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import gradio as gr
import numpy as np
import matplotlib.pyplot as plt
from sklearn.feature_selection import f_regression, mutual_info_regression
from functools import partial
def default(n_samples,
noise_var,
noise_bias,
feat2_freq,
feat1_scale,
feat1_power,
feat2_shift,
feat2_scale,
feat2_func,
counter,
func_name):
return train_models(
func_name,
counter,
n_samples= n_samples,
noise_var= noise_var,
noise_bias= noise_bias,
feat2_freq= feat2_freq,
feat1_scale= feat1_scale,
feat1_power= feat1_power,
feat2_shift= feat2_shift,
feat2_scale= feat2_scale,
feat2_func= feat2_func,
)
def gaussian(n_samples,
gaussian_center,
gaussian_width,
gaussian_scaling,
counter,
func_name):
return train_models(
func_name,
counter,
n_samples= n_samples,
gaussian_center= gaussian_center,
gaussian_width= gaussian_width,
gaussian_scaling= gaussian_scaling,
)
def piecewise(n_samples,
piecewise_thres,
piecewise_scale,
counter,
func_name):
return train_models(
func_name,
counter,
n_samples= n_samples,
piecewise_thres= piecewise_thres,
piecewise_scale= piecewise_scale,
)
def train_models(func_name, counter, **kwargs):
functions = dict()
if func_name == "default":
feat2_func_list = {
"Use sine function for feature 2": np.sin,
"Use cosine function for feature 2": np.cos,
}
functions.update({"feat2_func":feat2_func_list[kwargs["feat2_func"]]})
np.random.seed(0)
n_samples = kwargs["n_samples"]
X = np.random.rand(n_samples, 3)
if func_name == "piecewise":
mask = X[:, 1] < (kwargs["piecewise_thres"]*0.1)
functions.update ({
"default":
lambda X: (kwargs["feat1_scale"]* X[:, 0] ** kwargs["feat1_power"] +
kwargs["feat2_scale"] * functions["feat2_func"](kwargs["feat2_freq"] * np.pi * X[:, 1] + kwargs["feat2_shift"]) +
(kwargs["noise_var"]*0.1) * np.random.randn(n_samples) + (kwargs["noise_bias"]*0.1)),
"Gaussian":
lambda X: (X[:, 0] + np.exp(-(X[:, 1] - (kwargs["gaussian_center"]*0.1))**2 / (2 * (kwargs["gaussian_width"]*0.1)**2)) +
(kwargs["gaussian_scaling"]*0.1) * np.random.randn(n_samples)),
"piecewise":
lambda X: (np.where(mask, kwargs["piecewise_scale"] * X[:, 0], kwargs["piecewise_scale"] * -X[:, 0]) +
0.1 * np.random.randn(n_samples))
})
y = functions[func_name](X)
f_test, _ = f_regression(X, y)
f_test /= np.max(f_test)
mi = mutual_info_regression(X, y)
mi /= np.max(mi)
fig, ax = plt.subplots()
i = counter
ax.scatter(X[:, i], y, edgecolor="black", s=20)
ax.set_xlabel("$x_{}$".format(i + 1), fontsize=14)
ax.set_ylabel("$y$", fontsize=14)
ax.set_title("F-test={:.2f}, MI={:.2f}".format(f_test[i], mi[i]), fontsize=16)
return fig
def iter_grid(n_rows, n_cols):
# create a grid using gradio Block
for _ in range(n_rows):
with gr.Row():
for _ in range(n_cols):
with gr.Column():
yield
def plot_func(input_model, args):
input_models = {"default": default,
"Gaussian": gaussian,
"piecewise": piecewise}
counter = 0
for _ in iter_grid(1,3):
fn = partial(input_models[input_model], counter=counter, func_name=input_model)
if counter >= len(input_models):
break
plot = gr.Plot(label=input_model)
n_samples.change(fn=fn, inputs=args, outputs=plot)
if input_model == "default":
noise_var.change(fn=fn, inputs=args, outputs=plot)
noise_bias.change(fn=fn, inputs=args, outputs=plot)
feat2_freq.change(fn=fn, inputs=args, outputs=plot)
feat1_scale.change(fn=fn, inputs=args, outputs=plot)
feat1_power.change(fn=fn, inputs=args, outputs=plot)
feat2_shift.change(fn=fn, inputs=args, outputs=plot)
feat2_scale.change(fn=fn, inputs=args, outputs=plot)
feat2_func.change(fn=fn, inputs=args, outputs=plot)
elif input_model == "Gaussian":
gaussian_center.change(fn=fn, inputs=args, outputs=plot)
gaussian_width.change(fn=fn, inputs=args, outputs=plot)
gaussian_scaling.change(fn=fn, inputs=args, outputs=plot)
elif input_model == "piecewise":
piecewise_thres.change(fn=fn, inputs=args, outputs=plot)
piecewise_scale.change(fn=fn, inputs=args, outputs=plot)
counter += 1
title = "Comparison of F-test and mutual information"
with gr.Blocks(title=title) as demo:
gr.Markdown(f"## {title}")
gr.Markdown("This example illustrates the differences between univariate \
F-test statistics and mutual information. \
The plots below show the dependency of `y` against individual `x_i` and normalized \
values of univariate F-tests statistics and mutual information.\
In general, the F-test evaluates linear dependencies and tends to prioritize \
features with linear relationships, while mutual information assesses any type \
of dependency between variables and tends to identify features with strong \
relationships. In these examples, the most discriminative features identified \
by each approach may vary.")
gr.Markdown("In the follwing examples, we introduce parameterization to enable interaction \
with various parameters of the equation.")
n_samples = gr.Slider(minimum=500, maximum=1500, value=1000, step=100,
label = "Number of Samples")
with gr.Tab("Default Example function"):
gr.Markdown("We consider 3 features `x_1`, `x_2`, `x_3` distributed uniformly over `[0, 1]`, \
the target depends on them as follows:")
gr.Markdown("- `y = x_1 + sin(6 * pi * x_2) + 0.1 * N(0, 1)`")
gr.Markdown("that is the third feature is completely irrelevant.")
gr.Markdown("Parametrized equation:")
gr.Markdown("`y = f1_scale * x_1 **f1_power + f2_scale * f2_func(f2_freq * np.pi * x_2 + f2_shift + variance) * random(samples) + bias`")
with gr.Row():
with gr.Column():
feat1_scale = gr.Slider(minimum=1, maximum=10, step=1,
label = "Scale feature 1")
feat1_power = gr.Slider(minimum=1, maximum=4, step=1,
label = "Raised feature 1 to the power")
noise_var = gr.Slider(minimum=0, maximum=10, step=1,
label = "Noise variance")
noise_bias = gr.Slider(minimum=0, maximum=10, step=1,
label = "Noise bias")
with gr.Column():
feat2_freq = gr.Slider(minimum=1, maximum=10, step=1, value=6,
label = "Feature 2 frequency")
feat2_shift = gr.Slider(minimum=1, maximum=5, step=1,
label = "Shift feature 2")
feat2_scale = gr.Slider(minimum=1, maximum=4, step=1,
label = "Scale feature 2")
feat2_func = gr.Radio(choices=["Use sine function for feature 2",
"Use cosine function for feature 2"],
value="Use sine function for feature 2")
plot_func("default", [n_samples,
noise_var,
noise_bias,
feat2_freq,
feat1_scale,
feat1_power,
feat2_shift,
feat2_scale,
feat2_func,
])
with gr.Tab("Gaussian function"):
gr.Markdown("We consider 3 features `x_1`, `x_2`, `x_3` distributed uniformly over `[0, 1]`, \
the target depends on them as follows:")
gr.Markdown("- `y = x_1 + np.exp(-(x_2-0.5)**2 / (2 * 0.1**2)) + 0.1 * N(0, 1)`")
gr.Markdown("that is the third feature is completely irrelevant.")
gr.Markdown("Parametrized equation:")
gr.Markdown("`y = x_1 + exponential(-(x_2 - center)**2 / (2 * width)**2) + scaling * random(samples)`")
gaussian_center = gr.Slider(minimum=0, maximum=10, value=5, step=1,
label = "Gaussian center")
gaussian_width = gr.Slider(minimum=1, maximum=10, value=1, step=1,
label = "Gaussian width")
gaussian_scaling = gr.Slider(minimum=1, maximum=5, value=1, step=1,
label = "Gaussian scaling")
plot_func("Gaussian", [n_samples,
gaussian_center,
gaussian_width,
gaussian_scaling
])
with gr.Tab("Piecewise function"):
gr.Markdown("We consider 3 features `x_1`, `x_2`, `x_3` distributed uniformly over `[0, 1]`, \
the target depends on them as follows:")
gr.Markdown("- `mask = x_2 < 0.5`")
gr.Markdown("- `y = x_1` if `mask` is True")
gr.Markdown("- `y = -x_1` if `mask` is True")
gr.Markdown("that is the third feature is completely irrelevant.")
gr.Markdown("Parametrized equation:")
gr.Markdown("- `mask = x_2 < threshold`")
gr.Markdown("- `y = scaling*x_1` if `mask` is True")
gr.Markdown("- `y = scaling*-x_1` if `mask` is True")
piecewise_thres = gr.Slider(minimum=1, maximum=10, value=5, step=1,
label = "Piecewise threshold")
piecewise_scale = gr.Slider(minimum=1, maximum=10, value=1, step=1,
label = "Piecewise scaling")
plot_func("piecewise", [n_samples, piecewise_thres,
piecewise_scale
])
demo.launch()
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