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)
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: nadar logistic
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. preds = [] for x in x_test: weights
[ \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) ] However, standard logistic regression has a critical flaw: