Randomized Dimension Reduction on Massive Data

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as symmetric generalized eigendecomposition problems. In this paper we outline how taking into account the low rank structure assumption implicit in these dimension reduction approaches provides both computational and statistical advantages. We adapt recent randomized low-rank approximation algorithms to provide efficient solutions to three dimension reduction methods: Principal Component Analysis (PCA), Sliced Inverse Regression (SIR), and Localized Sliced Inverse Regression (LSIR). A key observation in this paper is that randomization serves a dual role, improving both computational and statistical performance. This point is highlighted in our experiments on real and simulated data.Comment: 31 pages, 6 figures, Key Words:dimension reduction, generalized eigendecompositon, low-rank, supervised, inverse regression, random projections, randomized algorithms, Krylov subspace method

On the Generalization Effects of Linear Transformations in Data Augmentation

Data augmentation is a powerful technique to improve performance in applications such as image and text classification tasks. Yet, there is little rigorous understanding of why and how various augmentations work. In this work, we consider a family of linear transformations and study their effects on the ridge estimator in an over-parametrized linear regression setting. First, we show that transformations which preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations which mix data can improve estimation by playing a regularization effect. Finally, we validate our theoretical insights on MNIST. Based on the insights, we propose an augmentation scheme that searches over the space of transformations by how uncertain the model is about the transformed data. We validate our proposed scheme on image and text datasets. For example, our method outperforms RandAugment by 1.24% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR datasets.Comment: International Conference on Machine learning (ICML) 2020. Added experimental results on ImageNe

Learning Manipulation under Physics Constraints with Visual Perception

Understanding physical phenomena is a key competence that enables humans and animals to act and interact under uncertain perception in previously unseen environments containing novel objects and their configurations. In this work, we consider the problem of autonomous block stacking and explore solutions to learning manipulation under physics constraints with visual perception inherent to the task. Inspired by the intuitive physics in humans, we first present an end-to-end learning-based approach to predict stability directly from appearance, contrasting a more traditional model-based approach with explicit 3D representations and physical simulation. We study the model's behavior together with an accompanied human subject test. It is then integrated into a real-world robotic system to guide the placement of a single wood block into the scene without collapsing existing tower structure. To further automate the process of consecutive blocks stacking, we present an alternative approach where the model learns the physics constraint through the interaction with the environment, bypassing the dedicated physics learning as in the former part of this work. In particular, we are interested in the type of tasks that require the agent to reach a given goal state that may be different for every new trial. Thereby we propose a deep reinforcement learning framework that learns policies for stacking tasks which are parametrized by a target structure.Comment: arXiv admin note: substantial text overlap with arXiv:1609.04861, arXiv:1711.00267, arXiv:1604.0006