Upload shap_plots.py

shap_plots.py

@@ -0,0 +1,730 @@
+import warnings
+import iml
+import numpy as np
+from iml import Instance, Model
+from iml.datatypes import DenseData
+from iml.explanations import AdditiveExplanation
+from iml.links import IdentityLink
+from scipy.stats import gaussian_kde
+import matplotlib
+try:
+    import matplotlib.pyplot as pl
+    from matplotlib.colors import LinearSegmentedColormap
+    from matplotlib.ticker import MaxNLocator
+
+    cdict1 = {
+        'red': ((0.0, 0.11764705882352941, 0.11764705882352941),
+                (1.0, 0.9607843137254902, 0.9607843137254902)),
+
+        'green': ((0.0, 0.5333333333333333, 0.5333333333333333),
+                  (1.0, 0.15294117647058825, 0.15294117647058825)),
+
+        'blue': ((0.0, 0.8980392156862745, 0.8980392156862745),
+                 (1.0, 0.3411764705882353, 0.3411764705882353)),
+
+        'alpha': ((0.0, 1, 1),
+                  (0.5, 0.3, 0.3),
+                  (1.0, 1, 1))
+    }  # #1E88E5 -> #ff0052
+    red_blue = LinearSegmentedColormap('RedBlue', cdict1)
+
+    cdict1 = {
+        'red': ((0.0, 0.11764705882352941, 0.11764705882352941),
+                (1.0, 0.9607843137254902, 0.9607843137254902)),
+
+        'green': ((0.0, 0.5333333333333333, 0.5333333333333333),
+                  (1.0, 0.15294117647058825, 0.15294117647058825)),
+
+        'blue': ((0.0, 0.8980392156862745, 0.8980392156862745),
+                 (1.0, 0.3411764705882353, 0.3411764705882353)),
+
+        'alpha': ((0.0, 1, 1),
+                  (0.5, 1, 1),
+                  (1.0, 1, 1))
+    }  # #1E88E5 -> #ff0052
+    red_blue_solid = LinearSegmentedColormap('RedBlue', cdict1)
+except ImportError:
+    pass
+
+labels = {
+    'MAIN_EFFECT': "SHAP main effect value for\n%s",
+    'INTERACTION_VALUE': "SHAP interaction value",
+    'INTERACTION_EFFECT': "SHAP interaction value for\n%s and %s",
+    'VALUE': "SHAP value (impact on model output)",
+    'VALUE_FOR': "SHAP value for\n%s",
+    'PLOT_FOR': "SHAP plot for %s",
+    'FEATURE': "Feature %s",
+    'FEATURE_VALUE': "Feature value",
+    'FEATURE_VALUE_LOW': "Low",
+    'FEATURE_VALUE_HIGH': "High",
+    'JOINT_VALUE': "Joint SHAP value"
+}
+
+def shap_summary_plot(shap_values, features=None, feature_names=None, max_display=None, plot_type="dot",
+                 color=None, axis_color="#333333", title=None, alpha=1, show=True, sort=True,
+                 color_bar=True, auto_size_plot=True, layered_violin_max_num_bins=20):
+    """Create a SHAP summary plot, colored by feature values when they are provided.
+
+    Parameters
+    ----------
+    shap_values : numpy.array
+        Matrix of SHAP values (# samples x # features)
+
+    features : numpy.array or pandas.DataFrame or list
+        Matrix of feature values (# samples x # features) or a feature_names list as shorthand
+
+    feature_names : list
+        Names of the features (length # features)
+
+    max_display : int
+        How many top features to include in the plot (default is 20, or 7 for interaction plots)
+
+    plot_type : "dot" (default) or "violin"
+        What type of summary plot to produce
+    """
+
+    assert len(shap_values.shape) != 1, "Summary plots need a matrix of shap_values, not a vector."
+
+    # default color:
+    if color is None:
+        color = "coolwarm" if plot_type == 'layered_violin' else "#ff0052"
+
+    # convert from a DataFrame or other types
+    if str(type(features)) == "<class 'pandas.core.frame.DataFrame'>":
+        if feature_names is None:
+            feature_names = features.columns
+        features = features.values
+    elif str(type(features)) == "<class 'list'>":
+        if feature_names is None:
+            feature_names = features
+        features = None
+    elif (features is not None) and len(features.shape) == 1 and feature_names is None:
+        feature_names = features
+        features = None
+
+    if feature_names is None:
+        feature_names = [labels['FEATURE'] % str(i) for i in range(shap_values.shape[1] - 1)]
+
+    mpl_fig = pl.figure(figsize=(1.5 * max_display + 1, 1 * max_display + 1))
+
+    # plotting SHAP interaction values
+    if len(shap_values.shape) == 3:
+        if max_display is None:
+            max_display = 7
+        else:
+            max_display = min(len(feature_names), max_display)
+
+        sort_inds = np.argsort(-np.abs(shap_values[:, :-1, :-1].sum(1)).sum(0))
+
+        # get plotting limits
+        delta = 1.0 / (shap_values.shape[1] ** 2)
+        slow = np.nanpercentile(shap_values, delta)
+        shigh = np.nanpercentile(shap_values, 100 - delta)
+        v = max(abs(slow), abs(shigh))
+        slow = -0.2
+        shigh = 0.2
+
+        # mpl_fig = pl.figure(figsize=(1.5 * max_display + 1, 1 * max_display + 1))
+        ax = mpl_fig.subplot(1, max_display, 1)
+        proj_shap_values = shap_values[:, sort_inds[0], np.hstack((sort_inds, len(sort_inds)))]
+        proj_shap_values[:, 1:] *= 2  # because off diag effects are split in half
+        shap_summary_plot(
+            proj_shap_values, features[:, sort_inds],
+            feature_names=feature_names[sort_inds],
+            sort=False, show=False, color_bar=False,
+            auto_size_plot=False,
+            max_display=max_display
+        )
+        pl.xlim((slow, shigh))
+        pl.xlabel("")
+        title_length_limit = 11
+        pl.title(shorten_text(feature_names[sort_inds[0]], title_length_limit))
+        for i in range(1, max_display):
+            ind = sort_inds[i]
+            pl.subplot(1, max_display, i + 1)
+            proj_shap_values = shap_values[:, ind, np.hstack((sort_inds, len(sort_inds)))]
+            proj_shap_values *= 2
+            proj_shap_values[:, i] /= 2  # because only off diag effects are split in half
+            shap_summary_plot(
+                proj_shap_values, features[:, sort_inds],
+                sort=False,
+                feature_names=["" for i in range(features.shape[1])],
+                show=False,
+                color_bar=False,
+                auto_size_plot=False,
+                max_display=max_display
+            )
+            pl.xlim((slow, shigh))
+            pl.xlabel("")
+            if i == max_display // 2:
+                pl.xlabel(labels['INTERACTION_VALUE'])
+            pl.title(shorten_text(feature_names[ind], title_length_limit))
+        pl.tight_layout(pad=0, w_pad=0, h_pad=0.0)
+        pl.subplots_adjust(hspace=0, wspace=0.1)
+        # if show:
+        # #     pl.show()
+        return mpl_fig
+
+    if max_display is None:
+        max_display = 20
+
+    if sort:
+        # order features by the sum of their effect magnitudes
+        feature_order = np.argsort(np.sum(np.abs(shap_values), axis=0)[:-1])
+        feature_order = feature_order[-min(max_display, len(feature_order)):]
+    else:
+        feature_order = np.flip(np.arange(min(max_display, shap_values.shape[1] - 1)), 0)
+
+    row_height = 0.4
+    if auto_size_plot:
+        pl.gcf().set_size_inches(8, len(feature_order) * row_height + 1.5)
+    pl.axvline(x=0, color="#999999", zorder=-1)
+
+    if plot_type == "dot":
+        for pos, i in enumerate(feature_order):
+            pl.axhline(y=pos, color="#cccccc", lw=0.5, dashes=(1, 5), zorder=-1)
+            shaps = shap_values[:, i]
+            values = None if features is None else features[:, i]
+            inds = np.arange(len(shaps))
+            np.random.shuffle(inds)
+            if values is not None:
+                values = values[inds]
+            shaps = shaps[inds]
+            colored_feature = True
+            try:
+                values = np.array(values, dtype=np.float64)  # make sure this can be numeric
+            except:
+                colored_feature = False
+            N = len(shaps)
+            # hspacing = (np.max(shaps) - np.min(shaps)) / 200
+            # curr_bin = []
+            nbins = 100
+            quant = np.round(nbins * (shaps - np.min(shaps)) / (np.max(shaps) - np.min(shaps) + 1e-8))
+            inds = np.argsort(quant + np.random.randn(N) * 1e-6)
+            layer = 0
+            last_bin = -1
+            ys = np.zeros(N)
+            for ind in inds:
+                if quant[ind] != last_bin:
+                    layer = 0
+                ys[ind] = np.ceil(layer / 2) * ((layer % 2) * 2 - 1)
+                layer += 1
+                last_bin = quant[ind]
+            ys *= 0.9 * (row_height / np.max(ys + 1))
+
+            if features is not None and colored_feature:
+                # trim the color range, but prevent the color range from collapsing
+                vmin = np.nanpercentile(values, 5)
+                vmax = np.nanpercentile(values, 95)
+                if vmin == vmax:
+                    vmin = np.nanpercentile(values, 1)
+                    vmax = np.nanpercentile(values, 99)
+                    if vmin == vmax:
+                        vmin = np.min(values)
+                        vmax = np.max(values)
+
+                assert features.shape[0] == len(shaps), "Feature and SHAP matrices must have the same number of rows!"
+                nan_mask = np.isnan(values)
+                pl.scatter(shaps[nan_mask], pos + ys[nan_mask], color="#777777", vmin=vmin,
+                           vmax=vmax, s=16, alpha=alpha, linewidth=0,
+                           zorder=3, rasterized=len(shaps) > 500)
+                pl.scatter(shaps[np.invert(nan_mask)], pos + ys[np.invert(nan_mask)],
+                           cmap=red_blue, vmin=vmin, vmax=vmax, s=16,
+                           c=values[np.invert(nan_mask)], alpha=alpha, linewidth=0,
+                           zorder=3, rasterized=len(shaps) > 500)
+            else:
+
+                pl.scatter(shaps, pos + ys, s=16, alpha=alpha, linewidth=0, zorder=3,
+                           color=color if colored_feature else "#777777", rasterized=len(shaps) > 500)
+
+    elif plot_type == "violin":
+        for pos, i in enumerate(feature_order):
+            pl.axhline(y=pos, color="#cccccc", lw=0.5, dashes=(1, 5), zorder=-1)
+
+        if features is not None:
+            global_low = np.nanpercentile(shap_values[:, :len(feature_names)].flatten(), 1)
+            global_high = np.nanpercentile(shap_values[:, :len(feature_names)].flatten(), 99)
+            for pos, i in enumerate(feature_order):
+                shaps = shap_values[:, i]
+                shap_min, shap_max = np.min(shaps), np.max(shaps)
+                rng = shap_max - shap_min
+                xs = np.linspace(np.min(shaps) - rng * 0.2, np.max(shaps) + rng * 0.2, 100)
+                if np.std(shaps) < (global_high - global_low) / 100:
+                    ds = gaussian_kde(shaps + np.random.randn(len(shaps)) * (global_high - global_low) / 100)(xs)
+                else:
+                    ds = gaussian_kde(shaps)(xs)
+                ds /= np.max(ds) * 3
+
+                values = features[:, i]
+                window_size = max(10, len(values) // 20)
+                smooth_values = np.zeros(len(xs) - 1)
+                sort_inds = np.argsort(shaps)
+                trailing_pos = 0
+                leading_pos = 0
+                running_sum = 0
+                back_fill = 0
+                for j in range(len(xs) - 1):
+
+                    while leading_pos < len(shaps) and xs[j] >= shaps[sort_inds[leading_pos]]:
+                        running_sum += values[sort_inds[leading_pos]]
+                        leading_pos += 1
+                        if leading_pos - trailing_pos > 20:
+                            running_sum -= values[sort_inds[trailing_pos]]
+                            trailing_pos += 1
+                    if leading_pos - trailing_pos > 0:
+                        smooth_values[j] = running_sum / (leading_pos - trailing_pos)
+                        for k in range(back_fill):
+                            smooth_values[j - k - 1] = smooth_values[j]
+                    else:
+                        back_fill += 1
+
+                vmin = np.nanpercentile(values, 5)
+                vmax = np.nanpercentile(values, 95)
+                if vmin == vmax:
+                    vmin = np.nanpercentile(values, 1)
+                    vmax = np.nanpercentile(values, 99)
+                    if vmin == vmax:
+                        vmin = np.min(values)
+                        vmax = np.max(values)
+                pl.scatter(shaps, np.ones(shap_values.shape[0]) * pos, s=9, cmap=red_blue_solid, vmin=vmin, vmax=vmax,
+                           c=values, alpha=alpha, linewidth=0, zorder=1)
+                # smooth_values -= nxp.nanpercentile(smooth_values, 5)
+                # smooth_values /= np.nanpercentile(smooth_values, 95)
+                smooth_values -= vmin
+                if vmax - vmin > 0:
+                    smooth_values /= vmax - vmin
+                for i in range(len(xs) - 1):
+                    if ds[i] > 0.05 or ds[i + 1] > 0.05:
+                        pl.fill_between([xs[i], xs[i + 1]], [pos + ds[i], pos + ds[i + 1]],
+                                        [pos - ds[i], pos - ds[i + 1]], color=red_blue_solid(smooth_values[i]),
+                                        zorder=2)
+
+        else:
+            parts = pl.violinplot(shap_values[:, feature_order], range(len(feature_order)), points=200, vert=False,
+                                  widths=0.7,
+                                  showmeans=False, showextrema=False, showmedians=False)
+
+            for pc in parts['bodies']:
+                pc.set_facecolor(color)
+                pc.set_edgecolor('none')
+                pc.set_alpha(alpha)
+
+    elif plot_type == "layered_violin":  # courtesy of @kodonnell
+        num_x_points = 200
+        bins = np.linspace(0, features.shape[0], layered_violin_max_num_bins + 1).round(0).astype(
+            'int')  # the indices of the feature data corresponding to each bin
+        shap_min, shap_max = np.min(shap_values[:, :-1]), np.max(shap_values[:, :-1])
+        x_points = np.linspace(shap_min, shap_max, num_x_points)
+
+        # loop through each feature and plot:
+        for pos, ind in enumerate(feature_order):
+            # decide how to handle: if #unique < layered_violin_max_num_bins then split by unique value, otherwise use bins/percentiles.
+            # to keep simpler code, in the case of uniques, we just adjust the bins to align with the unique counts.
+            feature = features[:, ind]
+            unique, counts = np.unique(feature, return_counts=True)
+            if unique.shape[0] <= layered_violin_max_num_bins:
+                order = np.argsort(unique)
+                thesebins = np.cumsum(counts[order])
+                thesebins = np.insert(thesebins, 0, 0)
+            else:
+                thesebins = bins
+            nbins = thesebins.shape[0] - 1
+            # order the feature data so we can apply percentiling
+            order = np.argsort(feature)
+            # x axis is located at y0 = pos, with pos being there for offset
+            y0 = np.ones(num_x_points) * pos
+            # calculate kdes:
+            ys = np.zeros((nbins, num_x_points))
+            for i in range(nbins):
+                # get shap values in this bin:
+                shaps = shap_values[order[thesebins[i]:thesebins[i + 1]], ind]
+                # if there's only one element, then we can't
+                if shaps.shape[0] == 1:
+                    warnings.warn(
+                        "not enough data in bin #%d for feature %s, so it'll be ignored. Try increasing the number of records to plot."
+                        % (i, feature_names[ind]))
+                    # to ignore it, just set it to the previous y-values (so the area between them will be zero). Not ys is already 0, so there's
+                    # nothing to do if i == 0
+                    if i > 0:
+                        ys[i, :] = ys[i - 1, :]
+                    continue
+                # save kde of them: note that we add a tiny bit of gaussian noise to avoid singular matrix errors
+                ys[i, :] = gaussian_kde(shaps + np.random.normal(loc=0, scale=0.001, size=shaps.shape[0]))(x_points)
+                # scale it up so that the 'size' of each y represents the size of the bin. For continuous data this will
+                # do nothing, but when we've gone with the unqique option, this will matter - e.g. if 99% are male and 1%
+                # female, we want the 1% to appear a lot smaller.
+                size = thesebins[i + 1] - thesebins[i]
+                bin_size_if_even = features.shape[0] / nbins
+                relative_bin_size = size / bin_size_if_even
+                ys[i, :] *= relative_bin_size
+            # now plot 'em. We don't plot the individual strips, as this can leave whitespace between them.
+            # instead, we plot the full kde, then remove outer strip and plot over it, etc., to ensure no
+            # whitespace
+            ys = np.cumsum(ys, axis=0)
+            width = 0.8
+            scale = ys.max() * 2 / width  # 2 is here as we plot both sides of x axis
+            for i in range(nbins - 1, -1, -1):
+                y = ys[i, :] / scale
+                c = pl.get_cmap(color)(i / (
+                        nbins - 1)) if color in pl.cm.datad else color  # if color is a cmap, use it, otherwise use a color
+                pl.fill_between(x_points, pos - y, pos + y, facecolor=c)
+        pl.xlim(shap_min, shap_max)
+
+    # draw the color bar
+    if color_bar and features is not None and (plot_type != "layered_violin" or color in pl.cm.datad):
+            import matplotlib.cm as cm
+            m = cm.ScalarMappable(cmap=red_blue_solid if plot_type != "layered_violin" else pl.get_cmap(color))
+            m.set_array([0, 1])
+            cb = pl.colorbar(m, ticks=[0, 1], aspect=1000)
+            cb.set_ticklabels([labels['FEATURE_VALUE_LOW'], labels['FEATURE_VALUE_HIGH']])
+            cb.set_label(labels['FEATURE_VALUE'], size=12, labelpad=0)
+            cb.ax.tick_params(labelsize=11, length=0)
+            cb.set_alpha(1)
+            cb.outline.set_visible(False)
+            bbox = cb.ax.get_window_extent().transformed(pl.gcf().dpi_scale_trans.inverted())
+            cb.ax.set_aspect((bbox.height - 0.9) * 20)
+        # cb.draw_all()
+
+    pl.gca().xaxis.set_ticks_position('bottom')
+    pl.gca().yaxis.set_ticks_position('none')
+    pl.gca().spines['right'].set_visible(False)
+    pl.gca().spines['top'].set_visible(False)
+    pl.gca().spines['left'].set_visible(False)
+    pl.gca().tick_params(color=axis_color, labelcolor=axis_color)
+    pl.yticks(range(len(feature_order)), [feature_names[i] for i in feature_order], fontsize=13)
+    pl.gca().tick_params('y', length=20, width=0.5, which='major')
+    pl.gca().tick_params('x', labelsize=11)
+    pl.ylim(-1, len(feature_order))
+    pl.xlabel(labels['VALUE'], fontsize=13)
+    pl.tight_layout()
+    # if show:
+    #     pl.show()
+    return mpl_fig
+
+
+
+
+
+
+def approx_interactions(index, shap_values, X):
+    """ Order other features by how much interaction they seem to have with the feature at the given index.
+
+    This just bins the SHAP values for a feature along that feature's value. For true Shapley interaction
+    index values for SHAP see the interaction_contribs option implemented in XGBoost.
+    """
+
+    if X.shape[0] > 10000:
+        a = np.arange(X.shape[0])
+        np.random.shuffle(a)
+        inds = a[:10000]
+    else:
+        inds = np.arange(X.shape[0])
+
+    x = X[inds, index]
+    srt = np.argsort(x)
+    shap_ref = shap_values[inds, index]
+    shap_ref = shap_ref[srt]
+    inc = max(min(int(len(x) / 10.0), 50), 1)
+    interactions = []
+    for i in range(X.shape[1]):
+        val_other = X[inds, i][srt].astype(np.float)
+        v = 0.0
+        if not (i == index or np.sum(np.abs(val_other)) < 1e-8):
+            for j in range(0, len(x), inc):
+                if np.std(val_other[j:j + inc]) > 0 and np.std(shap_ref[j:j + inc]) > 0:
+                    v += abs(np.corrcoef(shap_ref[j:j + inc], val_other[j:j + inc])[0, 1])
+        interactions.append(v)
+
+    return np.argsort(-np.abs(interactions))
+
+
+
+
+
+
+
+def shap_dependence_plot(ind, shap_values, features, feature_names=None, display_features=None,
+                    interaction_index="auto", color="#1E88E5", axis_color="#333333",
+                    dot_size=16, alpha=1, title=None, show=True):
+    """
+    Create a SHAP dependence plot, colored by an interaction feature.
+
+    Parameters
+    ----------
+    ind : int
+        Index of the feature to plot.
+
+    shap_values : numpy.array
+        Matrix of SHAP values (# samples x # features)
+
+    features : numpy.array or pandas.DataFrame
+        Matrix of feature values (# samples x # features)
+
+    feature_names : list
+        Names of the features (length # features)
+
+    display_features : numpy.array or pandas.DataFrame
+        Matrix of feature values for visual display (such as strings instead of coded values)
+
+    interaction_index : "auto", None, or int
+        The index of the feature used to color the plot.
+    """
+
+    # convert from DataFrames if we got any
+    if str(type(features)).endswith("'pandas.core.frame.DataFrame'>"):
+        if feature_names is None:
+            feature_names = features.columns
+        features = features.values
+    if str(type(display_features)).endswith("'pandas.core.frame.DataFrame'>"):
+        if feature_names is None:
+            feature_names = display_features.columns
+        display_features = display_features.values
+    elif display_features is None:
+        display_features = features
+
+    if feature_names is None:
+        feature_names = [labels['FEATURE'] % str(i) for i in range(shap_values.shape[1] - 1)]
+
+    # allow vectors to be passed
+    if len(shap_values.shape) == 1:
+        shap_values = np.reshape(shap_values, len(shap_values), 1)
+    if len(features.shape) == 1:
+        features = np.reshape(features, len(features), 1)
+
+    def convert_name(ind):
+        if type(ind) == str:
+            nzinds = np.where(feature_names == ind)[0]
+            if len(nzinds) == 0:
+                print("Could not find feature named: " + ind)
+                return None
+            else:
+                return nzinds[0]
+        else:
+            return ind
+
+    ind = convert_name(ind)
+
+    mpl_fig = pl.gcf()
+    ax = mpl_fig.gca()
+
+    # plotting SHAP interaction values
+    if len(shap_values.shape) == 3 and len(ind) == 2:
+        ind1 = convert_name(ind[0])
+        ind2 = convert_name(ind[1])
+        if ind1 == ind2:
+            proj_shap_values = shap_values[:, ind2, :]
+        else:
+            proj_shap_values = shap_values[:, ind2, :] * 2  # off-diag values are split in half
+
+        # TODO: remove recursion; generally the functions should be shorter for more maintainable code
+        return shap_dependence_plot(
+            ind1, proj_shap_values, features, feature_names=feature_names,
+            interaction_index=ind2, display_features=display_features, show=False
+        )
+
+        assert shap_values.shape[0] == features.shape[0], \
+            "'shap_values' and 'features' values must have the same number of rows!"
+        assert shap_values.shape[1] == features.shape[1], \
+            "'shap_values' must have the same number of columns as 'features'!"
+
+        # get both the raw and display feature values
+        xv = features[:, ind]
+        xd = display_features[:, ind]
+        s = shap_values[:, ind]
+        if type(xd[0]) == str:
+            name_map = {}
+            for i in range(len(xv)):
+                name_map[xd[i]] = xv[i]
+            xnames = list(name_map.keys())
+
+        # allow a single feature name to be passed alone
+        if type(feature_names) == str:
+            feature_names = [feature_names]
+        name = feature_names[ind]
+
+        # guess what other feature as the stongest interaction with the plotted feature
+        if interaction_index == "auto":
+            interaction_index = approx_interactions(ind, shap_values, features)[0]
+        interaction_index = convert_name(interaction_index)
+        categorical_interaction = False
+
+        # get both the raw and display color values
+        if interaction_index is not None:
+            cv = features[:, interaction_index]
+            cd = display_features[:, interaction_index]
+            clow = np.nanpercentile(features[:, interaction_index].astype(np.float), 5)
+            chigh = np.nanpercentile(features[:, interaction_index].astype(np.float), 95)
+            if type(cd[0]) == str:
+                cname_map = {}
+                for i in range(len(cv)):
+                    cname_map[cd[i]] = cv[i]
+                cnames = list(cname_map.keys())
+                categorical_interaction = True
+            elif clow % 1 == 0 and chigh % 1 == 0 and len(set(features[:, interaction_index])) < 50:
+                categorical_interaction = True
+
+        # discritize colors for categorical features
+        color_norm = None
+        if categorical_interaction and clow != chigh:
+            bounds = np.linspace(clow, chigh, chigh - clow + 2)
+            color_norm = matplotlib.colors.BoundaryNorm(bounds, red_blue.N)
+
+        # the actual scatter plot, TODO: adapt the dot_size to the number of data points?
+        if interaction_index is not None:
+            pl.scatter(xv, s, s=dot_size, linewidth=0, c=features[:, interaction_index], cmap=red_blue,
+                       alpha=alpha, vmin=clow, vmax=chigh, norm=color_norm, rasterized=len(xv) > 500)
+        else:
+            pl.scatter(xv, s, s=dot_size, linewidth=0, color="#1E88E5",
+                       alpha=alpha, rasterized=len(xv) > 500)
+
+        if interaction_index != ind and interaction_index is not None:
+            # draw the color bar
+            if type(cd[0]) == str:
+                tick_positions = [cname_map[n] for n in cnames]
+                if len(tick_positions) == 2:
+                    tick_positions[0] -= 0.25
+                    tick_positions[1] += 0.25
+                cb = pl.colorbar(ticks=tick_positions)
+                cb.set_ticklabels(cnames)
+            else:
+                cb = pl.colorbar()
+
+            cb.set_label(feature_names[interaction_index], size=13)
+            cb.ax.tick_params(labelsize=11)
+            if categorical_interaction:
+                cb.ax.tick_params(length=0)
+            cb.set_alpha(1)
+            cb.outline.set_visible(False)
+            bbox = cb.ax.get_window_extent().transformed(pl.gcf().dpi_scale_trans.inverted())
+            cb.ax.set_aspect((bbox.height - 0.7) * 20)
+
+        # make the plot more readable
+        if interaction_index != ind:
+            pl.gcf().set_size_inches(7.5, 5)
+        else:
+            pl.gcf().set_size_inches(6, 5)
+        # pl.xlabel(name, color=axis_color, fontsize=13)
+        # pl.ylabel(labels['VALUE_FOR'] % name, color=axis_color, fontsize=13)
+        if title is not None:
+            pl.title(title, color=axis_color, fontsize=13)
+        pl.gca().xaxis.set_ticks_position('bottom')
+        pl.gca().yaxis.set_ticks_position('left')
+        pl.gca().spines['right'].set_visible(False)
+        pl.gca().spines['top'].set_visible(False)
+        pl.gca().tick_params(color=axis_color, labelcolor=axis_color, labelsize=11)
+        for spine in pl.gca().spines.values():
+            spine.set_edgecolor(axis_color)
+        if type(xd[0]) == str:
+            pl.xticks([name_map[n] for n in xnames], xnames, rotation='vertical', fontsize=11)
+        # if show:
+            # pl.show()
+
+
+        if ind1 == ind2:
+            pl.ylabel(labels['MAIN_EFFECT'] % feature_names[ind1])
+        else:
+            pl.ylabel(labels['INTERACTION_EFFECT'] % (feature_names[ind1], feature_names[ind2]))
+
+        return mpl_fig, interaction_index
+
+
+        # # if show:
+        # #     pl.show()
+        # return
+        # return mpl_fig
+
+    # assert shap_values.shape[0] == features.shape[0], "'shap_values' and 'features' values must have the same number of rows!"
+    # assert shap_values.shape[1] == features.shape[1] + 1, "'shap_values' must have one more column than 'features'!"
+
+    # get both the raw and display feature values
+    xv = features[:, ind]
+    xd = display_features[:, ind]
+    s = shap_values[:, ind]
+    if type(xd[0]) == str:
+        name_map = {}
+        for i in range(len(xv)):
+            name_map[xd[i]] = xv[i]
+        xnames = list(name_map.keys())
+
+    # allow a single feature name to be passed alone
+    if type(feature_names) == str:
+        feature_names = [feature_names]
+    name = feature_names[ind]
+
+    # guess what other feature as the stongest interaction with the plotted feature
+    if interaction_index == "auto":
+        interaction_index = approx_interactions(ind, shap_values, features)[0]
+    interaction_index = convert_name(interaction_index)
+    categorical_interaction = False
+
+    # get both the raw and display color values
+    if interaction_index is not None:
+        cv = features[:, interaction_index]
+        cd = display_features[:, interaction_index]
+        clow = np.nanpercentile(features[:, interaction_index].astype(np.float), 5)
+        chigh = np.nanpercentile(features[:, interaction_index].astype(np.float), 95)
+        if type(cd[0]) == str:
+            cname_map = {}
+            for i in range(len(cv)):
+                cname_map[cd[i]] = cv[i]
+            cnames = list(cname_map.keys())
+            categorical_interaction = True
+        elif clow % 1 == 0 and chigh % 1 == 0 and len(set(features[:, interaction_index])) < 50:
+            categorical_interaction = True
+
+    # discritize colors for categorical features
+    color_norm = None
+    if categorical_interaction and clow != chigh:
+        bounds = np.linspace(clow, chigh, chigh - clow + 2)
+        color_norm = matplotlib.colors.BoundaryNorm(bounds, red_blue.N)
+
+    # the actual scatter plot, TODO: adapt the dot_size to the number of data points?
+    if interaction_index is not None:
+        pl.scatter(xv, s, s=dot_size, linewidth=0, c=features[:, interaction_index], cmap=red_blue,
+                   alpha=alpha, vmin=clow, vmax=chigh, norm=color_norm, rasterized=len(xv) > 500)
+    else:
+        pl.scatter(xv, s, s=dot_size, linewidth=0, color="#1E88E5",
+                   alpha=alpha, rasterized=len(xv) > 500)
+
+    if interaction_index != ind and interaction_index is not None:
+        # draw the color bar
+        if type(cd[0]) == str:
+            tick_positions = [cname_map[n] for n in cnames]
+            if len(tick_positions) == 2:
+                tick_positions[0] -= 0.25
+                tick_positions[1] += 0.25
+            cb = pl.colorbar(ticks=tick_positions)
+            cb.set_ticklabels(cnames)
+        else:
+            cb = pl.colorbar()
+
+        cb.set_label(feature_names[interaction_index], size=13)
+        cb.ax.tick_params(labelsize=11)
+        if categorical_interaction:
+            cb.ax.tick_params(length=0)
+        cb.set_alpha(1)
+        cb.outline.set_visible(False)
+        bbox = cb.ax.get_window_extent().transformed(pl.gcf().dpi_scale_trans.inverted())
+        cb.ax.set_aspect((bbox.height - 0.7) * 20)
+
+    # make the plot more readable
+    if interaction_index != ind:
+        pl.gcf().set_size_inches(7.5, 5)
+    else:
+        pl.gcf().set_size_inches(6, 5)
+    pl.xlabel(name, color=axis_color, fontsize=13)
+    pl.ylabel(labels['VALUE_FOR'] % name, color=axis_color, fontsize=13)
+    if title is not None:
+        pl.title(title, color=axis_color, fontsize=13)
+    pl.gca().xaxis.set_ticks_position('bottom')
+    pl.gca().yaxis.set_ticks_position('left')
+    pl.gca().spines['right'].set_visible(False)
+    pl.gca().spines['top'].set_visible(False)
+    pl.gca().tick_params(color=axis_color, labelcolor=axis_color, labelsize=11)
+    for spine in pl.gca().spines.values():
+        spine.set_edgecolor(axis_color)
+    if type(xd[0]) == str:
+        pl.xticks([name_map[n] for n in xnames], xnames, rotation='vertical', fontsize=11)
+    # if show:
+        # pl.show()
+    return mpl_fig, interaction_index