app.py

import gradio as gr
import matplotlib.pyplot as plt
import numpy as np
from sklearn.linear_model import BayesianRidge

SEED = 1234
ORDER = 3
MAX_SAMPLES = 100


def sin_wave(x: np.array):
    """Sinusoidal wave function"""
    return np.sin(2 * np.pi * x)


def generate_train_data(n_samples: int):
    """Generates sinuosidal data with noise"""
    rng = np.random.RandomState(SEED)
    x_train = rng.uniform(0.0, 1.0, n_samples)
    y_train = sin_wave(x_train) + rng.normal(scale=0.1, size=n_samples)
    X_train = np.vander(x_train, ORDER + 1, increasing=True)
    return x_train, X_train, y_train


def get_app_fn():
    """Returns the demo function with pre-generated data and model"""
    x_test = np.linspace(0.0, 1.0, 100)
    X_test = np.vander(x_test, ORDER + 1, increasing=True)
    y_test = sin_wave(x_test)
    reg = BayesianRidge(tol=1e-6, fit_intercept=False, compute_score=True)
    x_train_full, X_train_full, y_train_full = generate_train_data(MAX_SAMPLES)

    def app_fn(n_samples: int, alpha_init: float, lambda_init: float):
        """Train a Bayesian Ridge regression model and plot the predicted points"""

        rng = np.random.RandomState(SEED)
        subset_idx = rng.randint(0, MAX_SAMPLES, n_samples)

        x_train, X_train, y_train = (
            x_train_full[subset_idx],
            X_train_full[subset_idx],
            y_train_full[subset_idx],
        )
        reg.set_params(alpha_init=alpha_init, lambda_init=lambda_init)
        reg.fit(X_train, y_train)

        ymean, ystd = reg.predict(X_test, return_std=True)

        fig, ax = plt.subplots()
        ax.plot(x_test, y_test, color="blue", label="sin($2\\pi x$)")
        ax.scatter(x_train, y_train, s=50, alpha=0.5, label="observation")
        ax.plot(x_test, ymean, color="red", label="predicted mean")
        ax.fill_between(
            x_test,
            ymean - ystd,
            ymean + ystd,
            color="pink",
            alpha=0.5,
            label="predicted std",
        )
        ax.set_ylim(-1.3, 1.3)
        ax.set_xlabel("Cycles")
        ax.set_ylabel("Amplitude")
        ax.legend()
        text = "$\\alpha={:.1f}$\n$\\lambda={:.3f}$\n$L={:.1f}$".format(
            reg.alpha_, reg.lambda_, reg.scores_[-1]
        )
        ax.text(0.05, -1.0, text, fontsize=12)

        return fig

    return app_fn


title = "Bayesian Ridge Regression"
description = (
    "This demo is based on the [Bayesian Ridge Regression](https://scikit-learn.org/stable/auto_examples/linear_model/plot_bayesian_ridge_curvefit.html#curve-fitting-with-bayesian-ridge-regression) "
    "example from scikit-learn.\n"
    "The example shows the effect of different initial values for the regularisation parameters `alpha` and `lambda`. "
    "When starting from the default values (`alpha_init = 1.90`, `lambda_init = 1.`), the bias of the resulting curve is large, "
    "and the variance is small. So, `lambda_init` should be relatively small (e.g. `1.e-3`) to reduce the bias.\n"
    "By evaluating log marginal likelihood (`L`) of these models, we can determine which one is better. A model with larger `L` is more likely."
)
with gr.Blocks(title=title) as demo:
    gr.Markdown(f"## {title}")
    gr.Markdown(description)

    n_samples_input = gr.Slider(
        minimum=5, maximum=100, value=25, step=1, label="#observations"
    )
    alpha_input = gr.Slider(
        minimum=0.001, maximum=5, value=1.9, step=0.01, label="alpha_init"
    )
    lambda_input = gr.Slider(
        minimum=0.001, maximum=5, value=1.0, step=0.01, label="lambda_init"
    )
    outputs = gr.Plot(label="Output")
    inputs = [n_samples_input, alpha_input, lambda_input]
    app_fn = get_app_fn()

    n_samples_input.change(fn=app_fn, inputs=inputs, outputs=outputs)
    alpha_input.change(fn=app_fn, inputs=inputs, outputs=outputs)
    lambda_input.change(fn=app_fn, inputs=inputs, outputs=outputs)

demo.launch()