Diagnosing and Enhancing VAE Models

Although variational autoencoders (VAEs) represent a widely influential deep generative model, many aspects of the underlying energy function remain poorly understood. In particular, it is commonly believed that Gaussian encoder/decoder assumptions reduce the effectiveness of VAEs in generating realistic samples. In this regard, we rigorously analyze the VAE objective, differentiating situations where this belief is and is not actually true. We then leverage the corresponding insights to develop a simple VAE enhancement that requires no additional hyperparameters or sensitive tuning. Quantitatively, this proposal produces crisp samples and stable FID scores that are actually competitive with a variety of GAN models, all while retaining desirable attributes of the original VAE architecture. A shorter version of this work will appear in the ICLR 2019 conference proceedings (Dai and Wipf, 2019). The code for our model is available at https://github.com/daib13/ TwoStageVAE

Two-Manifold Problems

Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that solving a two-manifold problem can aid in learning a nonlinear dynamical system from limited data

On GANs and GMMs

A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in particular have shown the ability to generate remarkably realistic high resolution sampled images. At the same time, many authors have pointed out that GANs may fail to model the full distribution ("mode collapse") and that using the learned models for anything other than generating samples may be very difficult. In this paper, we examine the utility of GANs in learning statistical models of images by comparing them to perhaps the simplest statistical model, the Gaussian Mixture Model. First, we present a simple method to evaluate generative models based on relative proportions of samples that fall into predetermined bins. Unlike previous automatic methods for evaluating models, our method does not rely on an additional neural network nor does it require approximating intractable computations. Second, we compare the performance of GANs to GMMs trained on the same datasets. While GMMs have previously been shown to be successful in modeling small patches of images, we show how to train them on full sized images despite the high dimensionality. Our results show that GMMs can generate realistic samples (although less sharp than those of GANs) but also capture the full distribution, which GANs fail to do. Furthermore, GMMs allow efficient inference and explicit representation of the underlying statistical structure. Finally, we discuss how GMMs can be used to generate sharp images.Comment: Accepted to NIPS 201

Recovering 6D Object Pose and Predicting Next-Best-View in the Crowd

Object detection and 6D pose estimation in the crowd (scenes with multiple object instances, severe foreground occlusions and background distractors), has become an important problem in many rapidly evolving technological areas such as robotics and augmented reality. Single shot-based 6D pose estimators with manually designed features are still unable to tackle the above challenges, motivating the research towards unsupervised feature learning and next-best-view estimation. In this work, we present a complete framework for both single shot-based 6D object pose estimation and next-best-view prediction based on Hough Forests, the state of the art object pose estimator that performs classification and regression jointly. Rather than using manually designed features we a) propose an unsupervised feature learnt from depth-invariant patches using a Sparse Autoencoder and b) offer an extensive evaluation of various state of the art features. Furthermore, taking advantage of the clustering performed in the leaf nodes of Hough Forests, we learn to estimate the reduction of uncertainty in other views, formulating the problem of selecting the next-best-view. To further improve pose estimation, we propose an improved joint registration and hypotheses verification module as a final refinement step to reject false detections. We provide two additional challenging datasets inspired from realistic scenarios to extensively evaluate the state of the art and our framework. One is related to domestic environments and the other depicts a bin-picking scenario mostly found in industrial settings. We show that our framework significantly outperforms state of the art both on public and on our datasets.Comment: CVPR 2016 accepted paper, project page: http://www.iis.ee.ic.ac.uk/rkouskou/6D_NBV.htm

Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions. We provide an analytical description of these phenomena by finding new exact solutions to the nonlinear dynamics of deep learning. Our theoretical analysis also reveals the surprising finding that as the depth of a network approaches infinity, learning speed can nevertheless remain finite: for a special class of initial conditions on the weights, very deep networks incur only a finite, depth independent, delay in learning speed relative to shallow networks. We show that, under certain conditions on the training data, unsupervised pretraining can find this special class of initial conditions, while scaled random Gaussian initializations cannot. We further exhibit a new class of random orthogonal initial conditions on weights that, like unsupervised pre-training, enjoys depth independent learning times. We further show that these initial conditions also lead to faithful propagation of gradients even in deep nonlinear networks, as long as they operate in a special regime known as the edge of chaos.Comment: Submission to ICLR2014. Revised based on reviewer feedbac

Differentiating Concepts and Instances for Knowledge Graph Embedding

Concepts, which represent a group of different instances sharing common properties, are essential information in knowledge representation. Most conventional knowledge embedding methods encode both entities (concepts and instances) and relations as vectors in a low dimensional semantic space equally, ignoring the difference between concepts and instances. In this paper, we propose a novel knowledge graph embedding model named TransC by differentiating concepts and instances. Specifically, TransC encodes each concept in knowledge graph as a sphere and each instance as a vector in the same semantic space. We use the relative positions to model the relations between concepts and instances (i.e., instanceOf), and the relations between concepts and sub-concepts (i.e., subClassOf). We evaluate our model on both link prediction and triple classification tasks on the dataset based on YAGO. Experimental results show that TransC outperforms state-of-the-art methods, and captures the semantic transitivity for instanceOf and subClassOf relation. Our codes and datasets can be obtained from https:// github.com/davidlvxin/TransC

Understanding Machine-learned Density Functionals

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densities} are found via a modified Euler-Lagrange constrained minimization of the total energy. A projected gradient descent algorithm is derived using local principal component analysis. Additionally, a sparse grid representation of the density can be used without degrading the performance of the methods. The implications for machine-learned density functional approximations are discussed

An Alternative to EM for Gaussian Mixture Models: Batch and Stochastic Riemannian Optimization

We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which is its ability to fulfill positive definiteness constraints in closed form is of key importance. We propose an alternative to EM by appealing to the rich Riemannian geometry of positive definite matrices, using which we cast Gmm parameter estimation as a Riemannian optimization problem. Surprisingly, such an out-of-the-box Riemannian formulation completely fails and proves much inferior to EM. This motivates us to take a closer look at the problem geometry, and derive a better formulation that is much more amenable to Riemannian optimization. We then develop (Riemannian) batch and stochastic gradient algorithms that outperform EM, often substantially. We provide a non-asymptotic convergence analysis for our stochastic method, which is also the first (to our knowledge) such global analysis for Riemannian stochastic gradient. Numerous empirical results are included to demonstrate the effectiveness of our methods.Comment: 21 pages, 6 figure

Randomized Physics-based Motion Planning for Grasping in Cluttered and Uncertain Environments

Planning motions to grasp an object in cluttered and uncertain environments is a challenging task, particularly when a collision-free trajectory does not exist and objects obstructing the way are required to be carefully grasped and moved out. This paper takes a different approach and proposes to address this problem by using a randomized physics-based motion planner that permits robot-object and object-object interactions. The main idea is to avoid an explicit high-level reasoning of the task by providing the motion planner with a physics engine to evaluate possible complex multi-body dynamical interactions. The approach is able to solve the problem in complex scenarios, also considering uncertainty in the objects pose and in the contact dynamics. The work enhances the state validity checker, the control sampler and the tree exploration strategy of a kinodynamic motion planner called KPIECE. The enhanced algorithm, called p-KPIECE, has been validated in simulation and with real experiments. The results have been compared with an ontological physics-based motion planner and with task and motion planning approaches, resulting in a significant improvement in terms of planning time, success rate and quality of the solution path.Comment: IEEE Robotics and Automation Letters. Preprin Version. Accepted November, 201

Realtime State Estimation with Tactile and Visual Sensing for Inserting a Suction-held Object

We develop a real-time state estimation system to recover the pose and contact formation of an object relative to its environment. In this paper, we focus on the application of inserting an object picked by a suction cup into a tight space, an enabling technology for robotic packaging. We propose a framework that fuses force and visual sensing for improved accuracy and robustness. Visual sensing is versatile and non-intrusive, but suffers from occlusions and limited accuracy, especially for tasks involving contact. Tactile sensing is local, but provides accuracy and robustness to occlusions. The proposed algorithm to fuse them is based on iSAM, an on-line optimization technique, which we use to incorporate kinematic measurements from the robot, contact geometry of the object and the container, and visual tracking. In this paper, we generalize previous results in planar settings to a 3D task with more complex contact interactions. A key challenge in using force sensing is that we do not observe contact point locations directly. We propose a data-driven method to infer the contact formation, which is then used in real-time by the state estimator. We demonstrate and evaluate the algorithm in a setup instrumented to provide groundtruth.Comment: 8 pages, 10 figures, submitted to IROS 201