This article walks through linear regression by visualizing scattered data points, defining the line y = ax + b, deriving the mean‑squared‑error cost function, computing its gradients with the chain rule, and implementing gradient descent in Python to find the optimal parameters.
This article provides a comprehensive overview of linear regression, covering its definition, purpose, algorithmic steps, data preparation, feature scaling, parameter initialization, cost function computation, gradient descent optimization, visualization, normal equation solution, and regularization, accompanied by detailed Python code examples.
This article explains the intuition behind gradient descent, describing how the cost function surface is visualized, how the learning rate controls step size, and why updating parameters in the correct order is essential for converging to the optimal solution.
The article examines Druid’s cost‑based balance strategy introduced in version 0.12.0, explaining how the ‘cost’ algorithm randomly selects a segment, computes a pairwise exponential cost for each Historical node using a closed‑form integral, and moves the segment to the node with minimal cost to improve query parallelism.
