533 research outputs found
A Convex Feature Learning Formulation for Latent Task Structure Discovery
This paper considers the multi-task learning problem and in the setting where
some relevant features could be shared across few related tasks. Most of the
existing methods assume the extent to which the given tasks are related or
share a common feature space to be known apriori. In real-world applications
however, it is desirable to automatically discover the groups of related tasks
that share a feature space. In this paper we aim at searching the exponentially
large space of all possible groups of tasks that may share a feature space. The
main contribution is a convex formulation that employs a graph-based
regularizer and simultaneously discovers few groups of related tasks, having
close-by task parameters, as well as the feature space shared within each
group. The regularizer encodes an important structure among the groups of tasks
leading to an efficient algorithm for solving it: if there is no feature space
under which a group of tasks has close-by task parameters, then there does not
exist such a feature space for any of its supersets. An efficient active set
algorithm that exploits this simplification and performs a clever search in the
exponentially large space is presented. The algorithm is guaranteed to solve
the proposed formulation (within some precision) in a time polynomial in the
number of groups of related tasks discovered. Empirical results on benchmark
datasets show that the proposed formulation achieves good generalization and
outperforms state-of-the-art multi-task learning algorithms in some cases.Comment: ICML201
Transductive Ranking on Graphs
In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a real-valued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function in a transductive, graph-based setting, where the object space is finite and is represented as a graph in which vertices correspond to objects and edges encode similarities between objects. Building on recent developments in regularization theory for graphs and corresponding Laplacian-based learning methods, we develop an algorithmic framework for learning ranking functions on graphs. We derive generalization bounds for our algorithms in transductive models similar to those used to study other transductive learning problems, and give experimental evidence of the potential benefits of our framework
Learning Models over Relational Data using Sparse Tensors and Functional Dependencies
Integrated solutions for analytics over relational databases are of great
practical importance as they avoid the costly repeated loop data scientists
have to deal with on a daily basis: select features from data residing in
relational databases using feature extraction queries involving joins,
projections, and aggregations; export the training dataset defined by such
queries; convert this dataset into the format of an external learning tool; and
train the desired model using this tool. These integrated solutions are also a
fertile ground of theoretically fundamental and challenging problems at the
intersection of relational and statistical data models.
This article introduces a unified framework for training and evaluating a
class of statistical learning models over relational databases. This class
includes ridge linear regression, polynomial regression, factorization
machines, and principal component analysis. We show that, by synergizing key
tools from database theory such as schema information, query structure,
functional dependencies, recent advances in query evaluation algorithms, and
from linear algebra such as tensor and matrix operations, one can formulate
relational analytics problems and design efficient (query and data)
structure-aware algorithms to solve them.
This theoretical development informed the design and implementation of the
AC/DC system for structure-aware learning. We benchmark the performance of
AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting
and advertisement planning applications, AC/DC can learn polynomial regression
models and factorization machines with at least the same accuracy as its
competitors and up to three orders of magnitude faster than its competitors
whenever they do not run out of memory, exceed 24-hour timeout, or encounter
internal design limitations.Comment: 61 pages, 9 figures, 2 table
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