. Parameters ---------- X : array-like of shape (n_samples, n_features) Test data, where n_samples is the number of samples and n_features is the number of features. Returns ------- y : ndarray of shape (n_samples,) Predicted target classes for X. """ proba = self.predict_proba(X) idx = self._dense().argmax(proba, axis=1) return self.classes_[idx] 

## predict_proba(X)

Return probability estimates for the test data X.

Parameters:

Name Type Description Default
X array-like of shape (n_samples, n_features)

Test data, where n_samples is the number of samples and n_features is the number of features.

required

Returns:

Name Type Description
y ndarray of shape (n_samples, n_classes)

Returns the probability of the samples for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_.

Source code in bornrule/born.py
 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 def predict_proba(self, X): """Return probability estimates for the test data X. Parameters ---------- X : array-like of shape (n_samples, n_features) Test data, where n_samples is the number of samples and n_features is the number of features. Returns ------- y : ndarray of shape (n_samples, n_classes) Returns the probability of the samples for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_. """ self._check_fitted() X = self._sanitize(X) u = self._power(self._power(X, self.a) @ self._weights(), 1. / self.a) y = self._normalize(u, axis=1) if self._sparse().issparse(y): y = y.todense() return self._dense().asarray(y) 

## explain(X=None, sample_weight=None)

Global and local explanation

For each test vector $x$, the $a$-th power of the unnormalized probability for the $k$-th class is given by the matrix product:

$u_k^a = \sum_j W_{jk}x_j^a$

where $W$ is a matrix of non-negative weights that generally depends on the model's hyper-parameters ($a$, $b$, $h$). The classification probabilities are obtained by normalizing $u$ such that it sums up to $1$.

This method returns global or local feature importance weights, depending on X:

• When X is not provided, this method returns the global weights $W$.

• When X is a single sample, this method returns a matrix of entries $(j,k)$ where each entry is given by $W_{jk}x_j^a$.

• When X contains multiple samples, then the values above are computed for each sample and this method returns their weighted sum. By default, each sample is given unit weight.

Parameters:

Name Type Description Default
X array-like of shape (n_samples, n_features)

Test data, where n_samples is the number of samples and n_features is the number of features. If not provided, then global weights are returned.

None
sample_weight array-like of shape (n_samples,)

Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.

None

Returns:

Name Type Description
E array-like of shape (n_features, n_classes)

Returns the feature importance for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_.

Source code in bornrule/born.py
 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 def explain(self, X=None, sample_weight=None): r"""Global and local explanation For each test vector $x$, the $a$-th power of the unnormalized probability for the $k$-th class is given by the matrix product: math u_k^a = \sum_j W_{jk}x_j^a  where $W$ is a matrix of non-negative weights that generally depends on the model's hyper-parameters ($a$, $b$, $h$). The classification probabilities are obtained by normalizing $u$ such that it sums up to $1$. This method returns global or local feature importance weights, depending on X: - When X is not provided, this method returns the global weights $W$. - When X is a single sample, this method returns a matrix of entries $(j,k)$ where each entry is given by $W_{jk}x_j^a$. - When X contains multiple samples, then the values above are computed for each sample and this method returns their weighted sum. By default, each sample is given unit weight. Parameters ---------- X : array-like of shape (n_samples, n_features) Test data, where n_samples is the number of samples and n_features is the number of features. If not provided, then global weights are returned. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- E : array-like of shape (n_features, n_classes) Returns the feature importance for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_. """ self._check_fitted() if X is None: return self._weights() X = self._sanitize(X) X = self._normalize(X, axis=1) X = self._power(X, self.a) if sample_weight is not None: sample_weight = self._check_sample_weight(sample_weight, X) X = self._multiply(X, sample_weight.reshape(-1, 1)) return self._multiply(self._weights(), self._sum(X, axis=0).T)