scripts/plot_NN_2D.py

+#!/usr/bin/env python
+
+import sys
+import argparse
+
+parser = argparse.ArgumentParser(description='Create various 2D plots for a single neuron')
+parser.add_argument("project_dir")
+parser.add_argument("output_filename")
+parser.add_argument("varx")
+parser.add_argument("vary")
+parser.add_argument("-m", "--mode",
+                    choices=["mean_sig", "mean_bkg", "profile_sig", "profile_bkg", "hist_sig", "hist_bkg", "hist_actmax", "cond_actmax"],
+                    default="mean_sig")
+parser.add_argument("-l", "--layer", type=int, help="Layer index (takes last layer by default)")
+parser.add_argument("-n", "--neuron", type=int, default=0, help="Neuron index (takes first neuron by default)")
+parser.add_argument("-a", "--all-neurons", action="store_true", help="Create a summary plot for all neurons in all hidden layers")
+parser.add_argument("--log", action="store_true", help="Plot in color in log scale")
+parser.add_argument("--contour", action="store_true", help="Interpolate with contours")
+parser.add_argument("-b", "--nbins", default=20, type=int, help="Number of bins in x and y direction")
+parser.add_argument("-x", "--xrange", type=float, nargs="+", help="xrange (low, high)")
+parser.add_argument("-y", "--yrange", type=float, nargs="+", help="yrange (low, high)")
+parser.add_argument("-p", "--profile-metric", help="metric for profile modes", default="average", choices=["mean", "average", "max"])
+parser.add_argument("--ntries-cond-actmax", help="number of random events to be maximised and averaged per bin", default=20, type=int)
+parser.add_argument("--nit-cond-actmax", help="number of iterations for maximisation per bin", default=1, type=int)
+parser.add_argument("--ntries-actmax", help="number of random events to be maximised for hist_actmax", default=10000, type=int)
+parser.add_argument("-t", "--threshold", help="minimum activation threshold", default=0.2, type=float)
+parser.add_argument("-v", "--verbose", action="store_true")
+parser.add_argument("-s", "--step-size", help="step size for activation maximisation", default=1., type=float)
+
+args = parser.parse_args()
+
+import logging
+logging.basicConfig()
+
+import numpy as np
+
+import ROOT
+ROOT.gROOT.SetBatch()
+ROOT.PyConfig.IgnoreCommandLineOptions = True
+
+from KerasROOTClassification import load_from_dir
+from KerasROOTClassification.plotting import (
+    get_mean_event,
+    plot_NN_vs_var_2D,
+    plot_profile_2D,
+    plot_hist_2D_events,
+    plot_cond_avg_actmax_2D,
+    plot_NN_vs_var_2D_all,
+)
+from KerasROOTClassification.utils import (
+    get_single_neuron_function,
+    get_max_activation_events,
+    weighted_quantile,
+    get_ranges
+)
+
+if args.all_neurons and (not args.mode.startswith("mean")):
+    parser.error("--all-neurons currently only supported for mean_sig and mean_bkg")
+
+if args.verbose:
+    logging.getLogger().setLevel(logging.DEBUG)
+
+c = load_from_dir(args.project_dir)
+
+plot_vs_activation = (args.vary == "activation")
+
+layer = args.layer
+neuron = args.neuron
+
+if layer is None:
+    layer = len(c.model.layers)-1
+
+varx_index = c.fields.index(args.varx)
+if not plot_vs_activation:
+    vary_index = c.fields.index(args.vary)
+else:
+    vary_index = 0 # dummy value in this case
+
+varx_label = args.varx
+vary_label = args.vary
+
+total_weights = c.w_test*np.array(c.class_weight)[c.y_test.astype(int)]
+
+try:
+    mask_value = c.mask_value
+except AttributeError:
+    mask_value = None
+
+# varx_test = c.x_test[:,varx_index]
+# vary_test = c.x_test[:,vary_index]
+
+# x_not_masked = np.where(varx_test != mask_value)[0]
+# y_not_masked = np.where(vary_test != mask_value)[0]
+
+# percentilesx = weighted_quantile(varx_test[x_not_masked], [0.01, 0.99], sample_weight=total_weights[x_not_masked])
+# percentilesy = weighted_quantile(vary_test[y_not_masked], [0.01, 0.99], sample_weight=total_weights[y_not_masked])
+
+percentilesx = get_ranges(c.x_test, [0.01, 0.99], total_weights, mask_value=mask_value, filter_index=varx_index, max_evts=10000)[0][0]
+percentilesy = get_ranges(c.x_test, [0.01, 0.99], total_weights, mask_value=mask_value, filter_index=vary_index, max_evts=10000)[0][0]
+
+
+if args.xrange is not None:
+    if len(args.xrange) < 3:
+        args.xrange.append(args.nbins)
+    varx_range = args.xrange
+else:
+    varx_range = (percentilesx[0], percentilesx[1], args.nbins)
+
+if args.yrange is not None:
+    if len(args.yrange) < 3:
+        args.yrange.append(args.nbins)
+    vary_range = args.yrange
+else:
+    vary_range = (percentilesy[0], percentilesy[1], args.nbins)
+    if plot_vs_activation:
+        vary_range = (0, 1, args.nbins)
+
+if args.mode.startswith("mean"):
+
+    if args.mode == "mean_sig":
+        means = get_mean_event(c.x_test, c.y_test, 1, mask_value=mask_value)
+    elif args.mode == "mean_bkg":
+        means = get_mean_event(c.x_test, c.y_test, 0, mask_value=mask_value)
+
+    print(means)
+
+    if hasattr(c, "get_input_list"):
+        input_transform = lambda x : c.get_input_list(c.transform(x))
+    else:
+        input_transform = c.transform
+
+    if not args.all_neurons:
+        plot_NN_vs_var_2D(
+            args.output_filename,
+            means=means,
+            varx_index=varx_index,
+            vary_index=vary_index,
+            scorefun=get_single_neuron_function(
+                c.model, layer, neuron,
+                input_transform=input_transform
+            ),
+            xmin=varx_range[0], xmax=varx_range[1], nbinsx=varx_range[2],
+            ymin=vary_range[0], ymax=vary_range[1], nbinsy=vary_range[2],
+            varx_label=varx_label, vary_label=vary_label,
+            logscale=args.log, only_pixels=(not args.contour)
+        )
+    else:
+        if hasattr(c, "get_input_list"):
+            transform_function = lambda inp : c.get_input_list(c.scaler.transform(inp))
+        else:
+            transform_function = c.scaler.transform
+        plot_NN_vs_var_2D_all(
+            args.output_filename,
+            means=means,
+            model=c.model,
+            transform_function=transform_function,
+            varx_index=varx_index,
+            vary_index=vary_index,
+            xmin=varx_range[0], xmax=varx_range[1], nbinsx=varx_range[2],
+            ymin=vary_range[0], ymax=vary_range[1], nbinsy=vary_range[2],
+            logz=args.log,
+            plot_last_layer=False,
+        )
+
+elif args.mode.startswith("profile"):
+
+    def my_average(x, weights):
+        if weights.sum() <= 0:
+            return np.nan
+        else:
+            return np.average(x, weights=weights)
+
+    metric_dict = {
+        "mean" : np.mean,
+        "max" : np.max,
+        "average" : my_average,
+    }
+
+    if args.mode == "profile_sig":
+        class_index = 1
+    else:
+        class_index = 0
+    valsx = c.x_test[c.y_test==class_index][:,varx_index]
+    valsy = c.x_test[c.y_test==class_index][:,vary_index]
+    scores = c.scores_test[c.y_test==class_index].reshape(-1)
+
+    opt_kwargs = dict()
+
+    if args.profile_metric == "average":
+        opt_kwargs["weights"] = c.w_test[c.y_test==class_index]
+
+    plot_profile_2D(
+        args.output_filename,
+        valsx, valsy, scores,
+        xmin=varx_range[0], xmax=varx_range[1], nbinsx=varx_range[2],
+        ymin=vary_range[0], ymax=vary_range[1], nbinsy=vary_range[2],
+        metric=metric_dict[args.profile_metric],
+        varx_label=varx_label, vary_label=vary_label,
+        log=args.log,
+        **opt_kwargs
+    )
+
+elif args.mode.startswith("hist"):
+
+    if not args.mode == "hist_actmax":
+        if args.mode == "hist_sig":
+            class_index = 1
+        else:
+            class_index = 0
+
+        valsx = c.x_test[c.y_test==class_index][:,varx_index]
+        if not plot_vs_activation:
+            valsy = c.x_test[c.y_test==class_index][:,vary_index]
+        else:
+            valsy = c.scores_test[c.y_test==class_index].reshape(-1)
+        weights = c.w_test[c.y_test==class_index]
+    else:
+        # ranges in which to sample the random events
+        x_test_scaled = c.transform(c.x_test)
+        ranges = get_ranges(x_test_scaled, [0.01, 0.99], total_weights, mask_value=mask_value)
+        kwargs = {}
+        if hasattr(c, "get_input_list"):
+            kwargs["input_transform"] = c.get_input_list
+            kwargs["input_inverse_transform"] = c.get_input_flat
+        losses, events = get_max_activation_events(c.model, ranges,
+                                                   ntries=args.ntries_actmax,
+                                                   step=args.step_size,
+                                                   layer=layer,
+                                                   neuron=neuron,
+                                                   threshold=args.threshold,
+                                                   **kwargs)
+        events = c.inverse_transform(events)
+        valsx = events[:,varx_index]
+        if not plot_vs_activation:
+            valsy = events[:,vary_index]
+        else:
+            valsy = losses
+        weights = None
+
+    plot_hist_2D_events(
+        args.output_filename,
+        valsx, valsy,
+        xmin=varx_range[0], xmax=varx_range[1], nbinsx=varx_range[2],
+        ymin=vary_range[0], ymax=vary_range[1], nbinsy=vary_range[2],
+        weights=weights,
+        varx_label=varx_label, vary_label=vary_label,
+        log=args.log,
+    )
+
+elif args.mode.startswith("cond_actmax"):
+
+    x_test_scaled = c.transform(c.x_test)
+
+    # ranges in which to sample the random events
+    ranges = get_ranges(x_test_scaled, [0.01, 0.99], total_weights, mask_value=mask_value)
+
+    plot_cond_avg_actmax_2D(
+        args.output_filename,
+        c.model, layer, neuron, ranges,
+        varx_index,
+        vary_index,
+        xmin=varx_range[0], xmax=varx_range[1], nbinsx=varx_range[2],
+        ymin=vary_range[0], ymax=vary_range[1], nbinsy=vary_range[2],
+        scaler=c.scaler,
+        ntries=args.ntries_cond_actmax,
+        maxit=args.nit_cond_actmax,
+        step=args.step_size,
+        varx_label=varx_label, vary_label=vary_label,
+        log=args.log,
+    )

scripts/write_parametrized.py

+#!/usr/bin/env python
+"""
+Write new TTrees with signal parameters as branches. For the
+backgrounds the parameters are generated following the total
+distribution for all signals. The discrete values for the whole ntuple
+of signal parameters are counted, such that correlations between
+signal parameters are taken into account.
+"""
+
+import argparse, re, os
+
+import ROOT
+
+from root_numpy import list_trees
+from root_pandas import read_root
+import numpy as np
+
+if __name__ == "__main__":
+
+    input_filename = "/project/etp4/nhartmann/trees/allTrees_m1.8_NoSys.root"
+    output_filename = "/project/etp4/nhartmann/trees/allTrees_m1.8_NoSys_parametrized.root"
+
+    param_names = ["mg", "mc", "mn"]
+
+    param_match = "GG_oneStep_(.*?)_(.*?)_(.*?)_NoSys"
+
+    output_signal_treename = "GG_oneStep_NoSys"
+
+    bkg_trees = [
+        "diboson_Sherpa221_NoSys",
+        "singletop_NoSys",
+        "ttbar_NoSys",
+        "ttv_NoSys",
+        "wjets_Sherpa221_NoSys",
+        "zjets_Sherpa221_NoSys",
+    ]
+
+    # read in the number of events for each combination of parameters
+    f = ROOT.TFile.Open(input_filename)
+    count_dict = {}
+    for key in f.GetListOfKeys():
+        tree_name = key.GetName()
+        match = re.match(param_match, tree_name)
+        if match is not None:
+            tree = f.Get(tree_name)
+            params = tuple([float(i) for i in match.groups()])
+            if not params in count_dict:
+                count_dict[params] = 0
+            # TODO: might be better to use sum of weights
+            count_dict[params] += tree.GetEntries()
+    f.Close()
+
+    # calculate cumulative sum of counts to sample signal parameters for background from
+    numbers = np.array(count_dict.keys(), dtype=np.float)
+    counts = np.array(count_dict.values(), dtype=np.float)
+    probs = counts/counts.sum()
+    prob_bins = np.cumsum(probs)
+
+    # read and write the rest in chunks
+    if os.path.exists(output_filename):
+        os.remove(output_filename)
+    for tree_name in list_trees(input_filename):
+        match_signal = re.match(param_match, tree_name)
+        if match_signal is not None or tree_name in bkg_trees:
+            print("Writing {}".format(tree_name))
+            nwritten = 0
+            for df in read_root(input_filename, tree_name, chunksize=100000):
+                print("Writing event {}".format(nwritten))
+                if match_signal is None:
+                    rnd = np.random.random(len(df))
+                    rnd_idx = np.digitize(rnd, prob_bins)
+                    param_values = numbers[rnd_idx]
+                    for param_idx, param_name in enumerate(param_names):
+                        df[param_name] = param_values[:,param_idx]
+                    df["training_weight"] = df["eventWeight"]*df["genWeight"]
+                else:
+                    for param_name, param_value in zip(param_names, match_signal.groups()):
+                        df[param_name] = float(param_value)
+                    df["training_weight"] = df["eventWeight"]
+                if match_signal is None:
+                    out_tree_name = tree_name
+                else:
+                    out_tree_name = output_signal_treename
+                df.to_root(output_filename, mode="a", key=out_tree_name)
+                nwritten += len(df)

test/test_toolkit.py

+import pytest
+import numpy as np
+import root_numpy
+import pandas as pd
+from sklearn.datasets import make_classification
+from keras.layers import GRU
+
+from KerasROOTClassification import ClassificationProject, ClassificationProjectRNN
+
+
+def create_dataset(path):
+
+    # create example dataset with (low-weighted) noise added
+    X, y = make_classification(n_samples=10000, random_state=1)
+    X2 = np.random.normal(size=20*10000).reshape(-1, 20)
+    y2 = np.concatenate([np.zeros(5000), np.ones(5000)])
+    X = np.concatenate([X, X2])
+    y = np.concatenate([y, y2])
+    w = np.concatenate([np.ones(10000), 0.01*np.ones(10000)])
+
+    # shift and scale randomly (to check if transformation is working)
+    shift = np.random.rand(20)*100
+    scale = np.random.rand(20)*1000
+    X *= scale
+    X += shift
+
+    # write to root files
+    branches = ["var_{}".format(i) for i in range(len(X[0]))]
+    df = pd.DataFrame(X, columns=branches)
+    df["class"] = y
+    df["weight"] = w
+    tree_path_bkg = str(path / "bkg.root")
+    tree_path_sig = str(path / "sig.root")
+    root_numpy.array2root(df[df["class"]==0].to_records(), tree_path_bkg)
+    root_numpy.array2root(df[df["class"]==1].to_records(), tree_path_sig)
+    return branches, tree_path_sig, tree_path_bkg
+
+
+def test_ClassificationProject(tmp_path):
+    branches, tree_path_sig, tree_path_bkg = create_dataset(tmp_path)
+    c = ClassificationProject(
+        str(tmp_path / "project"),
+        bkg_trees = [(tree_path_bkg, "tree")],
+        signal_trees = [(tree_path_sig, "tree")],
+        branches = branches,
+        weight_expr = "weight",
+        identifiers = ["index"],
+        optimizer="Adam",
+        earlystopping_opts=dict(patience=5),
+        dropout=0.5,
+        layers=3,
+        nodes=128,
+    )
+
+    c.train(epochs=200)
+    c.plot_all_inputs()
+    c.plot_loss()
+    assert min(c.history.history["val_loss"]) < 0.18
+
+
+def test_ClassificationProjectRNN(tmp_path):
+    branches, tree_path_sig, tree_path_bkg = create_dataset(tmp_path)
+    c = ClassificationProjectRNN(
+        str(tmp_path / "project"),
+        bkg_trees = [(tree_path_bkg, "tree")],
+        signal_trees = [(tree_path_sig, "tree")],
+        branches = branches,
+        recurrent_field_names=[
+            [
+                ["var_1", "var_2", "var_3"],
+                ["var_4", "var_5", "var_6"]
+            ],
+            [
+                ["var_10", "var_11", "var_12"],
+                ["var_13", "var_14", "var_15"]
+            ],
+        ],
+        weight_expr = "weight",
+        identifiers = ["index"],
+        optimizer="Adam",
+        earlystopping_opts=dict(patience=5),
+        dropout=0.5,
+        layers=3,
+        nodes=128,
+    )
+    assert sum([isinstance(layer, GRU) for layer in c.model.layers]) == 2
+    c.train(epochs=200)
+    c.plot_all_inputs()
+    c.plot_loss()
+    assert min(c.history.history["val_loss"]) < 0.18

utils.py

+"Helper functions using keras or tensorflow"
+
+import logging
+
+import numpy as np
+
+import keras.backend as K
+from sklearn.preprocessing import RobustScaler
+from sklearn.preprocessing.data import _handle_zeros_in_scale
+
+from meme import cache
+
+logger = logging.getLogger(__name__)
+logger.addHandler(logging.NullHandler())
+
+def get_single_neuron_function(model, layer, neuron, input_transform=None):
+
+    inp = model.input
+    if not isinstance(inp, list):
+        inp = [inp]
+
+    f = K.function(inp+[K.learning_phase()], [model.layers[layer].output[:,neuron]])
+
+    def eval_single_neuron(x):
+        if input_transform is not None:
+            x_eval = input_transform(x)
+        else:
+            x_eval = x
+        if not isinstance(x_eval, list):
+            x_eval = [x_eval]
+        return f(x_eval)[0]
+
+    return eval_single_neuron
+
+
+def create_random_event(ranges, mask_probs=None, mask_value=None):
+    random_event = np.array([p[0]+(p[1]-p[0])*np.random.rand() for p in ranges])
+    random_event = random_event.reshape(-1, len(random_event))
+    # if given, mask values with a certain probability
+    if mask_probs is not None:
+        if mask_value is None:
+            raise ValueError("Need to provide mask_value if random events should be masked")
+        for var_index, mask_prob in enumerate(mask_probs):
+            random_event[:,var_index][np.random.rand(len(random_event)) < mask_prob] = mask_value
+    return random_event
+
+
+def get_ranges(x, quantiles, weights, mask_value=None, filter_index=None, max_evts=None):
+    "Get ranges for plotting or random event generation based on quantiles"
+    ranges = []
+    mask_probs = []
+    if max_evts is not None:
+        rnd_idx = np.random.permutation(np.arange(len(x)))
+        rnd_idx = rnd_idx[:max_evts]
+    for var_index in range(x.shape[1]):
+        if (filter_index is not None) and (var_index != filter_index):
+            continue
+        x_var = x[:,var_index]
+        if max_evts is not None:
+            x_var = x_var[rnd_idx]
+        not_masked = np.where(x_var != mask_value)[0]
+        masked = np.where(x_var == mask_value)[0]
+        ranges.append(weighted_quantile(x_var[not_masked], quantiles, sample_weight=weights[not_masked]))
+        mask_probs.append(float(len(masked))/float(len(x_var)))
+    return ranges, mask_probs
+
+
+def max_activation_wrt_input(gradient_function, random_event, threshold=None, maxthreshold=None, maxit=100, step=1, const_indices=[],
+                             input_transform=None, input_inverse_transform=None):
+    if input_transform is not None:
+        random_event = input_transform(random_event)
+    if not isinstance(random_event, list):
+        random_event = [random_event]
+
+    def iterate(random_event):
+        for i in range(maxit):
+            grads_out = gradient_function(random_event)
+            loss_value = grads_out[0][0]
+            grads_values = grads_out[1:]
+            # follow gradient for all inputs
+            for i, (grads_value, input_event) in enumerate(zip(grads_values, random_event)):
+                for const_index in const_indices:
+                    grads_value[0][const_index] = 0
+                if threshold is not None:
+                    if loss_value > threshold and (maxthreshold is None or loss_value < maxthreshold):
+                        # found an event within the thresholds
+                        return loss_value, random_event
+                    elif (maxthreshold is not None and loss_value > maxthreshold):
+                        random_event[i] -= grads_value*step
+                    else:
+                        random_event[i] += grads_value*step
+                else:
+                    random_event[i] += grads_value*step
+        else:
+            if threshold is not None:
+                # no event found for the given threshold
+                return None, None
+        # otherwise return last status
+        return loss_value, random_event
+
+    loss_value, random_event = iterate(random_event)
+    if input_inverse_transform is not None and random_event is not None:
+        random_event = input_inverse_transform(random_event)
+    elif random_event is None:
+        return None
+    return loss_value, random_event
+
+
+def get_grad_function(model, layer, neuron):
+
+    loss = model.layers[layer].output[:,neuron]
+
+    grads = K.gradients(loss, model.input)
+
+    # trick from https://blog.keras.io/how-convolutional-neural-networks-see-the-world.html
+    norm_grads = [grad/(K.sqrt(K.mean(K.square(grad))) + 1e-5) for grad in grads]
+
+    inp = model.input
+    if not isinstance(inp, list):
+        inp = [inp]
+
+    return K.function(inp, [loss]+norm_grads)
+
+
+@cache(useJSON=True,
+       argHashFunctions=[
+           lambda model: [hash(i.tostring()) for i in model.get_weights()],
+           lambda ranges: [hash(i.tostring()) for i in ranges],
+       ],
+       ignoreKwargs=["input_transform", "input_inverse_transform"],
+)
+def get_max_activation_events(model, ranges, ntries, layer, neuron, seed=42, mask_probs=None, mask_value=None, **kwargs):
+
+    gradient_function = get_grad_function(model, layer, neuron)
+
+    events = None
+    losses = None
+    np.random.seed(seed)
+    for i in range(ntries):
+        if not (i%100):
+            logger.info(i)
+        res = max_activation_wrt_input(
+            gradient_function,
+            create_random_event(
+                ranges,
+                mask_probs=mask_probs,
+                mask_value=mask_value
+            ),
+            **kwargs
+        )
+        if res is not None:
+            loss, event = res
+            loss = np.array([loss])
+        else:
+            continue
+        if events is None:
+            events = event
+            losses = loss
+        else:
+            events = np.concatenate([events, event])
+            losses = np.concatenate([losses, loss])
+
+    return losses, events
+
+"from https://stackoverflow.com/questions/21844024/weighted-percentile-using-numpy#29677616"
+def weighted_quantile(values, quantiles, sample_weight=None, values_sorted=False, old_style=False):
+    """ Very close to np.percentile, but supports weights.
+    NOTE: quantiles should be in [0, 1]!
+    :param values: np.array with data
+    :param quantiles: array-like with many quantiles needed
+    :param sample_weight: array-like of the same length as `array`
+    :param values_sorted: bool, if True, then will avoid sorting of initial array
+    :param old_style: if True, will correct output to be consistent with np.percentile.
+    :return: np.array with computed quantiles.
+    """
+    values = np.array(values)
+    quantiles = np.array(quantiles)
+    if sample_weight is None:
+        sample_weight = np.ones(len(values))
+    sample_weight = np.array(sample_weight)
+    assert np.all(quantiles >= 0) and np.all(quantiles <= 1), 'quantiles should be in [0, 1]'
+
+    if not values_sorted:
+        sorter = np.argsort(values)
+        values = values[sorter]
+        sample_weight = sample_weight[sorter]
+
+    weighted_quantiles = np.cumsum(sample_weight) - 0.5 * sample_weight
+    if old_style:
+        # To be convenient with np.percentile
+        weighted_quantiles -= weighted_quantiles[0]
+        weighted_quantiles /= weighted_quantiles[-1]
+    else:
+        weighted_quantiles /= np.sum(sample_weight)
+    return np.interp(quantiles, weighted_quantiles, values)
+
+
+class WeightedRobustScaler(RobustScaler):
+
+    def fit(self, X, y=None, weights=None, mask_value=None):
+        if not np.isnan(X).any() and mask_value is not None and weights is None:
+            # these checks don't work for nan values
+            return super(WeightedRobustScaler, self).fit(X, y)
+        else:
+            if weights is None:
+                weights = np.ones(len(self.X))
+            wqs = []
+            for i in range(X.shape[1]):
+                mask = ~np.isnan(X[:,i])
+                if mask_value is not None:
+                    mask &= (X[:,i] != mask_value)
+                wqs.append(
+                    weighted_quantile(
+                        X[:,i][mask],
+                        [0.25, 0.5, 0.75],
+                        sample_weight=weights[mask]
+                    )
+                )
+            wqs = np.array(wqs)
+            self.center_ = wqs[:,1]
+            self.scale_ = wqs[:,2]-wqs[:,0]
+            self.scale_ = _handle_zeros_in_scale(self.scale_, copy=False)
+            return self
+
+
+    def transform(self, X):
+        if np.isnan(X).any():
+            # we'd like to ignore nan values, so lets calculate without further checks
+            X -= self.center_
+            X /= self.scale_
+            return X
+        else:
+            return super(WeightedRobustScaler, self).transform(X)
+
+
+    def inverse_transform(self, X):
+        if np.isnan(X).any():
+            X *= self.scale_
+            X += self.center_
+            return X
+        else:
+            return super(WeightedRobustScaler, self).inverse_transform(X)
+
+
+def poisson_asimov_significance(s, ds, b, db):
+    "see `<http://www.pp.rhul.ac.uk/~cowan/stat/medsig/medsigNote.pdf>`_)"
+    db = np.sqrt(db**2+ds**2)
+    return np.sqrt(2*((s+b)*np.log(((s+b)*(b+db**2))/(b**2+(s+b)*db**2))-(b**2)/(db**2)*np.log(1+(db**2*s)/(b*(b+db**2)))))
+