import gradio as gr import numpy as np import matplotlib.pyplot as plt from sklearn.decomposition import PCA from sklearn.model_selection import train_test_split from sklearn.pipeline import make_pipeline from sklearn.linear_model import LinearRegression from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA from sklearn.cross_decomposition import PLSRegression #Data preparation def make_data(): rng = np.random.RandomState(0) n_samples = 500 cov = [[3, 3], [3, 4]] X = rng.multivariate_normal(mean=[0, 0], cov=cov, size=n_samples) return X,rng,n_samples def plot_scatter_pca(alpha): plt.scatter(X[:, 0], X[:, 1], alpha=alpha, label="samples") for i, (comp, var) in enumerate(zip(pca.components_, pca.explained_variance_)): comp = comp * var # scale component by its variance explanation power plt.plot( [0, comp[0]], [0, comp[1]], label=f"Component {i}", linewidth=5, color=f"C{i + 2}", ) plt.gca().set( aspect="equal", title="2-dimensional dataset with principal components", xlabel="first feature", ylabel="second feature", ) plt.legend() # plt.show() return plt def datagen_y(): y = X.dot(pca.components_[1]) + rng.normal(size=n_samples) / 2 return y def data_projections(): y = datagen_y() fig, axes = plt.subplots(1, 2, figsize=(10, 3)) axes[0].scatter(X.dot(pca.components_[0]), y, alpha=0.3) axes[0].set(xlabel="Projected data onto first PCA component", ylabel="y") axes[1].scatter(X.dot(pca.components_[1]), y, alpha=0.3) axes[1].set(xlabel="Projected data onto second PCA component", ylabel="y") plt.tight_layout() # plt.show() return plt def plot_pca_ls(): X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=rng) pcr = make_pipeline(StandardScaler(), PCA(n_components=1), LinearRegression()) pcr.fit(X_train, y_train) pca = pcr.named_steps["pca"] # retrieve the PCA step of the pipeline pls = PLSRegression(n_components=1) pls.fit(X_train, y_train) fig, axes = plt.subplots(1, 2, figsize=(10, 3)) axes[0].scatter(pca.transform(X_test), y_test, alpha=0.3, label="ground truth") axes[0].scatter( pca.transform(X_test), pcr.predict(X_test), alpha=0.3, label="predictions" ) axes[0].set( xlabel="Projected data onto first PCA component", ylabel="y", title="PCR / PCA" ) axes[0].legend() axes[1].scatter(pls.transform(X_test), y_test, alpha=0.3, label="ground truth") axes[1].scatter( pls.transform(X_test), pls.predict(X_test), alpha=0.3, label="predictions" ) axes[1].set(xlabel="Projected data onto first PLS component", ylabel="y", title="PLS") axes[1].legend() plt.tight_layout() # plt.show() return plt def get_components(): X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=rng) pcr = make_pipeline(StandardScaler(), PCA(n_components=1), LinearRegression()) pls = PLSRegression(n_components=1) return X_train, X_test, y_train, y_test, pcr, pls def print_results(): X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=rng) pcr = make_pipeline(StandardScaler(), PCA(n_components=1), LinearRegression()) pcr.fit(X_train, y_train) pca = pcr.named_steps["pca"] # retrieve the PCA step of the pipeline pls = PLSRegression(n_components=1) pls.fit(X_train, y_train) result1 = f"PCR r-squared {pcr.score(X_test, y_test):.3f}" result2 = f"PLS r-squared {pls.score(X_test, y_test):.3f}" mystr = result1 +"\n"+ result2 return mystr def calc_pcr_r2(): X_train, X_test, y_train, y_test, pcr, pls = get_components() pca_2 = make_pipeline(PCA(n_components=2), LinearRegression()) pca_2.fit(X_train, y_train) r2 = f"PCR r-squared with 2 components {pca_2.score(X_test, y_test):.3f}" return r2 X, rng, n_samples = make_data() pca = PCA(n_components=2).fit(X) y = datagen_y() # plot_scatter_pca(alpha) title = " Principal Component Regression vs Partial Least Squares Regression." with gr.Blocks(title=title, theme='gstaff/xkcd') as demo: gr.Markdown(f" # {title}") gr.Markdown( """ This example compares Principal Component Regression (PCR) and Partial Least Squares Regression (PLS) on a toy dataset. Our goal is to illustrate how PLS can outperform PCR when the target is strongly correlated with some directions in the data that have a low variance. PCR is a regressor composed of two steps: first, PCA is applied to the training data, possibly performing dimensionality reduction; then, a regressor (e.g. a linear regressor) is trained on the transformed samples. In PCA, the transformation is purely unsupervised, meaning that no information about the targets is used. As a result, PCR may perform poorly in some datasets where the target is strongly correlated with directions that have low variance. Indeed, the dimensionality reduction of PCA projects the data into a lower dimensional space where the variance of the projected data is greedily maximized along each axis. Despite them having the most predictive power on the target, the directions with a lower variance will be dropped, and the final regressor will not be able to leverage them. PLS is both a transformer and a regressor, and it is quite similar to PCR: it also applies a dimensionality reduction to the samples before applying a linear regressor to the transformed data. The main difference with PCR is that the PLS transformation is supervised. Therefore, as we will see in this example, it does not suffer from the issue we just mentioned. """) gr.Markdown("You can see the associated scikit-learn example [here](https://scikit-learn.org/stable/auto_examples/cross_decomposition/plot_pcr_vs_pls.html#sphx-glr-auto-examples-cross-decomposition-plot-pcr-vs-pls-py).") # loaded_model = load_hf_model_hub() with gr.Tab("Visualize Input dataset"): with gr.Row(equal_height=True): slider1 = gr.Slider(label="alpha", minimum=0.0, maximum=1.0) slider1.change(plot_scatter_pca, slider1, outputs= gr.Plot(label='Visualizing input dataset') ) with gr.Tab("PCA data projections"): btn_decision = gr.Button(value="PCA data projections") btn_decision.click(data_projections, outputs= gr.Plot(label='PCA data projections') ) with gr.Tab("predictive power"): btn_power = gr.Button(value="Predictive power") btn_power.click(plot_pca_ls, outputs= gr.Plot(label='Predictive power') ) with gr.Tab("Results tab"): gr.Markdown( """ As a final remark, we note that PCR with 2 components performs as well as PLS: this is because in this case, PCR was able to leverage the second component which has the most preditive power on the target. """) btn_power = gr.Button(value="Results") out = gr.Textbox(label="r2 score of both estimators") btn_power.click(print_results, outputs= out ) with gr.Tab("r2_score of predictors comparison"): with gr.Row(equal_height=True): gr.Markdown( """ We also print the R-squared scores of both estimators, which further confirms that PLS is a better alternative than PCR in this case. A negative R-squared indicates that PCR performs worse than a regressor that would simply predict the mean of the target. """) btn_1 = gr.Button(value="r2_score of predictors") out1 = gr.Textbox(label="r2_score of predictors") btn_1.click(calc_pcr_r2, outputs= out1 ) gr.Markdown( f"## End of page") demo.launch()