421 research outputs found
Learning Output Kernels for Multi-Task Problems
Simultaneously solving multiple related learning tasks is beneficial under a
variety of circumstances, but the prior knowledge necessary to correctly model
task relationships is rarely available in practice. In this paper, we develop a
novel kernel-based multi-task learning technique that automatically reveals
structural inter-task relationships. Building over the framework of output
kernel learning (OKL), we introduce a method that jointly learns multiple
functions and a low-rank multi-task kernel by solving a non-convex
regularization problem. Optimization is carried out via a block coordinate
descent strategy, where each subproblem is solved using suitable conjugate
gradient (CG) type iterative methods for linear operator equations. The
effectiveness of the proposed approach is demonstrated on pharmacological and
collaborative filtering data
Individualized Rank Aggregation using Nuclear Norm Regularization
In recent years rank aggregation has received significant attention from the
machine learning community. The goal of such a problem is to combine the
(partially revealed) preferences over objects of a large population into a
single, relatively consistent ordering of those objects. However, in many
cases, we might not want a single ranking and instead opt for individual
rankings. We study a version of the problem known as collaborative ranking. In
this problem we assume that individual users provide us with pairwise
preferences (for example purchasing one item over another). From those
preferences we wish to obtain rankings on items that the users have not had an
opportunity to explore. The results here have a very interesting connection to
the standard matrix completion problem. We provide a theoretical justification
for a nuclear norm regularized optimization procedure, and provide
high-dimensional scaling results that show how the error in estimating user
preferences behaves as the number of observations increase
Scalable Algorithms for Tractable Schatten Quasi-Norm Minimization
The Schatten-p quasi-norm is usually used to replace the standard
nuclear norm in order to approximate the rank function more accurately.
However, existing Schatten-p quasi-norm minimization algorithms involve
singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each
iteration, and thus may become very slow and impractical for large-scale
problems. In this paper, we first define two tractable Schatten quasi-norms,
i.e., the Frobenius/nuclear hybrid and bi-nuclear quasi-norms, and then prove
that they are in essence the Schatten-2/3 and 1/2 quasi-norms, respectively,
which lead to the design of very efficient algorithms that only need to update
two much smaller factor matrices. We also design two efficient proximal
alternating linearized minimization algorithms for solving representative
matrix completion problems. Finally, we provide the global convergence and
performance guarantees for our algorithms, which have better convergence
properties than existing algorithms. Experimental results on synthetic and
real-world data show that our algorithms are more accurate than the
state-of-the-art methods, and are orders of magnitude faster.Comment: 16 pages, 5 figures, Appears in Proceedings of the 30th AAAI
Conference on Artificial Intelligence (AAAI), Phoenix, Arizona, USA, pp.
2016--2022, 201
Data augmentation for recommender system: A semi-supervised approach using maximum margin matrix factorization
Collaborative filtering (CF) has become a popular method for developing
recommender systems (RS) where ratings of a user for new items is predicted
based on her past preferences and available preference information of other
users. Despite the popularity of CF-based methods, their performance is often
greatly limited by the sparsity of observed entries. In this study, we explore
the data augmentation and refinement aspects of Maximum Margin Matrix
Factorization (MMMF), a widely accepted CF technique for the rating
predictions, which have not been investigated before. We exploit the inherent
characteristics of CF algorithms to assess the confidence level of individual
ratings and propose a semi-supervised approach for rating augmentation based on
self-training. We hypothesize that any CF algorithm's predictions with low
confidence are due to some deficiency in the training data and hence, the
performance of the algorithm can be improved by adopting a systematic data
augmentation strategy. We iteratively use some of the ratings predicted with
high confidence to augment the training data and remove low-confidence entries
through a refinement process. By repeating this process, the system learns to
improve prediction accuracy. Our method is experimentally evaluated on several
state-of-the-art CF algorithms and leads to informative rating augmentation,
improving the performance of the baseline approaches.Comment: 20 page
- …