The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 65 observations. Starting from the left, the columns are A, and B₁,..., B5, i.e. each row has X and the transposed column vector B¹ (X). 0.00000 -0.04596 0.08497 0.04129 -0.08195 -0.00764 0.22778 -0.04274 0.07868 0.03430 -0.07599 0.00000 1.96117 -0.02092 0.04606 0.00000 -0.04090 0.00000 3.28220 0.00000 0.02263 0.00000 -0.02105 0.00000 0.00000 0.00000 0.00000 4.49485 0.00000 0.00375 0.00000 4.73846 0.00000 0.00000 0.00000 0.00000 You will perform computations using this table and report your results. A) Compute the maximum value of the L₁ norm for vectors of coefficients attained in this table, that is compute maxx ||BL (A)||₁ B) Consider the 2nd breakpoint from the top of the table, namely the breakpoint corresponding to A-0.22778. Compute the L₁ norm for the vector of coefficients at this point in the path, i.e. compute ||ß¹ (0.22778)||1 C) For the same 2nd breakpoint in the table, compute the shrinkage attained at this point in the path, i.e. compute ||3¹ (0.22778)||₁/maxx ||¹(A)||₁. Write this as a percentage between 0 and 100, together with decimals. D) Still considering the same 2nd breakpoint in the table. How many variables are active at this stage?
The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 65 observations. Starting from the left, the columns are A, and B₁,..., B5, i.e. each row has X and the transposed column vector B¹ (X). 0.00000 -0.04596 0.08497 0.04129 -0.08195 -0.00764 0.22778 -0.04274 0.07868 0.03430 -0.07599 0.00000 1.96117 -0.02092 0.04606 0.00000 -0.04090 0.00000 3.28220 0.00000 0.02263 0.00000 -0.02105 0.00000 0.00000 0.00000 0.00000 4.49485 0.00000 0.00375 0.00000 4.73846 0.00000 0.00000 0.00000 0.00000 You will perform computations using this table and report your results. A) Compute the maximum value of the L₁ norm for vectors of coefficients attained in this table, that is compute maxx ||BL (A)||₁ B) Consider the 2nd breakpoint from the top of the table, namely the breakpoint corresponding to A-0.22778. Compute the L₁ norm for the vector of coefficients at this point in the path, i.e. compute ||ß¹ (0.22778)||1 C) For the same 2nd breakpoint in the table, compute the shrinkage attained at this point in the path, i.e. compute ||3¹ (0.22778)||₁/maxx ||¹(A)||₁. Write this as a percentage between 0 and 100, together with decimals. D) Still considering the same 2nd breakpoint in the table. How many variables are active at this stage?
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Transcribed Image Text:The following table contains output from a lasso fit to a linear model with d= 5 variables and n = 65 observations. Starting from the left,
the columns are X, and B₁, ..., B5, i.e. each row has X and the transposed column vector B¹(X).
0.00000
0.00000 -0.04596 0.08497 0.04129 -0.08195 -0.00764
0.22778 -0.04274 0.07868 0.03430 -0.07599 0.00000
1.96117 -0.02092 0.04606 0.00000 -0.04090
3.28220 0.00000 0.02263 0.00000 -0.02105
4.49485 0.00000 0.00375 0.00000 0.00000
4.73846 0.00000 0.00000 0.00000 0.00000
0.00000
0.00000
0.00000
You will perform computations using this table and report your results.
A) Compute the maximum value of the L₁ norm for vectors of coefficients attained in this table, that is compute maxx ||3¹(A)||₁
B) Consider the 2nd breakpoint from the top of the table, namely the breakpoint corresponding to A-0.22778. Compute the L₁ norm for the
vector of coefficients at this point in the path, i.e. compute || (0.22778)||1
C) For the same 2nd breakpoint in the table, compute the shrinkage attained at this point in the path, i.e. compute
||B¹ (0.22778)||₁/max、 ||¹ (A)||₁. Write this as a percentage between 0 and 100, together with decimals.
D) Still considering the same 2nd breakpoint in the table. How many variables are active at this stage?
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