System and methods for finding hidden topics of documents and preference ranking documents
View Patent ↗Systems and methods are disclosed to perform preference learning on a set of documents includes receiving raw input features from the set of documents stored on a data storage device; generating polynomial combinations from the raw input features; generating one or more parameters; applying the parameters to one or more classifiers to generate outputs; determining a loss function and parameter gradients and updating parameters determining one or more sparse regularizing terms and updating the parameters; and expressing that one document is preferred over another in a search query and retrieving one or more documents responsive to the search query.
1. A method to perform preference learning on a set of documents, the method comprising:
receiving raw input features from the set of documents stored on a data storage device;
generating polynomial combinations from the raw input features;
generating one or more parameters W;
applying W to one or more classifiers to generate outputs;
determining a loss function and parameter gradients and updating W;
determining one or more sparse regularizing terms and updating W;
expressing that one document is preferred over another in a search query and retrieving one or more documents responsive to the search query; and
summing over all tuples (q,d + ,d − ) in R:
W
*
=
argmin
W
1
R
∑
(
q
,
d
+
,
d
-
)
∈
R
L
W
(
q
,
d
+
,
d
-
)
,
where R is a set of tuples,
q is a query,
d + is a preferred document,
d − is an unprefereed document, and
L w is a loss for W.
2. The method of claim 1 , comprising constraining W to be a plurality of sparse matrix zero entries for pairs of words irrelevant to the preference learning.
3. The method of claim 2 , comprising imposing an entry-wise l 1 regularization on W.
4. The method of claim 1 , comprising enforcing an l 1 regularization with mini-batch shrinking for every predetermined iterations in a stochastic gradient descent.
5. The method of claim 1 , comprising refitting the parameters to improve a preference prediction while keeping a learned sparsity pattern.
6. The method of claim 1 , comprising performing a stochastic (sub)gradient descent (SGD) with an online learning framework.
7. The method of claim 1 , comprising applying a learning rate η t for a t th iteration, a decaying learning rate is used with η t =C/√{square root over (t)}, where C is a pre-defined constant as an initial learning rate and t is an iteration count.
8. The method of claim 1 , comprising performing Stochastic Subgradient Descent (SGD) by:
randomly selecting a tuple (q,d+,d −)εR;
determining a subgradient of L W t−1 (q,d + ,d − ) with respect to W:∇L W t−1 (q,d 30 ,d − ); and
updating W t =W t−1 −η t ∇L W t−1 (q,d +,d − )
where
∇
L
W
(
q
,
d
+
,
d
-
)
=
{
-
q
(
d
+
-
d
-
)
T
if
q
T
W
(
d
+
-
d
-
)
<
1
0
otherwise
.
R is a set of tuples,
q is a query,
d + is a preferred document,
d − is an unprefereed document,
L w is a loss for W,
t is an iteration count, and
η t is a learning rate for a t th iteration.
9. The method of claim 1 , comprising adding an entry-wise l 1 norm to W as a regularization term to the loss function and optimized as the following objective function:
W
*
=
arg
min
W
1
R
∑
(
q
,
d
+
,
d
-
)
∈
R
L
W
(
q
,
d
+
,
d
-
)
+
λ
W
1
,
where ∥W∥ 1 =Σ i,j=1 D |W ij | is an entry-wise l 1 norm of W and λ is a regularization parameter which controls a sparsity level (number of nonzero entries) of W,
R is a set of tuples,
q is a query,
d + is a preferred document,
d − is an unprefereed document,
L w is a loss for W, and
D is a directory size.
10. The method of claim 1 , comprising:
solving the following optimization problem:
W
^
t
=
arg
min
W
1
2
W
-
W
t
F
2
+
λη
t
W
1
,
using Ŵ t as a starting point for the next iteration,
where ∥W∥ 1 =Σ i,j=1 D |W ij | is an entry-wise l 1 norm of W and λ is a regularization parameter which controls a sparsity level (number of nonzero entries) of W,
∥ ∥ F is a matrix Frobenius norm,
t is an iteration count, and
η t is a learning rate for a t th iteration.
11. The method of claim 1 , comprising shrinking W ij t with an absolute value less than λη t to zero and generating a sparse W matrix, where
λis a regularization parameter which controls a sparsity level (number of nonzero entries) of W,
t is an iteration count, and
η t is a learning rate for a t th iteration.
12. The method of claim 1 , comprising shrinking W wherein a cumulative regularization parameter is used for solving:
W
T
=
arg
min
W
1
2
W
-
W
0
F
2
+
λ
∑
t
=
1
T
η
t
W
1
,
where ∥W∥ 1 =Σ i,j=1 D |W ij | is an entry-wise l 1 norm of W and λ is a regularization parameter which controls a sparsity level (number of nonzero entries) of W,
∥ ∥ F is a matrix Frobenius norm,
t is an iteration count,
T is the number of iteration cycles, and
η t is a learning rate for a t th iteration.
13. The method of claim 1 , comprising performing shrinkage at every iteration to generate a sparse W .
14. The method of claim 1 , comprising:
initializing with W 0 εR D×D , T, learning rate sequence {η t };
randomly draw a tuple (q,d + ,d − )εR;
determining a subgradient of L W t−1 (q,d + ,d − ) with respect to W:∇L W t−1 (q,d + ,d − );
updating W t =W t−1 −η t ∇L W t−1 (q,d + ,d − ); and
if (t mod T=0) determining
W
T
=
arg
min
W
1
2
W
-
W
0
F
2
+
λ
∑
t
=
1
T
η
t
W
1
,
where ∥W∥ 1 =Σ i,j=1 D |W ij | is an entry-wise l 1 norm of W and λ is a regularization parameter which controls a sparsity level (number of nonzero entries) of W,
∥ ∥ F is a matrix Frobenius norm,
R is a set of tuples,
q is a query,
d + is a preferred document,
d − is an unprefereed document,
L w is a loss for W, and
D is a directory size,
t is an iteration count,
T is the number of iteration cycles, and
η t is a learning rate for a t th iteration.
15. A computer to perform preference learning on a set of documents, the computer comprising:
means for receiving raw input features from the set of documents stored on a data storage device;
means for generating polynomial combinations from the raw input features;
means for generating one or more parameters W;
means for applying W to one or more classifiers to generate outputs;
means for determining a loss function and parameter gradients and updating W;
means for determining one or more sparse regularizing terms and updating W;
means for expressing that one document is preferred over another in a search query and retrieving one or more documents responsive to the search query; and
means for summing over all tuples (q,d + ,d − ) in R:
W
*
=
argmin
W
1
R
∑
(
q
,
d
+
,
d
-
)
∈
R
L
W
(
q
,
d
+
,
d
-
)
,
where R is a set of tuples,
q is a query,
d + is a preferred document,
d − is an unprefereed document, and
L w is a loss for W.
16. The computer of claim 15 , comprising means for constraining W to be a plurality of sparse matrix zero entries for pairs of words irrelevant to the preference learning.
17. The computer of claim 16 , comprising means for imposing an entry-wise l 1 regularization on W.
18. The computer of claim 15 , comprising means for enforcing an l 1 regularization with mini-batch shrinking for every predetermined iterations in a stochastic gradient descent.
19. The computer of claim 15 , comprising means for refitting the parameters to improve a preference prediction while keeping a learned sparsity pattern.