5,045 research outputs found
Kronecker Sum Decompositions of Space-Time Data
In this paper we consider the use of the space vs. time Kronecker product
decomposition in the estimation of covariance matrices for spatio-temporal
data. This decomposition imposes lower dimensional structure on the estimated
covariance matrix, thus reducing the number of samples required for estimation.
To allow a smooth tradeoff between the reduction in the number of parameters
(to reduce estimation variance) and the accuracy of the covariance
approximation (affecting estimation bias), we introduce a diagonally loaded
modification of the sum of kronecker products representation [1]. We derive a
Cramer-Rao bound (CRB) on the minimum attainable mean squared predictor
coefficient estimation error for unbiased estimators of Kronecker structured
covariance matrices. We illustrate the accuracy of the diagonally loaded
Kronecker sum decomposition by applying it to video data of human activity.Comment: 5 pages, 8 figures, accepted to CAMSAP 201
Distral: Robust Multitask Reinforcement Learning
Most deep reinforcement learning algorithms are data inefficient in complex
and rich environments, limiting their applicability to many scenarios. One
direction for improving data efficiency is multitask learning with shared
neural network parameters, where efficiency may be improved through transfer
across related tasks. In practice, however, this is not usually observed,
because gradients from different tasks can interfere negatively, making
learning unstable and sometimes even less data efficient. Another issue is the
different reward schemes between tasks, which can easily lead to one task
dominating the learning of a shared model. We propose a new approach for joint
training of multiple tasks, which we refer to as Distral (Distill & transfer
learning). Instead of sharing parameters between the different workers, we
propose to share a "distilled" policy that captures common behaviour across
tasks. Each worker is trained to solve its own task while constrained to stay
close to the shared policy, while the shared policy is trained by distillation
to be the centroid of all task policies. Both aspects of the learning process
are derived by optimizing a joint objective function. We show that our approach
supports efficient transfer on complex 3D environments, outperforming several
related methods. Moreover, the proposed learning process is more robust and
more stable---attributes that are critical in deep reinforcement learning
Transfer learning through greedy subset selection
We study the binary transfer learning problem, focusing on how to select sources from a large pool and how to combine them to yield a good performance on a target task. In particular, we consider the transfer learning setting where one does not have direct access to the source data, but rather employs the source hypotheses trained from them. Building on the literature on the best subset selection problem, we propose an efficient algorithm that selects relevant source hypotheses and feature dimensions simultaneously. On three computer vision datasets we achieve state-of-the-art results, substantially outperforming transfer learning and popular feature selection baselines in a small-sample setting. Also, we theoretically prove that, under reasonable assumptions on the source hypotheses, our algorithm can learn effectively from few examples
Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learning
We show a Talagrand-type concentration inequality for Multi-Task Learning
(MTL), using which we establish sharp excess risk bounds for MTL in terms of
distribution- and data-dependent versions of the Local Rademacher Complexity
(LRC). We also give a new bound on the LRC for norm regularized as well as
strongly convex hypothesis classes, which applies not only to MTL but also to
the standard i.i.d. setting. Combining both results, one can now easily derive
fast-rate bounds on the excess risk for many prominent MTL methods,
including---as we demonstrate---Schatten-norm, group-norm, and
graph-regularized MTL. The derived bounds reflect a relationship akeen to a
conservation law of asymptotic convergence rates. This very relationship allows
for trading off slower rates w.r.t. the number of tasks for faster rates with
respect to the number of available samples per task, when compared to the rates
obtained via a traditional, global Rademacher analysis.Comment: In this version, some arguments and results (of the previous version)
have been corrected, or modifie
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