import numpy as np
import holoviews as hv

hv.extension("bokeh")

def BCE(y, y_hat):
    return y_hat, -y * np.log(y_hat) - (1 - y) * np.log(1 - y_hat)


def wBCE(y, y_hat):
    return y_hat, -y * np.log(y_hat) + y_hat

def d_dyhat(f):
    def d_dyhat_f(y, y_hat):
        f_x, f_y = f(y, y_hat)
        return f_x, np.diff(f_y)/np.diff(f_x)
    return d_dyhat_f

def comparison_plot(y, y_hat):
    return (
        hv.Curve(BCE(y, y_hat), label="BCE", kdims=["y_hat"], vdims=["loss"])
        * hv.Curve(wBCE(y, y_hat), label="wBCE", kdims=["y_hat"], vdims=["loss"])
        * hv.VLine(y).opts(color="k", line_dash="dashed")
    ).opts(
        show_grid=True,
        title=f"Functions (y={np.round(y, 3)})",
        xlim=(-0.1, 1.1),
        ylim=(0, 2),
        width=420
    )


def derivative_comparison_plot(y, y_hat):
    return (
        hv.Curve(d_dyhat(BCE)(y, y_hat), label="BCE", kdims="y_hat", vdims="gradient")
        * hv.Curve(d_dyhat(wBCE)(y, y_hat), label="wBCE", kdims="y_hat", vdims="gradient")
        * hv.VLine(y).opts(color="k", line_dash="dashed")
        * hv.HLine(0).opts(color="k", line_dash="dashed")
    ).opts(
        show_grid=True,
        title=f"Derivatives (y={np.round(y, 3)})",
        xlim=(-0.1, 1.1),
        ylim=(-3, 3),
        width=420
    )

y_hat = np.linspace(1e-9, 1 - 1e-09, 1000)
plots = 21

holomap = hv.HoloMap(
    {
        y: (comparison_plot(y, y_hat) + derivative_comparison_plot(y, y_hat)).cols(1)
        for y in np.linspace(0, 1, plots)
    },
    kdims=hv.Dimension("y", default=0.5),
).collate()
hv.output(holomap, widget_location="top")

👆⬆️ Use the Slider to move y ⬆️👆