Capter 4 - Training Models Exerc

1 .Which linear regression training algorithm can you use if you have a training set with millions of features?

Stochastic Gradient Descent or Mini-batch Gradient Descent

2. Suppose the features in your training set have very different scales. Which algorithms might suffer from this, and how? What can you do about it ?

If the features in your training set have very differnt scales, the cost function will have the shape of an elongated bowl, so the Gradient Descent algorithms will take a long time to converge. To solve this you should scale the data before training the model. Note that the Normal Equation or SVD approach will work just fine without scaling. Moreover, regularized modes may converge to suboptimal solution if the features are not scaled: since regularization penalized large weights, features with smaller value will tend to be ignored compared to features with large values.

3. Can gradient descent get stuck in a local minimum when training a logistic regression model?

Gradient Descent cannot get stuck in a local minimum when training a Logistic Regression model because the cost functioin convex.

4. Do all gradient descent algorithms lead to the same model, provided you let them run long enough?

If the optimization problem is convex(Such as Linear Regression or Logistic Regression), and assuming the learning rate is not too high, then all gradient Descent algorithms will approach the global optimum and end up producing fairly similar modes. However, unless you gradually reduce the learning rate, Stochastic GD and Mini-batch GD will nerver truly converge; instead, they will keep jumping back and forth around the global optimum. This means that even if you let them run for a very long time, these Gradient Descent algorithms will produce slightly differnt models.

5. Suppose you use batch gradient descent and you plot the validation error at every epoch. If you notice that the validation error consistently goes up, what is likely going on? How can you fix this?

If the validation error consistentlygose up after every epoch, the one possibility is that the learning rate is too hight and the algorithm is diverging. If the training error also goes up, then this clearly the problem and you should reduce the learning rate. However, if training error is not going up, then your model is overfitting the training set and you should stop training.

6. Is it a good idea to stop mini-batch gradient descent immediately when the validation error goes up?

Due to their random nature, neither Stochastic Gradient Descent nor Mini-batch Gradient Descent is guaranteed to make progress at every single training iteration. So if you immediately stop training when the validation error goes up, you may stop much too eraly, before the optimum is reached. A better option is to save the model at regular intervals; then, when it hs not improved for a long time(meaning it will problably never beet the record), you can revert to the best saved model.

7. Which gradient descent algorithm (among those we discussed) will reach the vicinity of the optimal solution the fastest? Which will actually converge? ow can you make the others converge as well?

Stochastic Gradient Descent has the fastest training iteration since it consider only one training instance at one time, so it generally the first to reach the vicinity of golbal optimum(or Mini-batch GD with a very small mini-batch size). However, only Batch Gradient Descent will actually converge, given enough training time.
As mention, Stochastic GD and Mini-batch GD will nounce around the optimum, unless you gradually reduce the learning rate.

8. Suppose you are using polynomial regression. You plot the learning curves and you notice that there is a large gap between the training error and the validation error. What is happening? What are three ways to solve this?

If the validation erro is much higher than the training error, this is likely because your model is overfitting the training set. One way to try to fix this is reduce the polynomial degree: a model with fewer degrees of freedom is less likely to overfit. Another thing you can try is to regularize the model-for example, by adding an l2 penaly(Ridge) or an l1 penalty(Lasso) to the cost function. This will also reduce the degrees of freedom of the model. Lastly, yopu can try to increase the size of the traniing set.

9. Suppose you are using ridge regression and you notice that the training error and the validation error are almost equal and fairly high. Would you say that the model suffers from high bias or high variance? Should you increase the regularization hyperparameter α or reduce it?

If both the training error and the validation error are almost equal and fairly high, the model is likely underfitting the tranining set, which mean it has a high bias. You should try reducing the regularization hyperarameter a.

10. Why would you want to use:

1. Ridge regression instead of plain linear regression (i.e., without any regularization)?
   A model with some regularization typically performs better than without any regularization, so you should generally prefer Ridge Regression over plain Linear Regression.
2. Lasso instead of ridge regression?
   Lasso Regression uses an L1 penalty, which tends to push the weights down to exactly zero. This leads to spares models, where all wights are zero except for the most import weights, this a way to perform feature selection automatically, which is good if you suspect the only a few features actually matter. When you are not sure, you should prefer Ridge Regression.
3. Elastic net instead of lasso regression?
   Elastic Net is generally preferred over Lasso since Lasso may behave erratically in some cases(when several features are strongly correalated or when there are more features that training instances). However, it does add an extra hyperparameter to tune. if you want Lasso without the erratic behavior , you can just use Elasticv Net with an 11_ratio close to 1.

11. Suppose you want to classify pictures as outdoor/indoor and daytime/nighttime. Should you implement two logistic regression classifiers or one softmax regression classifier?

If you want to classify pictures as outdoor/indoor and daytime/nighttime , since these are not exclusive classes(i.e. all for combinations are possible) you should train two Logistic Regression classifiers.