def minimizeStochastic(targetFn, gradientFn, x, y, theta0, alpha0=0.01): data = zip(x, y) theta = theta0 alpha = alpha0 minTheta, minValue = None, float("inf") iterationsWithNoMovement = 0 while iterationsWithNoMovement < 100: value = sum([targetFn(xi, yi, theta) for xi, yi in data]) if value < minValue: minTheta, minValue = theta, value iterationsWithNoMovement = 0 alpha = alpha0 else: iterationsWithNoMovement += 1 alpha *= 0.9 for xi, yi in inRandomOrder(x, y): gradientI = gradientFn(xi, yi, theta) theta = vectorSubtract(theta, scalarMultiply(alpha, gradientI)) return minTheta
def removeProjectionsFromVector(v, w): return vectorSubtract(v, project(v, w))