TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: <lb>We consider a situation in which we see samples Xn ∈ R drawn i.i.d. from some<lb>distribution with mean zero and unknown covariance A. We wish to compute the<lb>top eigenvector of A in an incremental fashion with an algorithm that maintains<lb>an estimate of the top eigenvector in O(d) space, and incrementally adjusts the<lb>estimate with each new data point that arrives. Two classical such schemes are<lb>due to Krasulina (1969) and Oja (1983). We give finite-sample convergence rates<lb>for both.

SOLUTION: The Fast Convergence of Incremental PCA

PROBLEM: We consider linear models for stochastic dynamics. To any such model can be as-<lb>sociated a network (namely a directed graph) describing which degrees of freedom<lb>interact under the dynamics. We tackle the problem of learning such a network<lb>from observation of the system trajectory over a time interval T .<lb>We analyze the l1-regularized least squares algorithm and, in the setting in which<lb>the underlying network is sparse, we prove performance guarantees that are uni-<lb>form in the sampling rate as long as this is sufficiently high. This result substan-<lb>tiates the notion of a well defined ‘time complexity’ for the network inference<lb>problem. keywords: Gaussian processes, model selection and structure learning, graphical models, sparsity<lb>and feature selection.

SOLUTION: Learning Networks of Stochastic Differential Equations

PROBLEM: The term “affordance” denotes the behavioral meaning of objects. We propose a cognitive architecture for the detection of affordances in the visual modality. This model is based on the internal simulation of movement sequences. For each movement step, the resulting sensory state is predicted by a forward model, which in turn triggers the generation of a new (simulated) motor command by an inverse model. Thus, a series of mental images in the sensory and in the motor domain is evoked. Starting from a real sensory state, a large number of such sequences is simulated in parallel. Final affordance detection is based on the generated motor commands. We apply this model to a real–world mobile robot which is faced with obstacle arrangements some of which are passable (corridor) and some of which are not (dead ends). The robot’s task is to detect the right affordance (“pass–through–able” or “non–pass–through–able”). The required internal models are acquired in a hierarchical training process. Afterwards, the robotic agent is able to distinguish reliably between corridors and dead ends. This real–world result enhances the validity of the proposed mental simulation approach. In addition, we compare several key factors in the simulation process regarding performance and efficiency. Funding statement: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. 1 ar X iv :1 61 1. 00 27 4v 1 [ cs .A I] 1 N ov 2 01 6

SOLUTION:
Detecting Affordances by Visuomotor Simulation