I'm currently learning multilinear regression and I'm stuck on this question that wants me to define a function that will "Minimize the average loss calculated from using different theta vectors, and estimate the optimal theta for the model".
from scipy.optimize import minimize
def l1(y, y_hat):
return np.abs(y - y_hat)
def l2(y, y_hat):
return (y - y_hat)**2
def minimize_average_loss(loss_function, model, X, y):
"""
Minimize the average loss calculated from using different theta vectors, and
estimate the optimal theta for the model.
Parameters
-----------
loss_function: either the squared or absolute loss functions defined above
model: the model (as defined in Question 1b)
X: a 2D dataframe of numeric features (one-hot encoded)
y: a 1D vector of tip amounts
Returns
-----------
The estimate for the optimal theta vector that minimizes our loss
"""
## Notes on the following function call which you need to finish:
#
# 0. The first '...' should be replaced with the average loss evaluated on
# the data X, y using the model and appropriate loss function.
# 1. x0 are the initial values for THETA. Yes, this is confusing
# but optimization people like x to be the thing they are
# optimizing. Replace the second '...' with an initial value for theta,
# and remember that theta is now a vector. DO NOT hard-code the length of x0;
# it should depend on the number of features in X.
# 2. Your answer will be very similar to your answer to question 2 from lab 7.
...
return minimize(lambda theta: ..., x0=...)['x']
# Notice above that we extract the 'x' entry in the dictionary returned by `minimize`.
# This entry corresponds to the optimal theta estimated by the function.
minimize_average_loss(l2, linear_model, one_hot_X, tips)
For context, my linear model is defined as this:
def linear_model(thetas, X):
"""
Return the linear combination of thetas and features as defined above.
Parameters
-----------
thetas: a 1D vector representing the parameters of our model ([theta1, theta2, ...])
X: a 2D dataframe of numeric features
Returns
-----------
A 1D vector representing the linear combination of thetas and features as defined above.
"""
return np.dot(X, thetas)
Currently, I have:
def minimize_average_loss(loss_function, model, X, y):
return minimize(lambda theta: loss_function(y, linear_model(theta, X)), x0= [0.0, 0.0])['x']
Does anyone know how I'm supposed to do this? Thanks!
