Uploaded main app file and package requirements

app.py

@@ -0,0 +1,239 @@
+"""
+Demo is Derived from  https://scikit-learn.org/stable/auto_examples/decomposition/plot_pca_vs_fa_model_selection.html#sphx-glr-auto-examples-decomposition-plot-pca-vs-fa-model-selection-py
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+from scipy import linalg
+import gradio as gr
+import matplotlib.pyplot as plt
+
+from sklearn.decomposition import PCA, FactorAnalysis
+from sklearn.covariance import ShrunkCovariance, LedoitWolf
+from sklearn.model_selection import cross_val_score
+from sklearn.model_selection import GridSearchCV
+
+
+def create_dataset(n_samples=500, n_features=25, rank=5, sigma=1.0, random_state=42, n_components=5):
+    '''
+    Function to create a dataset with homoscedastic noise and heteroscedastic noise
+    '''
+    
+    # Create a random dataset and add homoscedastic noise and heteroscedastic noise
+
+    rng = np.random.RandomState(random_state)
+    U, _, _ = linalg.svd(rng.randn(n_features, n_features))
+    # here n_features must be >= rank as we do a dot product with U[:, :rank].T
+    X = np.dot(rng.randn(n_samples, rank), U[:, :rank].T)
+
+    # Adding homoscedastic noise
+    X_homo = X + sigma * rng.randn(n_samples, n_features)
+
+    # Adding heteroscedastic noise
+    sigmas = sigma * rng.rand(n_features) + sigma / 2.0
+    X_hetero = X + rng.randn(n_samples, n_features) * sigmas
+    n_components_range = np.arange(0, n_features, n_components)
+    return X_homo, X_hetero, n_components_range, rank
+
+
+def compute_scores(X, n_components_range):
+    ''' 
+    Function to run PCA and FA with different number of componenets and run cross validation
+    
+    Returns mean PCA and FA scores
+    '''
+    
+    pca = PCA(svd_solver="full")
+    fa = FactorAnalysis()
+
+    pca_scores, fa_scores = [], []
+    for n in n_components_range:
+        pca.n_components = n
+        fa.n_components = n
+        pca_scores.append(np.mean(cross_val_score(pca, X)))
+        fa_scores.append(np.mean(cross_val_score(fa, X)))
+
+    return pca_scores, fa_scores
+
+
+def shrunk_cov_score(X):
+    shrinkages = np.logspace(-2, 0, 30)
+    cv = GridSearchCV(ShrunkCovariance(), {"shrinkage": shrinkages})
+    return np.mean(cross_val_score(cv.fit(X).best_estimator_, X))
+
+
+def lw_score(X):
+    return np.mean(cross_val_score(LedoitWolf(), X))
+
+#TODO - allow selection of one or both methods
+# def plot_pca_fa_analysis(n_features, n_components):
+    
+#     '''
+#     Function to plot results of PCA and FA cross validation analysis
+#     '''
+    
+#     X_homo, X_hetero, n_components_range, rank = create_dataset(n_features=n_features, n_components = n_components)
+    
+    
+#     for X, title in [(X_homo, "Homoscedastic Noise"), (X_hetero, "Heteroscedastic Noise")]:        
+        
+#         # compute the pca and fa scores
+#         pca_scores, fa_scores = compute_scores(X, n_components_range=n_components_range)
+#         n_components_pca = n_components_range[np.argmax(pca_scores)]
+#         n_components_fa = n_components_range[np.argmax(fa_scores)]
+
+#         pca = PCA(svd_solver="full", n_components="mle")
+#         pca.fit(X)
+#         n_components_pca_mle = pca.n_components_
+
+#         print("best n_components by PCA CV = %d" % n_components_pca)
+#         print("best n_components by FactorAnalysis CV = %d" % n_components_fa)
+#         print("best n_components by PCA MLE = %d" % n_components_pca_mle)
+
+#         fig = plt.figure()
+#         fig, (ax1, ax2) = plt.subplots(1,2)
+#         plt.plot(n_components_range, pca_scores, "b", label="PCA scores")
+#         plt.plot(n_components_range, fa_scores, "r", label="FA scores")
+#         plt.axvline(rank, color="g", label="TRUTH: %d" % rank, linestyle="-")
+#         plt.axvline(
+#             n_components_pca,
+#             color="b",
+#             label="PCA CV: %d" % n_components_pca,
+#             linestyle="--",
+#         )
+#         plt.axvline(
+#             n_components_fa,
+#             color="r",
+#             label="FactorAnalysis CV: %d" % n_components_fa,
+#             linestyle="--",
+#         )
+#         plt.axvline(
+#             n_components_pca_mle,
+#             color="k",
+#             label="PCA MLE: %d" % n_components_pca_mle,
+#             linestyle="--",
+#         )
+
+#         # compare with other covariance estimators
+#         plt.axhline(
+#             shrunk_cov_score(X),
+#             color="violet",
+#             label="Shrunk Covariance MLE",
+#             linestyle="-.",
+#         )
+#         plt.axhline(
+#             lw_score(X),
+#             color="orange",
+#             label="LedoitWolf MLE" % n_components_pca_mle,
+#             linestyle="-.",
+#         )
+        
+#         plt.xlabel("nb of components")
+#         plt.ylabel("CV scores")
+#         plt.legend(loc="lower right")
+#         plt.title(title)
+
+#     return fig
+
+def plot_pca_fa_analysis_side(n_samples, n_features, n_components):
+    
+    X_homo, X_hetero, n_components_range, rank = create_dataset(n_samples = n_samples, n_features=n_features, n_components = n_components)
+    
+    # set up figure - here we will be doing a side by side plot    
+    fig, axes = plt.subplots(2,1, sharey= False, sharex=True, figsize = (10,8))
+    
+    for X, title, idx in [(X_homo, "Homoscedastic Noise", 0), (X_hetero, "Heteroscedastic Noise", 1)]:       
+        
+        # compute the pca and fa scores
+        pca_scores, fa_scores = compute_scores(X, n_components_range=n_components_range)
+        n_components_pca = n_components_range[np.argmax(pca_scores)]
+        n_components_fa = n_components_range[np.argmax(fa_scores)]
+
+        pca = PCA(svd_solver="full", n_components="mle")
+        pca.fit(X)
+        n_components_pca_mle = pca.n_components_
+
+        print("best n_components by PCA CV = %d" % n_components_pca)
+        print("best n_components by FactorAnalysis CV = %d" % n_components_fa)
+        print("best n_components by PCA MLE = %d" % n_components_pca_mle)
+        
+        
+        axes[idx].plot(n_components_range, pca_scores, "b", label="PCA scores")
+        axes[idx].plot(n_components_range, fa_scores, "r", label="FA scores")
+        axes[idx].axvline(rank, color="g", label="TRUTH: %d" % rank, linestyle="-")
+        axes[idx].axvline(
+            n_components_pca,
+            color="b",
+            label="PCA CV: %d" % n_components_pca,
+            linestyle="--",
+        )
+        axes[idx].axvline(
+            n_components_fa,
+            color="r",
+            label="FactorAnalysis CV: %d" % n_components_fa,
+            linestyle="--",
+        )
+        axes[idx].axvline(
+            n_components_pca_mle,
+            color="k",
+            label="PCA MLE: %d" % n_components_pca_mle,
+            linestyle="--",
+        )
+
+        # compare with other covariance estimators
+        axes[idx].axhline(
+            shrunk_cov_score(X),
+            color="violet",
+            label="Shrunk Covariance MLE",
+            linestyle="-.",
+        )
+        axes[idx].axhline(
+            lw_score(X),
+            color="orange",
+            label="LedoitWolf MLE" % n_components_pca_mle,
+            linestyle="-.",
+        )
+        
+    
+        # axes[idx].legend(bbox_to_anchor=(1.01, 1.05))
+        # plt.xlabel("nb of components")
+        # plt.ylabel("CV scores")
+        axes[idx].set_xlabel("nb of components")
+        axes[idx].set_ylabel("CV scores")
+        axes[idx].legend(loc="lower right")
+        axes[idx].set_title(title)
+
+    return fig
+
+
+
+title = " Illustration of Model Selection with Probabilistic PCA and Factor Analysis (FA)"
+with gr.Blocks(title=title) as demo:
+    gr.Markdown(f"# {title}")
+    gr.Markdown(" This example shows how one can use Prinicipal Components Analysis (PCA) and Factor Analysis (FA) for model selection by observing the likelihood of a held-out dataset with added noise <br>"
+    " The number of samples (n_samples) will determine the number of data points to produce.  <br>"
+    " The number of components (n_components) will determine the number of components each method will fit to, and will affect the likelihood of the held-out set.  <br>"
+    " The number of features (n_components) determine the number of features the toy dataset X variable will have.  <br>"
+    " Play with the n_components parameter to see.<br>")
+
+    gr.Markdown(" **[Demo is based on sklearn docs](https://scikit-learn.org/stable/auto_examples/decomposition/plot_pca_vs_fa_model_selection.html#sphx-glr-auto-examples-decomposition-plot-pca-vs-fa-model-selection-py)** <br>")
+
+    gr.Markdown(" **Dataset** : A toy dataset with corrupted with homoscedastic noise (noise variance is the same for each feature) or heteroscedastic noise (noise variance is the different for each feature) . <br>")
+    gr.Markdown(" Different number of features and number of components affect how well the low rank space is recovered. <br>"
+                "  Larger Depth trying to overfit and learn even the finner details of the data.<br>"
+               )
+
+    with gr.Row():
+        n_samples = gr.Slider(value=100, min=100, maximum=1000, step=100, label="n_samples")
+        n_components = gr.Slider(value=2, min=1, maximum=20, step=1, label="n_components")
+        n_features = gr.Slider(value=5, min=5, maximum=25, step=1, label="n_features")
+        
+    
+      # options for n_components    
+    btn = gr.Button(value="Submit")
+    btn.click(plot_pca_fa_analysis_side, inputs= [n_samples, n_features, n_components], outputs= gr.Plot(label='Multi-output regression with decision trees') ) # 
+    
+
+demo.launch()

requirements.txt

@@ -0,0 +1,3 @@
+scikit-learn==1.2.2
+matplotlib==3.5.1
+numpy==1.21.6