예제 #1
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def labels_io():
    from shogun import RegressionLabels, CSVFile
    lab = RegressionLabels()
    f = CSVFile("../data/label_train_regression.dat", "r")
    f.set_delimiter(" ")
    lab.load(f)
    #print lab.get_labels()
    return lab
def evaluation_meansquarederror(ground_truth, predicted):
    from shogun import RegressionLabels
    from shogun import MeanSquaredError

    ground_truth_labels = RegressionLabels(ground_truth)
    predicted_labels = RegressionLabels(predicted)

    evaluator = MeanSquaredError()
    mse = evaluator.evaluate(predicted_labels, ground_truth_labels)

    return mse
예제 #3
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def regression_chaidtree(num_train=500,num_test=50,x_range=15,noise_var=0.2,ft=feattypes):
	try:
		from shogun import RealFeatures, RegressionLabels, CSVFile, CHAIDTree, PT_REGRESSION
		from numpy import random
	except ImportError:
		print("Could not import Shogun and/or numpy modules")
		return

	random.seed(1)

	# form training dataset : y=x with noise
	X_train=random.rand(1,num_train)*x_range;
	Y_train=X_train+random.randn(num_train)*noise_var

	# form test dataset
	X_test=array([[float(i)/num_test*x_range for i in range(num_test)]])

	# wrap features and labels into Shogun objects
	feats_train=RealFeatures(X_train)
	feats_test=RealFeatures(X_test)
	train_labels=RegressionLabels(Y_train[0])

	# CHAID Tree formation
	c=CHAIDTree(2,feattypes,50)
	c.set_labels(train_labels)
	c.train(feats_train)

	# Regress on test data
	output=c.apply_regression(feats_test).get_labels()

	return c,output
예제 #4
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        def RunLASSOShogun():
            totalTimer = Timer()

            # Load input dataset.
            # If the dataset contains two files then the second file is the responses
            # file.
            try:
                Log.Info("Loading dataset", self.verbose)
                if len(self.dataset) >= 2:
                    testSet = np.genfromtxt(self.dataset[1], delimiter=',')

                # Get all the parameters.
                lambda1 = None
                if "lambda1" in options:
                    lambda1 = float(options.pop("lambda1"))

                if len(options) > 0:
                    Log.Fatal("Unknown parameters: " + str(options))
                    raise Exception("unknown parameters")

                # Use the last row of the training set as the responses.
                X, y = SplitTrainData(self.dataset)

                with totalTimer:
                    model = LeastAngleRegression(lasso=True)
                    if lambda1:
                        model.set_max_l1_norm(lambda1)
                    model.set_labels(RegressionLabels(y))
                    model.train(RealFeatures(X.T))

            except Exception as e:
                return -1

            return totalTimer.ElapsedTime()
    def RunLinearRidgeRegressionShogun():
      totalTimer = Timer()

      # Load input dataset.
      # If the dataset contains two files then the second file is the responses
      # file.
      Log.Info("Loading dataset", self.verbose)
      if len(self.dataset) >= 2:
        testSet = np.genfromtxt(self.dataset[1], delimiter=',')

      # Use the last row of the training set as the responses.
      X, y = SplitTrainData(self.dataset)
      if "alpha" in options:
        tau = float(options.pop("alpha"))
      else:
        Log.Fatal("Required parameter 'alpha' not specified!")
        raise Exception("missing parameter")

      if len(options) > 0:
        Log.Fatal("Unknown parameters: " + str(options))
        raise Exception("unknown parameters")

      try:
        with totalTimer:
          # Perform linear ridge regression.
          model = LRR(tau, RealFeatures(X.T), RegressionLabels(y))
          model.train()

          if len(self.dataset) >= 2:
            model.apply_regression(RealFeatures(testSet.T))

      except Exception as e:
        return [-1]

      return [totalTimer.ElapsedTime(), model]
예제 #6
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        def RunLARSShogun():
            totalTimer = Timer()

            # Load input dataset.
            try:
                Log.Info("Loading dataset", self.verbose)
                inputData = np.genfromtxt(self.dataset[0], delimiter=',')
                responsesData = np.genfromtxt(self.dataset[1], delimiter=',')
                inputFeat = RealFeatures(inputData.T)
                responsesFeat = RegressionLabels(responsesData)

                # Get all the parameters.
                lambda1 = None
                if "lambda1" in options:
                    lambda1 = float(options.pop("lambda1"))

                if len(options) > 0:
                    Log.Fatal("Unknown parameters: " + str(options))
                    raise Exception("unknown parameters")

                with totalTimer:
                    # Perform LARS.
                    model = LeastAngleRegression(False)
                    if lambda1:
                        model.set_max_l1_norm(lambda1)
                    model.set_labels(responsesFeat)
                    model.train(inputFeat)
                    model.get_w_for_var(model.get_path_size() - 1)
            except Exception as e:
                return -1

            return totalTimer.ElapsedTime()
예제 #7
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def transfer_multitask_leastsquares_regression(fm_train=traindat,
                                               fm_test=testdat,
                                               label_train=label_traindat):
    from shogun import RegressionLabels, RealFeatures, Task, TaskGroup
    try:
        from shogun import MultitaskLeastSquaresRegression
    except ImportError:
        print("MultitaskLeastSquaresRegression not available")
        exit(0)

    features = RealFeatures(traindat)
    labels = RegressionLabels(label_train)

    n_vectors = features.get_num_vectors()
    task_one = Task(0, n_vectors // 2)
    task_two = Task(n_vectors // 2, n_vectors)
    task_group = TaskGroup()
    task_group.append_task(task_one)
    task_group.append_task(task_two)

    mtlsr = MultitaskLeastSquaresRegression(0.1, features, labels, task_group)
    mtlsr.set_regularization(1)  # use regularization ratio
    mtlsr.set_tolerance(1e-2)  # use 1e-2 tolerance
    mtlsr.train()
    mtlsr.set_current_task(0)
    out = mtlsr.apply_regression().get_labels()
    return out
예제 #8
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def regression_svrlight (fm_train=traindat,fm_test=testdat,label_train=label_traindat, \
				    width=1.2,C=1,epsilon=1e-5,tube_epsilon=1e-2,num_threads=3):


	from shogun import RegressionLabels, RealFeatures
	from shogun import GaussianKernel
	try:
		from shogun import SVRLight
	except ImportError:
		print('No support for SVRLight available.')
		return

	feats_train=RealFeatures(fm_train)
	feats_test=RealFeatures(fm_test)

	kernel=GaussianKernel(feats_train, feats_train, width)

	labels=RegressionLabels(label_train)

	svr=SVRLight(C, epsilon, kernel, labels)
	svr.set_tube_epsilon(tube_epsilon)
	svr.parallel.set_num_threads(num_threads)
	svr.train()

	kernel.init(feats_train, feats_test)
	out = svr.apply().get_labels()

	return out, kernel
예제 #9
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def get_labels(raw=False, type='binary'):
    data = concatenate(
        array(
            (-ones(NUM_EXAMPLES, dtype=double), ones(NUM_EXAMPLES,
                                                     dtype=double))))
    if raw:
        return data
    else:
        if type == 'binary':
            return BinaryLabels(data)
        if type == 'regression':
            return RegressionLabels(data)
        return None
예제 #10
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  def __init__(self, method_param, run_param):
    self.info = "SHOGUN_LARS ("  + str(method_param) +  ")"

    # Assemble run model parameter.
    self.data = load_dataset(method_param["datasets"], ["csv"])
    self.data_split = split_dataset(self.data[0])

    self.train_features = RealFeatures(self.data_split[0].T)
    self.train_labels = RegressionLabels(self.data_split[1])

    if len(self.data) >= 2:
      self.test_features = RealFeatures(self.data[1].T)

    self.lasso = True
    if "lasso" in method_param:
      self.lasso = bool(method_param["lasso"])

    self.solver = "auto"
    if "solver" in method_param:
      self.solver = str(method_param["solver"])
예제 #11
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    def __init__(self, method_param, run_param):
        self.info = "SHOGUN_LINEARREGRESSION (" + str(method_param) + ")"

        # Assemble run model parameter.
        self.data = load_dataset(method_param["datasets"], ["csv"])
        self.data_split = split_dataset(self.data[0])

        self.train_feat = RealFeatures(self.data_split[0].T)
        self.train_labels = RegressionLabels(self.data_split[1])

        if len(self.data) >= 2:
            self.test_feat = RealFeatures(self.data[1].T)

        self.bias = 0
        if "bias" in method_param:
            self.bias = float(method_param["bias"])

        self.solver = "auto"
        if "solver" in method_param:
            self.solver = str(method_param["solver"])
예제 #12
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파일: dtr.py 프로젝트: zoq/benchmarks
  def __init__(self, method_param, run_param):
    self.info = "SHOGUN_DTR ("  + str(method_param) +  ")"

    # Assemble run model parameter.
    self.data = load_dataset(method_param["datasets"], ["csv"])
    self.data_split = split_dataset(self.data[0])

    self.train_feat = RealFeatures(self.data_split[0].T)
    self.train_labels = RegressionLabels(self.data_split[1])

    if len(self.data) >= 2:
      self.test_feat = RealFeatures(self.data[1].T)

    # Flag for Cross Validation Pruning
    self.cv_prune = False
    if "pruning" in method_param:
      self.cv_prune = bool(method_param["pruning"])

    self.num_folds = 2
    if "k" in method_param:
      # Making sure that the value is of the right type
      self.num_folds = int(method_param["k"])
def evaluation_cross_validation_regression(train_fname=traindat,
                                           label_fname=label_traindat,
                                           width=0.8,
                                           tau=1e-6):
    from shogun import CrossValidation, CrossValidationResult
    from shogun import MeanSquaredError, CrossValidationSplitting
    from shogun import RegressionLabels, RealFeatures
    from shogun import GaussianKernel, KernelRidgeRegression, CSVFile

    # training data
    features = RealFeatures(CSVFile(train_fname))
    labels = RegressionLabels(CSVFile(label_fname))

    # kernel and predictor
    kernel = GaussianKernel()
    predictor = KernelRidgeRegression(tau, kernel, labels)

    # splitting strategy for 5 fold cross-validation (for classification its better
    # to use "StratifiedCrossValidation", but here, the std x-val is used
    splitting_strategy = CrossValidationSplitting(labels, 5)

    # evaluation method
    evaluation_criterium = MeanSquaredError()

    # cross-validation instance
    cross_validation = CrossValidation(predictor, features, labels,
                                       splitting_strategy,
                                       evaluation_criterium)

    # (optional) repeat x-val 10 times
    cross_validation.set_num_runs(10)

    # (optional) tell machine to precompute kernel matrix. speeds up. may not work
    predictor.data_lock(labels, features)

    # perform cross-validation and print(results)
    result = cross_validation.evaluate()
예제 #14
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        def RunSVRShogun():
            totalTimer = Timer()
            # Load input dataset.
            Log.Info("Loading dataset", self.verbose)
            # Use the last row of the training set as the responses.
            X, y = SplitTrainData(self.dataset)

            # Get all the parameters.
            self.C = 1.0
            self.epsilon = 1.0
            self.width = 0.1
            if "c" in options:
                self.C = float(options.pop("c"))
            if "epsilon" in options:
                self.epsilon = float(options.pop("epsilon"))
            if "gamma" in options:
                self.width = np.true_divide(1, float(options.pop("gamma")))

            if len(options) > 0:
                Log.Fatal("Unknown parameters: " + str(options))
                raise Exception("unknown parameters")

            data = RealFeatures(X.T)
            labels_train = RegressionLabels(y)
            self.kernel = GaussianKernel(data, data, self.width)

            try:
                with totalTimer:
                    # Perform SVR.
                    model = LibSVR(self.C, self.epsilon, self.kernel,
                                   labels_train)
                    model.train()
            except Exception as e:
                return -1

            return totalTimer.ElapsedTime()
예제 #15
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def regression_randomforest(num_train=500,
                            num_test=50,
                            x_range=15,
                            noise_var=0.2,
                            ft=feattypes):
    try:
        from shogun import RealFeatures, RegressionLabels, CSVFile, RandomForest, MeanRule, PT_REGRESSION
    except ImportError:
        print("Could not import Shogun modules")
        return

    random.seed(1)

    # form training dataset : y=x with noise
    X_train = random.rand(1, num_train) * x_range
    Y_train = X_train + random.randn(num_train) * noise_var

    # form test dataset
    X_test = array([[float(i) / num_test * x_range for i in range(num_test)]])

    # wrap features and labels into Shogun objects
    feats_train = RealFeatures(X_train)
    feats_test = RealFeatures(X_test)
    train_labels = RegressionLabels(Y_train[0])

    # Random Forest formation
    rand_forest = RandomForest(feats_train, train_labels, 20, 1)
    rand_forest.set_feature_types(ft)
    rand_forest.set_machine_problem_type(PT_REGRESSION)
    rand_forest.set_combination_rule(MeanRule())
    rand_forest.train()

    # Regress test data
    output = rand_forest.apply_regression(feats_test).get_labels()

    return rand_forest, output
예제 #16
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def stochasticgbmachine(train=traindat,
                        train_labels=label_traindat,
                        ft=feat_types):
    try:
        from shogun import RealFeatures, RegressionLabels, CSVFile, CARTree, StochasticGBMachine, SquaredLoss
    except ImportError:
        print("Could not import Shogun modules")
        return

    # wrap features and labels into Shogun objects
    feats = RealFeatures(CSVFile(train))
    labels = RegressionLabels(CSVFile(train_labels))

    # divide into training (90%) and test dataset (10%)
    p = np.random.permutation(labels.get_num_labels())
    num = labels.get_num_labels() * 0.9

    cart = CARTree()
    cart.set_feature_types(ft)
    cart.set_max_depth(1)
    loss = SquaredLoss()
    s = StochasticGBMachine(cart, loss, 500, 0.01, 0.6)

    # train
    feats.add_subset(np.int32(p[0:int(num)]))
    labels.add_subset(np.int32(p[0:int(num)]))
    s.set_labels(labels)
    s.train(feats)
    feats.remove_subset()
    labels.remove_subset()

    # apply
    feats.add_subset(np.int32(p[int(num):len(p)]))
    labels.add_subset(np.int32(p[int(num):len(p)]))
    output = s.apply_regression(feats)

    feats.remove_subset()
    labels.remove_subset()

    return s, output
예제 #17
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def stochasticgbmachine(train=traindat,train_labels=label_traindat,ft=feat_types):
	try:
		from shogun import RealFeatures, RegressionLabels, CSVFile, CARTree, StochasticGBMachine, SquaredLoss
	except ImportError:
		print("Could not import Shogun modules")
		return

	# wrap features and labels into Shogun objects
	feats=RealFeatures(CSVFile(train))
	labels=RegressionLabels(CSVFile(train_labels))

	# divide into training (90%) and test dataset (10%)
	p=np.random.permutation(labels.get_num_labels())
	num=labels.get_num_labels()*0.9

	cart=CARTree()
	cart.set_feature_types(ft)
	cart.set_max_depth(1)
	loss=SquaredLoss()
	s=StochasticGBMachine(cart,loss,500,0.01,0.6)

	# train
	feats.add_subset(np.int32(p[0:int(num)]))
	labels.add_subset(np.int32(p[0:int(num)]))
	s.set_labels(labels)
	s.train(feats)
	feats.remove_subset()
	labels.remove_subset()

	# apply
	feats.add_subset(np.int32(p[int(num):len(p)]))
	labels.add_subset(np.int32(p[int(num):len(p)]))
	output=s.apply_regression(feats)

	feats.remove_subset()
	labels.remove_subset()

	return s,output
예제 #18
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def modelselection_grid_search_libsvr (fm_train=traindat,fm_test=testdat,label_train=label_traindat,\
           width=2.1,C=1,epsilon=1e-5,tube_epsilon=1e-2):
    from shogun import CrossValidation, CrossValidationResult
    from shogun import MeanSquaredError
    from shogun import CrossValidationSplitting
    from shogun import RegressionLabels
    from shogun import RealFeatures
    from shogun import GaussianKernel
    from shogun import LibSVR
    from shogun import GridSearchModelSelection
    from shogun import ModelSelectionParameters, R_EXP
    from shogun import ParameterCombination

    # training data
    features_train = RealFeatures(traindat)
    labels = RegressionLabels(label_traindat)

    # kernel
    kernel = GaussianKernel(features_train, features_train, width)

    # print all parameter available for modelselection
    # Dont worry if yours is not included but, write to the mailing list
    #kernel.print_modsel_params()

    labels = RegressionLabels(label_train)

    # predictor
    predictor = LibSVR(C, tube_epsilon, kernel, labels)
    predictor.set_epsilon(epsilon)

    # splitting strategy for 5 fold cross-validation (for classification its better
    # to use "StratifiedCrossValidation", but the standard
    # "StratifiedCrossValidationSplitting" is also available
    splitting_strategy = CrossValidationSplitting(labels, 5)

    # evaluation method
    evaluation_criterium = MeanSquaredError()

    # cross-validation instance
    cross_validation = CrossValidation(predictor, features_train, labels,
                                       splitting_strategy,
                                       evaluation_criterium)

    #	 (optional) repeat x-val (set larger to get better estimates)
    cross_validation.set_num_runs(2)

    # print all parameter available for modelselection
    # Dont worry if yours is not included but, write to the mailing list
    #predictor.print_modsel_params()

    # build parameter tree to select C1 and C2
    param_tree_root = ModelSelectionParameters()
    c1 = ModelSelectionParameters("C1")
    param_tree_root.append_child(c1)
    c1.build_values(-1.0, 0.0, R_EXP)

    c2 = ModelSelectionParameters("C2")
    param_tree_root.append_child(c2)
    c2.build_values(-1.0, 0.0, R_EXP)

    # model selection instance
    model_selection = GridSearchModelSelection(cross_validation,
                                               param_tree_root)

    # perform model selection with selected methods
    #print "performing model selection of"
    #print "parameter tree"
    #param_tree_root.print_tree()

    #print "starting model selection"
    # print the current parameter combination, if no parameter nothing is printed
    print_state = False
    # lock data before since model selection will not change the kernel matrix
    # (use with care) This avoids that the kernel matrix is recomputed in every
    # iteration of the model search
    predictor.data_lock(labels, features_train)
    best_parameters = model_selection.select_model(print_state)

    # print best parameters
    #print "best parameters:"
    #best_parameters.print_tree()

    # apply them and print result
    best_parameters.apply_to_machine(predictor)
    result = cross_validation.evaluate()
예제 #19
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def modelselection_grid_search_krr (fm_train=traindat,fm_test=testdat,label_train=label_traindat,\
           width=2.1,C=1,epsilon=1e-5,tube_epsilon=1e-2):
    from shogun import CrossValidation, CrossValidationResult
    from shogun import MeanSquaredError
    from shogun import CrossValidationSplitting
    from shogun import RegressionLabels
    from shogun import RealFeatures
    from shogun import KernelRidgeRegression
    from shogun import GridSearchModelSelection
    from shogun import ModelSelectionParameters

    # training data
    features_train = RealFeatures(traindat)
    features_test = RealFeatures(testdat)
    labels = RegressionLabels(label_traindat)

    # labels
    labels = RegressionLabels(label_train)

    # predictor, set tau=0 here, doesnt matter
    predictor = KernelRidgeRegression()

    # splitting strategy for 5 fold cross-validation (for classification its better
    # to use "StratifiedCrossValidation", but the standard
    # "StratifiedCrossValidationSplitting" is also available
    splitting_strategy = CrossValidationSplitting(labels, 5)

    # evaluation method
    evaluation_criterium = MeanSquaredError()

    # cross-validation instance
    cross_validation = CrossValidation(predictor, features_train, labels,
                                       splitting_strategy,
                                       evaluation_criterium)

    # (optional) repeat x-val (set larger to get better estimates)
    cross_validation.set_num_runs(2)

    # print all parameter available for modelselection
    # Dont worry if yours is not included but, write to the mailing list
    #predictor.print_modsel_params()

    # build parameter tree to select regularization parameter
    param_tree_root = create_param_tree()

    # model selection instance
    model_selection = GridSearchModelSelection(cross_validation,
                                               param_tree_root)

    # perform model selection with selected methods
    #print "performing model selection of"
    #print "parameter tree:"
    #param_tree_root.print_tree()

    #print "starting model selection"
    # print the current parameter combination, if no parameter nothing is printed
    print_state = False

    best_parameters = model_selection.select_model(print_state)

    # print best parameters
    #print "best parameters:"
    #best_parameters.print_tree()

    # apply them and print result
    best_parameters.apply_to_machine(predictor)
    result = cross_validation.evaluate()
예제 #20
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X = Xall[0:ntrain, :]
y = yall[0:ntrain]

Xtest = Xall[ntrain:, :]
ytest = yall[ntrain:]

# preprocess data
for i in xrange(p):
    X[:, i] -= np.mean(X[:, i])
    X[:, i] /= np.linalg.norm(X[:, i])
y -= np.mean(y)

# train LASSO
LeastAngleRegression = LeastAngleRegression()
LeastAngleRegression.set_labels(RegressionLabels(y))
LeastAngleRegression.train(RealFeatures(X.T))

# train ordinary LSR
if use_ridge:
    lsr = LinearRidgeRegression(0.01, RealFeatures(X.T), Labels(y))
    lsr.train()
else:
    lsr = LeastSquaresRegression()
    lsr.set_labels(RegressionLabels(y))
    lsr.train(RealFeatures(X.T))

# gather LASSO path
path = np.zeros((p, LeastAngleRegression.get_path_size()))
for i in xrange(path.shape[1]):
    path[:, i] = LeastAngleRegression.get_w(i)
예제 #21
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파일: svr.py 프로젝트: zoq/benchmarks
    def __init__(self, method_param, run_param):
        self.info = "SHOGUN_SVR (" + str(method_param) + ")"

        # Assemble run model parameter.
        self.data = load_dataset(method_param["datasets"], ["csv"])
        self.data_split = split_dataset(self.data[0])

        self.train_feat = RealFeatures(self.data_split[0].T)
        self.train_labels = RegressionLabels(self.data_split[1])

        if len(self.data) >= 2:
            self.test_feat = RealFeatures(self.data[1].T)

        self.solver_type = "epsilon"
        if "libsvr-solver" in method_param:
            self.solver_type = str(method_param["libsvr-solver"])

        self.C = 1.0
        if "C" in method_param:
            self.C = float(method_param["C"])

        self.svr_param = 1.0
        if "svr-paramter" in method_param:
            self.svr_param = float(method_param["svr-parameter"])

        self.kernel = "Gaussian"
        if "kernel" in method_param:
            self.kernel = str(method_param["kernel"])

        self.degree = 3
        if "degree" in method_param:
            self.degree = int(method_param["degree"])

        self.gamma = 2.0
        if "gamma" in method_param:
            self.gamma = float(method_param["gamma"])

        self.distance = "Euclidean"
        if "distance" in method_param:
            self.distance = str(method_param["distance"])

        self.cache_size = 10
        if "cache-size" in method_param:
            cache_size = int(method_param["cache-size"])

        self.coef0 = 1.0
        if "coef0" in method_param:
            self.coef0 = float(method_param["coef0"])

        self.order = 2.0
        if "order" in method_param:
            self.order = float(method_param["order"])

        self.width = 2.0
        if "width" in method_param:
            self.width = float(method_param["width"])

        self.sigma = 1.5
        if "sigma" in method_param:
            self.sigma = float(method_param["sigma"])

        self.const = 2.0
        if "constant" in method_param:
            const = float(method_param["constant"])
예제 #22
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def regression_gaussian_process_modelselection (n=100, n_test=100, \
  x_range=5, x_range_test=10, noise_var=0.4):

    from shogun import RealFeatures, RegressionLabels
    from shogun import GaussianKernel
    from shogun import GradientModelSelection, ModelSelectionParameters
    from shogun import GaussianLikelihood, ZeroMean, \
     ExactInferenceMethod, GaussianProcessRegression, GradientCriterion, \
     GradientEvaluation

    # easy regression data: one dimensional noisy sine wave
    X_train = random.rand(1, n) * x_range
    X_test = array([[float(i) / n_test * x_range_test for i in range(n_test)]])

    y_test = sin(X_test)
    y_train = sin(X_train) + random.randn(n) * noise_var

    # shogun representation
    labels = RegressionLabels(y_train[0])
    feats_train = RealFeatures(X_train)
    feats_test = RealFeatures(X_test)

    # GP specification
    kernel = GaussianKernel(10, 0.05)

    mean = ZeroMean()

    likelihood = GaussianLikelihood(0.8)

    inf = ExactInferenceMethod(kernel, feats_train, mean, labels, likelihood)
    inf.set_scale(2.5)

    gp = GaussianProcessRegression(inf)

    means = gp.get_mean_vector(feats_test)
    variances = gp.get_variance_vector(feats_test)

    # plot results
    figure()

    subplot(2, 1, 1)
    title('Initial parameter\'s values')

    plot(X_train[0], y_train[0], 'bx')  # training observations

    plot(X_test[0], y_test[0], 'g-')  # ground truth of test
    plot(X_test[0], means, 'r-')  # mean predictions of test

    fill_between(X_test[0],
                 means - 1.96 * sqrt(variances),
                 means + 1.96 * sqrt(variances),
                 color='grey')

    legend(["training", "ground truth", "mean predictions"])

    # evaluate our inference method for its derivatives
    grad = GradientEvaluation(gp, feats_train, labels, GradientCriterion(),
                              False)
    grad.set_function(inf)

    # handles all of the above structures in memory
    grad_search = GradientModelSelection(grad)

    # search for best parameters
    best_combination = grad_search.select_model(True)

    # outputs all result and information
    best_combination.apply_to_machine(gp)

    means = gp.get_mean_vector(feats_test)
    variances = gp.get_variance_vector(feats_test)

    # plot results
    subplot(2, 1, 2)
    title('Selected by gradient search parameter\'s values')

    plot(X_train[0], y_train[0], 'bx')  # training observations

    plot(X_test[0], y_test[0], 'g-')  # ground truth of test
    plot(X_test[0], means, 'r-')  # mean predictions of test

    fill_between(X_test[0],
                 means - 1.96 * sqrt(variances),
                 means + 1.96 * sqrt(variances),
                 color='grey')

    legend(["training", "ground truth", "mean predictions"])

    show()