Annealed sparsity via adaptive and dynamic shrinking

A system for acquiring data from an input signal using multitask regression, comprising:

• a memory to receive the input signal, the input signal including data that includes a plurality of features;
• a processor configured to:
• determine at least two computational tasks to analyze within the input signal;
• regularize all of the at least two tasks using shared adaptive weights;
• perform a multitask regression on the input signal to create a solution path for all of the at least two tasks, wherein the processor performs the multitask regression by:
• concurrently updating a model coefficient and a regularization weight together under an equality norm constraint until convergence is reached to produce a sparse model in the solution path;
• concurrently updating the model coefficient and regularization weight together under an updated equality norm constraint that has a greater l1-penalty than the previous equality norm constraint until convergence is reached to produce another sparse model in the solution path;
• and
• gradually strengthening a global magnitude of the l1-penalty by adjusting the equality norm constraint on the regularization weight by annealing to improve the convergence and reduce a sensitivity on initial conditions,
• wherein the shared adaptive weights w=[w1, w2, . . . , wD]T are used for the regularizing over all K tasks, as
• min
• w
• ,
• B
• ⁢
• ∑
• K
• k
• =
• 1
• ⁢
• (
• 
• X
• k
• ⁢
• β
• k
• -
• y
• k
• 
• 2
• 2
• +
• 
• w
• -
• γ
• ⊙
• β
• k
• 
• )
• ,
• s.t. Σdwd=ω, wd≥0, wherein βk∈D×1 represents the model coefficient for a kth task for k=1, 2, . . . , K, and B=[β1, β2, . . . , βk];
• select a sparse model from the solution path;
• and
• construct an image using the sparse model;
• and
• a display for displaying the constructed image.

A non-transitory computer-readable storage medium including a computer-readable program for assigning labels to an object, wherein the computer-readable program when executed on a computer causes the computer to perform the steps of:

• receiving, into a memory, the input signal, the input signal including data that includes a plurality of features;
• determining at least two computational tasks to analyze within the input signal;
• regularizing all of the at least two tasks using shared adaptive weights;
• performing, using a processor, a multitask regression on the input signal to create a solution path for all of the at least two tasks, wherein the multitask regression includes:
• updating a model coefficient and a regularization weight together under an equality norm constraint until convergence is reached to produce a sparse model in the solution path;
• updating the model coefficient and regularization weight together under an updated equality norm constraint that has a greater l1-penalty than the previous equality norm constraint until convergence is reached to produce another sparse model in the solution path;
• and
• gradually strengthening a global magnitude of the l1-penalty by adjusting the equality norm constraint on the regularization weight by annealing to improve the convergence and reduce a sensitivity on initial conditions,
• wherein the shared adaptive weights w=[w1, w2, . . . , wD]T are used for the regularizing over all K tasks, as
• min
• w
• ,
• B
• ⁢
• ∑
• K
• k
• =
• 1
• ⁢
• (
• 
• X
• k
• ⁢
• β
• k
• -
• y
• k
• 
• 2
• 2
• +
• 
• w
• -
• γ
• ⊙
• β
• k
• 
• )
• ,
• s.t. Σdwd=ω, wd≥0, wherein βk∈D×1 represents the model coefficient for a kth task for k=1, 2, . . . , K, and B=[β1, β2, . . . , βk];
• selecting a sparse model from the solution path;
• constructing an image using the sparse model;
• and
• displaying the image on a display.