Tasks

Unconditional case

Classification

Classifier description

\[P(C=c|X=x) \propto \pi_c \hat{f}_c(X=x)\]

\[\underset{c}{\mathrm{argmax}} \quad P(C=c|X=x)\]

Example:

from kdelearn.kde_tasks import KDEClassification

# Prepare train data
m_train = 1000
cov = [[1, 0], [0, 1]]

## class 1
x_train1 = np.random.multivariate_normal([0, 0], cov, m_train // 2)
labels_train1 = np.full(m_train // 2, 1)
## class 2
x_train2 = np.random.multivariate_normal([3, 3], cov, m_train // 2)
labels_train2 = np.full(m_train // 2, 2)

x_train = np.concatenate((x_train1, x_train2))  # shape (1000, 2)
labels_train = np.concatenate((labels_train1, labels_train2))  # shape (1000,)

# Prepare 2d grid for plotting decision boundary
grid_size = 70
x1 = np.linspace(-6, 8, grid_size)
x2 = np.linspace(-6, 8, grid_size)
x1v, x2v = np.meshgrid(x1, x2)
x1p = x1v.reshape(-1, 1)
x2p = x2v.reshape(-1, 1)
x_test = np.hstack((x1p, x2p))  # shape (10000, 2)

# Classify grid points
classifier = KDEClassification().fit(x_train, labels_train)
labels_pred = classifier.predict(x_test)

for label, color in zip(np.unique(labels_train), ["cornflowerblue", "goldenrod"]):
    mask1 = (labels_train == label)
    plt.scatter(x_train[mask1, 0], x_train[mask1, 1], facecolors="none",
                edgecolors=color, label=f"class {label}")
    mask2 = (labels_pred == label)
    plt.scatter(x1p[mask2, 0], x2p[mask2, 0],
                color=color, marker=".", alpha=0.15)
plt.xlim(-6, 8); plt.ylim(-6, 8);
plt.xlabel("$x_1$", fontsize=11); plt.ylabel("$x_2$", rotation=0, fontsize=11);
plt.legend(); plt.title("Decision boundry determined by KDEClassifier", fontsize=11);

(Source code, png, hires.png, pdf)

Outliers Detection

TODO

Clustering

TODO

Conditional case