Spaces:
Sleeping
Sleeping
File size: 8,833 Bytes
0a25afe |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 |
import gradio as gr
import numpy as np
import sympy as sp
import seaborn as sns
from matplotlib import pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline
sns.set_style(style="darkgrid")
sns.set_context(context="notebook", font_scale=0.7)
MAX_NOISE = 20
DEFAULT_NOISE = 6
SLIDE_NOISE_STEP = 2
MAX_POINTS = 100
DEFAULT_POINTS = 20
SLIDE_POINTS_STEP = 5
def generate_equation(process_params):
process_params = process_params.astype(float).values.tolist()
# Define symbols
x = sp.symbols('x')
coefficients = sp.symbols('a b c d e')
# Create the polynomial expression
polynomial_expression = None
for i, coef in enumerate(reversed(coefficients)):
polynomial_expression = polynomial_expression + coef * x**i if polynomial_expression else coef * x**i
# Parameter mapping
parameters = {coef: value for coef, value in zip(coefficients, process_params[0])}
# Substitute parameter values into the expression
polynomial_with_values = polynomial_expression.subs(parameters)
latex_representation = sp.latex(polynomial_with_values)
return fr"$${latex_representation}$$"
def true_process(x, process_params):
"""The true process we want to model."""
process_params = process_params.astype(float).values.tolist()
return (
process_params[0][0] * (x ** 4)
+ process_params[0][1] * (x ** 3)
+ process_params[0][2] * (x ** 2)
+ process_params[0][3] * x
+ process_params[0][4]
)
def generate_data(num_points, noise_level, process_params):
# x is the list of input values
input_values = np.linspace(-5, 2, num_points)
input_values_dense = np.linspace(-5, 2, MAX_POINTS)
# y = f(x) is the underlying process we want to model
y = [true_process(x, process_params) for x in input_values]
y_dense = [true_process(x, process_params) for x in input_values_dense]
# however, we can only observe a noisy version of f(x)
noise = np.random.normal(0, noise_level, len(input_values))
y_noisy = y + noise
return input_values, input_values_dense, y, y_dense, y_noisy
def make_plot(
num_points, noise_level, process_params,
show_true_process, show_original_points,
show_noisy_points, show_added_noise,
show_learned_process, show_predicted_points,
show_prediction_error,
polynomial_degree=None
):
x, x_dense, y, y_dense, y_noisy = generate_data(num_points, noise_level, process_params)
fig = plt.figure(dpi=400)
if show_true_process:
plt.plot(
x_dense, y_dense, "-", color="#363A4F",
label="True Process",
lw=1.5,
)
if show_added_noise:
plt.vlines(
x, y, y_noisy, color="#556D9A",
linestyles="dashed",
alpha=0.75,
lw=1,
label="Added Noise",
)
if show_original_points:
plt.plot(
x, y, "-o", color="none",
ms=6,
markerfacecolor="white",
markeredgecolor="#556D9A",
markeredgewidth=1.2,
label="Original Points",
)
if show_noisy_points and not polynomial_degree:
plt.plot(
x, y_noisy, "-o", color="none",
ms=6.5,
markerfacecolor="#556D9A",
markeredgecolor="none",
markeredgewidth=1.5,
alpha=1,
label="Noisy Points",
)
# Fit the selected regression model
if polynomial_degree:
degree = polynomial_degree
model = make_pipeline(PolynomialFeatures(degree), LinearRegression())
model.fit(x.reshape(-1, 1), y_noisy)
# Plot the fitted regression model
y_pred_dense = model.predict(x_dense.reshape(-1, 1))
y_pred = model.predict(x.reshape(-1, 1))
if show_learned_process:
plt.plot(
x_dense, y_pred_dense, "-", color="#327747",
label="Learned Process",
lw=1.5,
alpha=0.75,
)
if show_prediction_error:
plt.vlines(
x, y_pred, y_noisy, color="#43A461",
linestyles="dashed",
alpha=0.75,
lw=1,
label="Prediction Error",
)
if show_noisy_points:
plt.plot(
x, y_noisy, "-o", color="none",
ms=6.5,
markerfacecolor="#556D9A",
markeredgecolor="none",
markeredgewidth=1.5,
alpha=1,
label="Training Points",
)
if show_predicted_points:
plt.plot(
x, y_pred, "-o", color="none",
ms=6.5,
markerfacecolor="#43A461",
markeredgecolor="none",
markeredgewidth=1.5,
label="Predicted Points",
alpha=1,
)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(fontsize=7.5)
plt.tight_layout()
return fig
# Custom CSS
css = """
.train-button {
font-size: 1.2em;
width: 20%!important;
margin: 0;
}
.model-section {
font-size: 1em;
width: 100%!important;
margin: 0 0 1em 0;
}
.gradio-container {
width: 40%!important;
min-width: 800px;
}
"""
with gr.Blocks(css=css) as demo:
with gr.Row():
with gr.Column():
gr.Markdown("## Underlying Process")
with gr.Row():
process_params = gr.DataFrame(
value=[[0.5, 2, -0.5, -2, 1]],
label="Polynomial Coefficients",
type="pandas",
column_widths=("2", "1", "1", "1", "1w"),
headers=["x ** 4", "x ** 3", "x ** 2", "x", "1"],
interactive=True
)
equation = gr.Markdown()
gr.Markdown("## Data Generation")
with gr.Row():
num_points = gr.Slider(
minimum=5,
maximum=MAX_POINTS,
value=DEFAULT_POINTS,
step=SLIDE_POINTS_STEP,
label="Number of Points"
)
noise_level = gr.Slider(
minimum=0,
maximum=MAX_NOISE,
value=DEFAULT_NOISE,
step=SLIDE_NOISE_STEP,
label="Noise Level"
)
show_params = []
with gr.Row():
with gr.Column():
show_params.append(gr.Checkbox(label="Underlying Process", value=True))
show_params.append(gr.Checkbox(label="Original Points", value=True))
show_params.append(gr.Checkbox(label="Noisy Points", value=True))
show_params.append(gr.Checkbox(label="Added Noise", value=True))
with gr.Column():
show_params.append(gr.Checkbox(label="Learned Process", value=True))
show_params.append(gr.Checkbox(label="Predicted Points", value=True))
show_params.append(gr.Checkbox(label="Prediction Error", value=True))
# Add model choice dropdown and training trigger button
gr.Markdown("## Modelisation")
with gr.Row(elem_classes=["model-section"]):
polynomial_degree = gr.Number(label="Choose the degree of your regression model", value=1, minimum=1, maximum=15, step=1, scale=2)
train_button = gr.Button(value="Train Model", elem_classes=["train-button"], scale=1)
scatter_plot = gr.Plot(elem_classes=["main-plot"])
num_points.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
noise_level.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
process_params.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
process_params.change(fn=generate_equation, inputs=[process_params], outputs=equation)
train_button.click(make_plot, inputs=[num_points, noise_level, process_params, *show_params, polynomial_degree], outputs=scatter_plot)
for component in show_params:
component.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
demo.load(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
demo.load(fn=generate_equation, inputs=[process_params], outputs=equation)
if __name__ == "__main__":
demo.launch()
|