Robot Composite Learning and the Nunchaku Flipping Challenge

Advanced motor skills are essential for robots to physically coexist with humans. Much research on robot dynamics and control has achieved success on hyper robot motor capabilities, but mostly through heavily case-specific engineering. Meanwhile, in terms of robot acquiring skills in a ubiquitous manner, robot learning from human demonstration (LfD) has achieved great progress, but still has limitations handling dynamic skills and compound actions. In this paper, we present a composite learning scheme which goes beyond LfD and integrates robot learning from human definition, demonstration, and evaluation. The method tackles advanced motor skills that require dynamic time-critical maneuver, complex contact control, and handling partly soft partly rigid objects. We also introduce the "nunchaku flipping challenge", an extreme test that puts hard requirements to all these three aspects. Continued from our previous presentations, this paper introduces the latest update of the composite learning scheme and the physical success of the nunchaku flipping challenge

Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations

Low rank matrix approximation is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns and provides concise representations for the data. Research on low rank approximation usually focus on real matrices. However, in many applications data are binary (categorical) rather than continuous. This leads to the problem of low rank approximation of binary matrix. Here we are given a $d \times n$ binary matrix $A$ and a small integer $k$. The goal is to find two binary matrices $U$ and $V$ of sizes $d \times k$ and $k \times n$ respectively, so that the Frobenius norm of $A - U V$ is minimized. There are two models of this problem, depending on the definition of the dot product of binary vectors: The $\mathrm{GF}(2)$ model and the Boolean semiring model. Unlike low rank approximation of real matrix which can be efficiently solved by Singular Value Decomposition, approximation of binary matrix is $NP$-hard even for $k=1$. In this paper, we consider the problem of Column Subset Selection (CSS), in which one low rank matrix must be formed by $k$ columns of the data matrix. We characterize the approximation ratio of CSS for binary matrices. For $GF(2)$ model, we show the approximation ratio of CSS is bounded by $\frac{k}{2}+1+\frac{k}{2(2^k-1)}$ and this bound is asymptotically tight. For Boolean model, it turns out that CSS is no longer sufficient to obtain a bound. We then develop a Generalized CSS (GCSS) procedure in which the columns of one low rank matrix are generated from Boolean formulas operating bitwise on columns of the data matrix. We show the approximation ratio of GCSS is bounded by $2^{k-1}+1$, and the exponential dependency on $k$ is inherent.Comment: 38 page

A Deep Embedding Model for Co-occurrence Learning

Co-occurrence Data is a common and important information source in many areas, such as the word co-occurrence in the sentences, friends co-occurrence in social networks and products co-occurrence in commercial transaction data, etc, which contains rich correlation and clustering information about the items. In this paper, we study co-occurrence data using a general energy-based probabilistic model, and we analyze three different categories of energy-based model, namely, the $L_1$, $L_2$ and $L_k$ models, which are able to capture different levels of dependency in the co-occurrence data. We also discuss how several typical existing models are related to these three types of energy models, including the Fully Visible Boltzmann Machine (FVBM) ($L_2$), Matrix Factorization ($L_2$), Log-BiLinear (LBL) models ($L_2$), and the Restricted Boltzmann Machine (RBM) model ($L_k$). Then, we propose a Deep Embedding Model (DEM) (an $L_k$ model) from the energy model in a \emph{principled} manner. Furthermore, motivated by the observation that the partition function in the energy model is intractable and the fact that the major objective of modeling the co-occurrence data is to predict using the conditional probability, we apply the \emph{maximum pseudo-likelihood} method to learn DEM. In consequence, the developed model and its learning method naturally avoid the above difficulties and can be easily used to compute the conditional probability in prediction. Interestingly, our method is equivalent to learning a special structured deep neural network using back-propagation and a special sampling strategy, which makes it scalable on large-scale datasets. Finally, in the experiments, we show that the DEM can achieve comparable or better results than state-of-the-art methods on datasets across several application domains