16 research outputs found
Less is More: Nystr\"om Computational Regularization
We study Nystr\"om type subsampling approaches to large scale kernel methods,
and prove learning bounds in the statistical learning setting, where random
sampling and high probability estimates are considered. In particular, we prove
that these approaches can achieve optimal learning bounds, provided the
subsampling level is suitably chosen. These results suggest a simple
incremental variant of Nystr\"om Kernel Regularized Least Squares, where the
subsampling level implements a form of computational regularization, in the
sense that it controls at the same time regularization and computations.
Extensive experimental analysis shows that the considered approach achieves
state of the art performances on benchmark large scale datasets.Comment: updated version of NIPS 2015 (oral
Generalization Properties and Implicit Regularization for Multiple Passes SGM
We study the generalization properties of stochastic gradient methods for
learning with convex loss functions and linearly parameterized functions. We
show that, in the absence of penalizations or constraints, the stability and
approximation properties of the algorithm can be controlled by tuning either
the step-size or the number of passes over the data. In this view, these
parameters can be seen to control a form of implicit regularization. Numerical
results complement the theoretical findings.Comment: 26 pages, 4 figures. To appear in ICML 201
Structured Prediction for CRiSP Inverse Kinematics Learning with Misspecified Robot Models
With the recent advances in machine learning, problems that traditionally
would require accurate modeling to be solved analytically can now be
successfully approached with data-driven strategies. Among these, computing the
inverse kinematics of a redundant robot arm poses a significant challenge due
to the non-linear structure of the robot, the hard joint constraints and the
non-invertible kinematics map. Moreover, most learning algorithms consider a
completely data-driven approach, while often useful information on the
structure of the robot is available and should be positively exploited. In this
work, we present a simple, yet effective, approach for learning the inverse
kinematics. We introduce a structured prediction algorithm that combines a
data-driven strategy with the model provided by a forward kinematics function
-- even when this function is misspecified -- to accurately solve the problem.
The proposed approach ensures that predicted joint configurations are well
within the robot's constraints. We also provide statistical guarantees on the
generalization properties of our estimator as well as an empirical evaluation
of its performance on trajectory reconstruction tasks.Comment: Accepted for publication in IEEE Robotics and Automation Letters
(2021) and presentation at IEEE International Conference on Robotics and
Automation (2021) Updated funding informatio
NYTRO: When Subsampling Meets Early Stopping
Early stopping is a well known approach to reduce the time complexity for performing training and model selection of large scale learning machines. On the other hand, memory/space (rather than time) complexity is the main constraint in many applications, and randomized subsampling techniques have been proposed to tackle this issue. In this paper we ask whether early stopping and subsampling ideas can be combined in a fruitful way. We consider the question in a least squares regression setting and propose a form of randomized iterative regularization based on early stopping and subsampling. In this context, we analyze the statistical and computational properties of the proposed method. Theoretical results are complemented and validated by a thorough experimental analysis
A structured prediction approach for robot imitation learning
We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised learning that enables learning models to operate on output spaces with complex structures. Through the lens of structured prediction, we show how robots can learn to imitate trajectories belonging to not only Euclidean spaces but also Riemannian manifolds. Exploiting ideas from information theory, we propose a class of loss functions based on the f-divergence to measure the information loss between the demonstrated and reproduced probabilistic trajectories. Different types of f-divergence will result in different policies, which we call imitation modes. Furthermore, our approach enables the incorporation of spatial and temporal trajectory modulation, which is necessary for robots to be adaptive to the change in working conditions. We benchmark our algorithm against state-of-the-art methods in terms of trajectory reproduction and adaptation. The quantitative evaluation shows that our approach outperforms other algorithms regarding both accuracy and efficiency. We also report real-world experimental results on learning manifold trajectories in a polishing task with a KUKA LWR robot arm, illustrating the effectiveness of our algorithmic framework
A Structured Prediction Approach for Robot Imitation Learning
We propose a structured prediction approach for robot imitation learning from
demonstrations. Among various tools for robot imitation learning, supervised
learning has been observed to have a prominent role. Structured prediction is a
form of supervised learning that enables learning models to operate on output
spaces with complex structures. Through the lens of structured prediction, we
show how robots can learn to imitate trajectories belonging to not only
Euclidean spaces but also Riemannian manifolds. Exploiting ideas from
information theory, we propose a class of loss functions based on the
f-divergence to measure the information loss between the demonstrated and
reproduced probabilistic trajectories. Different types of f-divergence will
result in different policies, which we call imitation modes. Furthermore, our
approach enables the incorporation of spatial and temporal trajectory
modulation, which is necessary for robots to be adaptive to the change in
working conditions. We benchmark our algorithm against state-of-the-art methods
in terms of trajectory reproduction and adaptation. The quantitative evaluation
shows that our approach outperforms other algorithms regarding both accuracy
and efficiency. We also report real-world experimental results on learning
manifold trajectories in a polishing task with a KUKA LWR robot arm,
illustrating the effectiveness of our algorithmic framework
Mapping Regions of Provenance for Italy
In the follow-up of 1999/105/CE Directive on national level, the new map of regions of provenance for forest reproductive materials of Italy is adopted as reference for the national register of forest basic materials. The new map was outlined to match needs linked to the transposition of European legislation to the complexity of the Peninsula’s environment and the national nursery system. The main objective in this technical note is to present the map units in relation to the distribution of main forest species. The map units of ecoregional meaning might facilitate new allocations for forest reproductive materials which are needed to increase genetic diversity. Furthermore, studies on genetic variability of forest species are required to understand the possible interactions between the ecological amplitude of forest species, their actual genetic diversity, and possible adaptation to future climate conditions
Less is more: Nystr\uf6m computational regularization
We study Nystr\uf6m type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling and high probability estimates are considered. In particular, we prove that these approaches can achieve optimal learning bounds, provided the subsampling level is suitably chosen. These results suggest a simple incremental variant of Nystr\uf6m Kernel Regularized Least Squares, where the subsampling level implements a form of computational regularization, in the sense that it controls at the same time regularization and computations. Extensive experimental analysis shows that the considered approach achieves state of the art performances on benchmark large scale datasets