Nadar Logistic 🔥 Fast

: When linear logistic regression fails your validation set, and your data has few features—let the Nadaraya–Watson estimator draw you a smoother, more truthful curve.

What happens when the relationship is curved, clustered, or changes direction? Enter —a non-parametric, kernel-based method that lets the data "speak for itself." What is the Nadaraya–Watson Estimator? Originally designed for regression (continuous outcomes), the Nadaraya–Watson (NW) estimator predicts a value at a point ( x ) by calculating a weighted average of all observed outcomes. The weights are determined by a kernel (e.g., Gaussian, Epanechnikov), which gives high weight to training points near ( x ) and low weight to distant points. nadar logistic

[ \haty(x) = \frac\sum_i=1^n K\left(\fracx - x_ih\right) y_i\sum_i=1^n K\left(\fracx - x_ih\right) ] : When linear logistic regression fails your validation

preds = [] for x in x_test: weights = kernel_func((x - X_train) / h) weights = weights.flatten() p = np.sum(weights * y_train) / np.sum(weights) preds.append(p) return np.array(preds) Originally designed for regression (continuous outcomes)

Where ( K ) is the kernel function and ( h ) is the (smoothing parameter). Extending to Logistic Regression (Binary Outcomes) For binary outcomes (0/1), taking a simple weighted average would give a probability, but that probability would be unbounded and lack the formal link function of logistic regression. The Nadaraya–Watson approach adapts by estimating the conditional probability ( P(Y=1 | X=x) ) directly as a kernel-weighted average of the binary labels:

[ \hatp(x) = \frac\sum_i=1^n K\left(\fracx - x_ih\right) y_i\sum_i=1^n K\left(\fracx - x_ih\right) ]

In the world of binary classification (Yes/No, Churn/Stay, Sick/Healthy), Logistic Regression is the undisputed workhorse. However, standard logistic regression has a critical flaw: it assumes the log-odds of the outcome change linearly with the input features.