Incremental Robot Learning of New Objects with Fixed Update Time

We consider object recognition in the context of lifelong learning, where a robotic agent learns to discriminate between a growing number of object classes as it accumulates experience about the environment. We propose an incremental variant of the Regularized Least Squares for Classification (RLSC) algorithm, and exploit its structure to seamlessly add new classes to the learned model. The presented algorithm addresses the problem of having an unbalanced proportion of training examples per class, which occurs when new objects are presented to the system for the first time. We evaluate our algorithm on both a machine learning benchmark dataset and two challenging object recognition tasks in a robotic setting. Empirical evidence shows that our approach achieves comparable or higher classification performance than its batch counterpart when classes are unbalanced, while being significantly faster.

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage.

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.

Less is More: Nyström 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.

Incremental Semiparametric Inverse Dynamics Learning

This 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. This yields to 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.

Holographic Embeddings of Knowledge Graphs

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets.

Enabling Depth-driven Visual Attention on the iCub Humanoid Robot: Instructions for Use and New Perspectives

The importance of depth perception in the interactions that humans have within their nearby space is a well established fact. Consequently, it is also well known that the possibility of exploiting good stereo information would ease and, in many cases, enable, a large variety of attentional and interactive behaviors on humanoid robotic platforms. However, the difficulty of computing real-time and robust binocular disparity maps from moving stereo cameras often prevents from relying on this kind of cue to visually guide robots' attention and actions in real-world scenarios. The contribution of this paper is two-fold: first, we show that the Efficient Large-scale Stereo Matching algorithm (ELAS) by A. Geiger et al. 2010 for computation of the disparity map is well suited to be used on a humanoid robotic platform as the iCub robot; second, we show how, provided with a fast and reliable stereo system, implementing relatively challenging visual behaviors in natural settings can require much less effort. As a case of study we consider the common situation where the robot is asked to focus the attention on one object close in the scene, showing how a simple but effective disparity-based segmentation solves the problem in this case. Indeed this example paves the way to a variety of other similar applications.

Deep Convolutional Networks are Hierarchical Kernel Machines

In i-theory a typical layer of a hierarchical architecture consists of HW modules pooling the dot products of the inputs to the layer with the transformations of a few templates under a group. Such layers include as special cases the convolutional layers of Deep Convolutional Networks (DCNs) as well as the non-convolutional layers (when the group contains only the identity). Rectifying nonlinearities -- which are used by present-day DCNs -- are one of the several nonlinearities admitted by i-theory for the HW module. We discuss here the equivalence between group averages of linear combinations of rectifying nonlinearities and an associated kernel. This property implies that present-day DCNs can be exactly equivalent to a hierarchy of kernel machines with pooling and non-pooling layers. Finally, we describe a conjecture for theoretically understanding hierarchies of such modules. A main consequence of the conjecture is that hierarchies of trained HW modules minimize memory requirements while computing a selective and invariant representation.

Learning with incremental iterative regularization

Within a statistical learning setting, we propose and study an iterative regularization algorithm for least squares defined by an incremental gradient method. In particular, we show that, if all other parameters are fixed a priori, the number of passes over the data (epochs) acts as a regularization parameter, and prove strong universal consistency, i.e. almost sure convergence of the risk, as well as sharp finite sample bounds for the iterates. Our results are a step towards understanding the effect of multiple epochs in stochastic gradient techniques in machine learning and rely on integrating statistical and optimization results.

Convex Learning of Multiple Tasks and their Structure

Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context a fundamental question is how to incorporate the tasks structure in the learning problem.We tackle this question by studying a general computational framework that allows to encode a-priori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches. Within this framework, we show that tasks and their structure can be efficiently learned considering a convex optimization problem that can be approached by means of block coordinate methods such as alternating minimization and for which we prove convergence to the global minimum.