Part B local code added

src/partA.py

@@ -223,9 +223,9 @@ if __name__ == "__main__":
     - estimate Gaussian parameters (MLE) per class
     - plot 3D pdf surfaces
     """
-    df = load_csv(dataset1, header=None)
+    df1 = load_csv(dataset1, header=None)
 
-    X, y, classes = split_dataset_by_class(df)
+    X, y, classes = split_dataset_by_class(df1)
     params = estimate_gaussians_mle(classes)
 
     # Optional parameters printing

src/partB.py

@@ -0,0 +1,324 @@
+# ------------------------------------------------------------
+# Part B - Parzen Window Density Estimation (1D)
+# Pattern Recognition – Semester Assignment
+#
+# Author:
+#   Christos Choutouridis (ΑΕΜ 8997)
+#   cchoutou@ece.auth.gr
+#
+# Description:
+#   This module implements Part B of the assignment:
+#   - 1D Parzen window density estimation using uniform and
+#     Gaussian kernels
+#   - Computation of predicted likelihood for varying bandwidth h
+#   - Comparison with the true N(1, 4) distribution
+#   - MSE analysis and optimal bandwidth selection
+#
+# ------------------------------------------------------------
+
+import sys
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from typing import Sequence
+from toolbox import load_csv, dataset2
+
+
+# --------------------------------------------------
+# Optional: D-dimensional Bishop-style kernels (not used in Part B)
+# --------------------------------------------------
+def kernel_hypercube(u: np.ndarray) -> float:
+    """
+    D-dimensional uniform kernel (hypercube).
+
+    Bishop eq. (2.247):
+        k(u) = 1 if |u_i| <= 1/2 for all i, else 0
+
+    In 1D this reduces to:
+        k(u) = 1 if |u| <= 1/2 else 0
+
+    This kernel integrates to 1:
+        ∫_{-1/2}^{1/2} 1 du = 1
+    """
+    return float(np.all(np.abs(u) <= 0.5))
+
+
+def kernel_gaussian(u: np.ndarray) -> float:
+    """
+    D-dimensional Gaussian kernel.
+
+    k(u) = (2π)^(-D/2) * exp(-||u||^2 / 2)
+
+    Integral over R^D is 1.
+    """
+    d = u.shape[0]
+    norm_const = 1.0 / ((2.0 * np.pi) ** (d / 2.0))
+    return float(norm_const * np.exp(-0.5 * np.dot(u, u)))
+
+
+# --------------------------------------------------
+# 1D Parzen kernels (used in this Part)
+# --------------------------------------------------
+def parzen_kernel_uniform(u: np.ndarray) -> np.ndarray:
+    """
+    1D uniform Parzen kernel (box).
+
+    Bishop-style in 1D:
+        k(u) = 1 if |u| <= 1/2
+             = 0 otherwise
+
+    Integral:
+        ∫_{-1/2}^{1/2} 1 du = 1
+
+    Parameters
+    ----------
+    u : ndarray
+        Array of values where the kernel is evaluated.
+
+    Returns
+    -------
+    values : ndarray
+        Kernel values at u.
+    """
+    return (np.abs(u) <= 0.5).astype(float)
+
+
+def parzen_kernel_gaussian(u: np.ndarray) -> np.ndarray:
+    """
+    1D Gaussian kernel with mean 0, variance 1.
+
+    k(u) = (1 / sqrt(2π)) * exp(-u^2 / 2)
+
+    Integral over R is 1.
+
+    Parameters
+    ----------
+    u : ndarray
+
+    Returns
+    -------
+    values : ndarray
+    """
+    return (1.0 / np.sqrt(2.0 * np.pi)) * np.exp(-0.5 * (u ** 2))
+
+
+# --------------------------------------------------
+# Parzen estimator (1D, point-wise)
+# --------------------------------------------------
+def parzen_estimate_1d(x_eval: float, data: np.ndarray, h: float, kernel_fn) -> float:
+    """
+    Parzen window density estimate in 1D, for a single point x_eval.
+
+    Implements:
+        p_hat(x_eval) = (1 / (N h)) * sum_n k((x_eval - x_n) / h)
+
+    Parameters
+    ----------
+    x_eval : float
+        Point where the density is estimated.
+    data : ndarray, shape (N,)
+        1D data samples.
+    h : float
+        Bandwidth (window width).
+    kernel_fn : callable
+        Kernel function K(u), applied elementwise on u.
+
+    Returns
+    -------
+    f_hat : float
+        Estimated pdf value at x_eval.
+    """
+    N = data.shape[0]
+    u = (x_eval - data) / h
+    return float(np.sum(kernel_fn(u)) / (N * h))
+
+
+def evaluate_parzen(data: np.ndarray, h: float, kernel_fn) -> np.ndarray:
+    """
+    Evaluates the Parzen estimate at each sample in 'data' itself.
+
+    For each x_i in data:
+        p_hat(x_i) = (1 / (N h)) * sum_n k((x_i - x_n) / h)
+
+    Parameters
+    ----------
+    data : ndarray, shape (N,)
+        1D data samples.
+    h : float
+        Bandwidth.
+    kernel_fn : callable
+        Kernel function K(u).
+
+    Returns
+    -------
+    estimates : ndarray, shape (N,)
+        Estimated pdf values at each data point.
+    """
+    N = data.shape[0]
+    estimates = np.zeros(N, dtype=float)
+
+    for i in range(N):
+        estimates[i] = parzen_estimate_1d(data[i], data, h, kernel_fn)
+
+    return estimates
+
+
+# --------------------------------------------------
+# True pdf and error
+# --------------------------------------------------
+def true_normal_pdf_1d(x: np.ndarray, mu: float, var: float) -> np.ndarray:
+    """
+    True normal pdf N(mu, var) at points x (array).
+
+    Parameters
+    ----------
+    x : ndarray
+        Points where the pdf is evaluated.
+    mu : float
+        Mean
+    var : float
+        Variance
+
+    Returns
+    -------
+    pdf : ndarray
+        The normal pdf N(mu, var)
+    """
+    sigma = np.sqrt(var)
+    coef = 1.0 / (np.sqrt(2.0 * np.pi) * sigma)
+    z = (x - mu) / sigma
+    return coef * np.exp(-0.5 * z * z)
+
+
+def mse(y_true: np.ndarray, y_pred: np.ndarray) -> float:
+    """
+    Mean squared error between two arrays.
+
+    Parameters
+    ----------
+    y_true : ndarray
+    y_pred : ndarray
+
+    Returns
+    -------
+    err : float
+        Mean squared error.
+    """
+    return float(np.mean((y_true - y_pred) ** 2))
+
+
+def scan_bandwidths_parzen(
+    data: np.ndarray, h_values: Sequence[float], kernel_fn, mu_true: float = 1.0, var_true: float = 4.0
+) -> np.ndarray:
+    """
+    For each h in h_values, computes:
+
+    - estimated pdf via Parzen (predicted likelihood)
+    - true pdf via N(mu_true, var_true) (true likelihood)
+    - MSE between them
+
+    Parameters
+    ----------
+    data : ndarray, shape (N,)
+        1D data samples.
+    h_values : sequence of float
+        Bandwidth values to test.
+    kernel_fn : callable
+        Kernel function K(u).
+    mu_true : float
+        True mean, default to 1.0.
+    var_true : float
+        True variance, default to 4.0.
+
+    Returns
+    -------
+    errors : ndarray, shape (len(h_values),)
+        MSE between estimated and true pdf as array of len(h_values)
+    """
+    true_values = true_normal_pdf_1d(data, mu=mu_true, var=var_true)
+    errors_list = []
+
+    for h in h_values:
+        est_values = evaluate_parzen(data, h, kernel_fn)
+        err = mse(true_values, est_values)
+        errors_list.append(err)
+
+    return np.array(errors_list, dtype=float)
+
+
+# --------------------------------------------------
+# Plotting helpers
+# --------------------------------------------------
+def plot_h_vs_error(h_values: np.ndarray, errors: np.ndarray, title: str) -> None:
+    """
+    Simple plot of bandwidth vs error.
+
+    Parameters
+    ----------
+    h_values : ndarray
+    errors : ndarray
+    title : str
+    """
+    plt.figure(figsize=(8, 5))
+    plt.plot(h_values, errors, marker='o')
+    plt.xlabel("h")
+    plt.ylabel("MSE")
+    plt.title(title)
+    plt.grid(True)
+    plt.show()
+
+
+def plot_histogram_with_pdf(
+    data: np.ndarray, mu_true: float = 1.0, var_true: float = 4.0, bins: int = 30
+) -> None:
+    """
+    Plots a histogram of the data and overlays the true N(mu_true, var_true) pdf.
+    """
+    plt.figure(figsize=(8, 5))
+
+    plt.hist(data, bins=bins, density=True, alpha=0.5, label="Data histogram")
+
+    x_min, x_max = np.min(data), np.max(data)
+    x_plot = np.linspace(x_min, x_max, 200)
+    pdf_true = true_normal_pdf_1d(x_plot, mu=mu_true, var=var_true)
+
+    plt.plot(x_plot, pdf_true, label=f"True N({mu_true}, {var_true}) pdf")
+    plt.xlabel("x")
+    plt.ylabel("Density")
+    plt.title("Dataset2 histogram vs true N({mu_true}, {var_true}) pdf")
+    plt.legend()
+    plt.grid(True)
+    plt.show()
+
+
+# --------------------------------------------------
+# Part B: main runner
+# --------------------------------------------------
+if __name__ == "__main__":
+    # Load dataset2 (from GitHub via toolbox)
+    df2 = load_csv(dataset2, header=None)
+    data2 = df2.iloc[:, 0].values
+
+    mu = float(sys.argv[1]) if len(sys.argv) > 1 else 1.0
+    var = float(sys.argv[2]) if len(sys.argv) > 2 else 4.0
+
+    # Optional: histogram + true pdf
+    plot_histogram_with_pdf(data2, mu_true=mu, var_true=var, bins=30)
+
+    # Range of h: [0.1, 10] with step 0.1
+    h_values = np.arange(0.1, 10.1, 0.1)
+
+    # Uniform kernel (parzen)
+    errors_uniform = scan_bandwidths_parzen(data2, h_values, parzen_kernel_uniform, mu_true=mu, var_true=var)
+    best_h_uniform = h_values[np.argmin(errors_uniform)]
+
+    # Gaussian kernel
+    errors_gaussian = scan_bandwidths_parzen(data2, h_values, parzen_kernel_gaussian, mu_true=mu, var_true=var)
+    best_h_gaussian = h_values[np.argmin(errors_gaussian)]
+
+    print("Best h (uniform):", best_h_uniform, " with error: ", errors_uniform[np.argmin(errors_uniform)])
+    print("Best h (gaussian):", best_h_gaussian, " with error: ", errors_gaussian[np.argmin(errors_gaussian)])
+
+    plot_h_vs_error(h_values, errors_uniform, "Uniform kernel: h vs MSE")
+    plot_h_vs_error(h_values, errors_gaussian, "Gaussian kernel: h vs MSE")

src/toolbox.py

@@ -1,6 +1,10 @@
-# -----------------------------
+# ------------------------------------------------------------
-# Toolbox
+# Common tools for the entire assignment
-# -----------------------------
+#
+# Author:
+#   Christos Choutouridis (ΑΕΜ 8997)
+#   cchoutou@ece.auth.gr
+# ------------------------------------------------------------
 
 import pandas as pd
 
@@ -8,10 +12,12 @@ import pandas as pd
 def github_raw(user, repo, branch, path):
     return f"https://raw.githubusercontent.com/{user}/{repo}/{branch}/{path}"
 
-dataset1 = (github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/dataset1.csv"))
+
-dataset2 = (github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/dataset2.csv"))
+dataset1 = github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/dataset1.csv")
-dataset3 = (github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/dataset3.csv"))
+dataset2 = github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/dataset2.csv")
-testset = (github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/testset.csv"))
+dataset3 = github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/dataset3.csv")
+testset  = github_raw("hoo2", "PR-Assignment2025_26", "master", "datasets/testset.csv")
+
 
 def load_csv(path, header=None):
     """