1,720,982 research outputs found
Less is more: Nyström computational regularization
No full textWe study Nyström 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 Nyström kernel ridge regression, where the subsampling level 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
Generalization properties and implicit regularization for multiple passes SGM
No full textWe 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
Incremental semiparametric inverse dynamics learning
No full textThis paper presents a novel approach for incremental semiparametric inverse dynamics learning. In particular, we consider the mixture of two approaches: Parametric modeling based on rigid body dynamics equations and nonparametric modeling based on incremental kernel methods, with no prior information on the mechanical properties of the system. The result is an incremental semiparametric approach, leveraging the advantages of both the parametric and nonparametric models. We validate the proposed technique learning the dynamics of one arm of the iCub humanoid robot
Online semi-parametric learning for inverse dynamics modeling
No full textThis paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equation, while the latter exploits a suitable kernel function. We provide an extensive comparison with other methods from the literature using real data from the iCub humanoid robot. In doing so we also compare two different techniques, namely cross validation and marginal likelihood optimization, for estimating the hyperparameters of the kernel function
Structured Prediction for CRiSP Inverse Kinematics Learning with Misspecified Robot Models
No full textWith 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
La diagnosi funzionale mediante tecniche di gait analysis: esempio di quantificazione di parametri nel cammino della spina bifida
No full textDirichlet-based Gaussian Processes for Large-scale Calibrated Classification
No full textThis paper studies the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is hardly sustainable in large-scale problems and devising efficient alternatives is a challenge. In this work, we investigate if and how Gaussian process regression directly applied to classification labels can be used to tackle this question. While in this case training is remarkably faster, predictions need to be calibrated for classification and uncertainty estimation. To this aim, we propose a novel regression approach where the labels are obtained through the interpretation of classification labels as the coefficients of a degenerate Dirichlet distribution. Extensive experimental results show that the proposed approach provides essentially the same accuracy and uncertainty quantification as Gaussian process classification while requiring only a fraction of computational resources
Derivative-free online learning of inverse dynamics models
No full textThis paper discusses online algorithms for inverse dynamics modeling in robotics. Several model classes, including rigid body dynamics models, data-driven models and semiparametric models (which are combination of the previous two classes), are placed in a common framework. While model classes used in the literature typically exploit joint velocities and accelerations, which needs to be approximated resorting to numerical differentiation schemes, in this paper, a new 'derivative-free' (DF) framework is proposed, which does not require this preprocessing step. An extensive experimental study with real data from the right arm of the iCub robot is presented, comparing different model classes and estimation procedures, showing that the proposed DF methods outperform existing methodologies
Dirichlet-based gaussian processes for large-scale calibrated classification
No full textThis paper studies the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is hardly sustainable in large-scale problems and devising efficient alternatives is a challenge. In this work, we investigate if and how Gaussian process regression directly applied to classification labels can be used to tackle this question. While in this case training is remarkably faster, predictions need to be calibrated for classification and uncertainty estimation. To this aim, we propose a novel regression approach where the labels are obtained through the interpretation of classification labels as the coefficients of a degenerate Dirichlet distribution. Extensive experimental results show that the proposed approach provides essentially the same accuracy and uncertainty quantification as Gaussian process classification while requiring only a fraction of computational resources
NYTRO: When Subsampling Meets Early Stopping
No full textEarly 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
- …
