Question

When would you want to use L1 regularization as opposed to L2 regularization

Answer #1

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The main difference between L1 and L2 regularization is that L1 can yield sparse models while L2 doesn't. Sparse model is a great property to have when dealing with high dimensional data, for at least 2 reasons.

- Model compression: increasingly important due to the mobile growth
- Feature selection: it helps to know which features are important and which features are not or redundant.

The difference between L1 and L2 regularization are as follows:

·

L1/Laplace tends to tolerate both large values as well as very small values of coefficients more than L2/Gaussian

·

L1 can yield sparse models while L2 doesn't

·

L1 and L2 regularization prevents overfitting by shrinking on the coefficients

·

L2 (Ridge) shrinks all the coefficient by the same proportions but eliminates none, while L1 (Lasso) can shrink some coefficients to zero, performing variable selection

·

L1 is the first moment norm |x1-x2| that is simply the absolute dıstance between two points where L2 is second moment norm corresponding to Euclidean Distance that is |x1-x2|^2.

·

L2 regularization tends to spread error among all the terms, while L1 is more binary/sparse

Show that if languages L1 and L2 are decidable, then the
intersection of L1 and L2 is also decidable.

Show that if languages L1 and L2 are decidable, then
concatenation of L1 and L2 is also decidable.

Which claim is always true: L1 and L2 are regular languages, L =
L1 - L2, then L
is finite
is regular
is complicated
is infinite

Given two sorted lists, L1 and L2, write a procedure
to compute L1 ∪ L2 using only the basic list operations.

Given two sorted lists, L1 and L2, write a procedure
to compute L1 ∩ L2 using only the basic list operations.

(Formal languages)
Determine if the following statements are true or not:
If L1 and L2 are non-regular languages then is L1 intersection
L2 non regular? (T/F)
If L1 is a non regular language and L2 is a finite language is it
true that L1 union L2 is regular?
Is it true that the union of two regular languages must be
regular?

When would you want to do a between-subjects design as opposed
to a with-in subjects design?

ABC ltd is a circuit board producer and produces two products,
L1 & L2. The company currently uses traditional costing system
for making business decisions. However, recently the company is
considering a move towards the Activity-Based Costing (ABC) system.
As one of the company’s accountant’s you have been asked to prepare
a statement comparing both the costing methods for the next company
board meeting. Your supervisor has given you the following
quarterly data: -
Total Indirect Costs for the quarter:...

Are lines L1 and L2 perpendicular: L1 (-7,1) and (5,-2) L2 (3,7)
and (0,-5) a.) No, the lines are not perpendicular because the
product of their slope equals -1. B.) Yes , the lines are
perpendicular because the product of their slopes does not equal
-1. C.) No, the lines are not perpendicular because the product of
their slopes does not equal -1. D.) Yes, the lines are
perpendicular because the product of their slope equals -1.

Let L1 be the language of the Regular Expression 1(1
+ 0)*.
Let L2 be the language of the Regular Expression 11*
0.
Let L3 be the language of the Regular Expression 1*
0.
Which of the following statements are true?
L2 L1
L2 L3
L1 L2
L3 L2

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