On the Optimality of Misspecified Kernel Ridge Regression

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function $f_{\rho}^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0,1)$. The existing minimax optimal results require $\|f_{\rho}^{*}\|_{L^{\infty}}<\infty$ which implicitly requires $s > \alpha_{0}$ where $\alpha_{0}\in (0,1)$ is the embedding index, a constant depending on $\mathcal{H}$. Whether the KRR is optimal for all $s\in (0,1)$ is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any $s\in (0,1)$ when the $\mathcal{H}$ is a Sobolev RKHS.

Statistical Optimality of Deep Wide Neural Networks

In this paper, we consider the generalization ability of deep wide feedforward ReLU neural networks defined on a bounded domain $\mathcal X \subset \mathbb R^{d}$. We first demonstrate that the generalization ability of the neural network can be fully characterized by that of the corresponding deep neural tangent kernel (NTK) regression. We then investigate on the spectral properties of the deep NTK and show that the deep NTK is positive definite on $\mathcal{X}$ and its eigenvalue decay rate is $(d+1)/d$. Thanks to the well established theories in kernel regression, we then conclude that multilayer wide neural networks trained by gradient descent with proper early stopping achieve the minimax rate, provided that the regression function lies in the reproducing kernel Hilbert space (RKHS) associated with the corresponding NTK. Finally, we illustrate that the overfitted multilayer wide neural networks can not generalize well on $\mathbb S^{d}$.

Kernel interpolation generalizes poorly

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in the literature on deep networks. In this paper, under mild conditions, we show that for any $\varepsilon>0$, the generalization error of kernel interpolation is lower bounded by $\Omega(n^{-\varepsilon})$. In other words, the kernel interpolation generalizes poorly for a large class of kernels. As a direct corollary, we can show that overfitted wide neural networks defined on sphere generalize poorly.

Generalization Ability of Wide Neural Networks on $\mathbb{R}$

We perform a study on the generalization ability of the wide two-layer ReLU neural network on $\mathbb{R}$. We first establish some spectral properties of the neural tangent kernel (NTK): $a)$ $K_{d}$, the NTK defined on $\mathbb{R}^{d}$, is positive definite; $b)$ $\lambda_{i}(K_{1})$, the $i$-th largest eigenvalue of $K_{1}$, is proportional to $i^{-2}$. We then show that: $i)$ when the width $m\rightarrow\infty$, the neural network kernel (NNK) uniformly converges to the NTK; $ii)$ the minimax rate of regression over the RKHS associated to $K_{1}$ is $n^{-2/3}$; $iii)$ if one adopts the early stopping strategy in training a wide neural network, the resulting neural network achieves the minimax rate; $iv)$ if one trains the neural network till it overfits the data, the resulting neural network can not generalize well. Finally, we provide an explanation to reconcile our theory and the widely observed ``benign overfitting phenomenon''.

A Semi-Supervised Learning Approach with Two Teachers to Improve Breakdown Identification in Dialogues

Identifying breakdowns in ongoing dialogues helps to improve communication effectiveness. Most prior work on this topic relies on human annotated data and data augmentation to learn a classification model. While quality labeled dialogue data requires human annotation and is usually expensive to obtain, unlabeled data is easier to collect from various sources. In this paper, we propose a novel semi-supervised teacher-student learning framework to tackle this task. We introduce two teachers which are trained on labeled data and perturbed labeled data respectively. We leverage unlabeled data to improve classification in student training where we employ two teachers to refine the labeling of unlabeled data through teacher-student learning in a bootstrapping manner. Through our proposed training approach, the student can achieve improvements over single-teacher performance. Experimental results on the Dialogue Breakdown Detection Challenge dataset DBDC5 and Learning to Identify Follow-Up Questions dataset LIF show that our approach outperforms all previous published approaches as well as other supervised and semi-supervised baseline methods.

SMORES-EP, a Modular Robot with Parallel Self-assembly

Self-assembly of modular robotic systems enables the construction of complex robotic configurations to adapt to different tasks. This paper presents a framework for SMORES types of modular robots to efficiently self-assemble into tree topologies. These modular robots form kinematic chains that have been shown to be capable of a large variety of manipulation and locomotion tasks, yet they can reconfigure using a mobile reconfiguration. A desired kinematic topology can be mapped onto a planar pattern with optimal module assignment based on the modules' locations, then the mobile reconfiguration assembly process can be executed in parallel. A docking controller is developed to guarantee the success of docking processes. A hybrid control architecture is designed to handle a large number of modules and complex behaviors of each individual, and achieve efficient and robust self-assembly actions. The framework is demonstrated in hardware on the SMORES-EP platform.

Boosting High-Level Vision with Joint Compression Artifacts Reduction and Super-Resolution

Due to the limits of bandwidth and storage space, digital images are usually down-scaled and compressed when transmitted over networks, resulting in loss of details and jarring artifacts that can lower the performance of high-level visual tasks. In this paper, we aim to generate an artifact-free high-resolution image from a low-resolution one compressed with an arbitrary quality factor by exploring joint compression artifacts reduction (CAR) and super-resolution (SR) tasks. First, we propose a context-aware joint CAR and SR neural network (CAJNN) that integrates both local and non-local features to solve CAR and SR in one-stage. Finally, a deep reconstruction network is adopted to predict high quality and high-resolution images. Evaluation on CAR and SR benchmark datasets shows that our CAJNN model outperforms previous methods and also takes 26.2% shorter runtime. Based on this model, we explore addressing two critical challenges in high-level computer vision: optical character recognition of low-resolution texts, and extremely tiny face detection. We demonstrate that CAJNN can serve as an effective image preprocessing method and improve the accuracy for real-scene text recognition (from 85.30% to 85.75%) and the average precision for tiny face detection (from 0.317 to 0.611).

MLCask: Efficient Management of Component Evolution in Collaborative Data Analytics Pipelines

With the ever-increasing adoption of machine learning for data analytics, maintaining a machine learning pipeline is becoming more complex as both the datasets and trained models evolve with time. In a collaborative environment, the changes and updates due to pipeline evolution often cause cumbersome coordination and maintenance work, raising the costs and making it hard to use. Existing solutions, unfortunately, do not address the version evolution problem, especially in a collaborative environment where non-linear version control semantics are necessary to isolate operations made by different user roles. The lack of version control semantics also incurs unnecessary storage consumption and lowers efficiency due to data duplication and repeated data pre-processing, which are avoidable. In this paper, we identify two main challenges that arise during the deployment of machine learning pipelines, and address them with the design of versioning for an end-to-end analytics system MLCask. The system supports multiple user roles with the ability to perform Git-like branching and merging operations in the context of the machine learning pipelines. We define and accelerate the metric-driven merge operation by pruning the pipeline search tree using reusable history records and pipeline compatibility information. Further, we design and implement the prioritized pipeline search, which gives preference to the pipelines that probably yield better performance. The effectiveness of MLCask is evaluated through an extensive study over several real-world deployment cases. The performance evaluation shows that the proposed merge operation is up to 7.8x faster and saves up to 11.9x storage space than the baseline method that does not utilize history records.

The Blessing and the Curse of the Noise behind Facial Landmark Annotations

The evolving algorithms for 2D facial landmark detection empower people to recognize faces, analyze facial expressions, etc. However, existing methods still encounter problems of unstable facial landmarks when applied to videos. Because previous research shows that the instability of facial landmarks is caused by the inconsistency of labeling quality among the public datasets, we want to have a better understanding of the influence of annotation noise in them. In this paper, we make the following contributions: 1) we propose two metrics that quantitatively measure the stability of detected facial landmarks, 2) we model the annotation noise in an existing public dataset, 3) we investigate the influence of different types of noise in training face alignment neural networks, and propose corresponding solutions. Our results demonstrate improvements in both accuracy and stability of detected facial landmarks.

LoCEC: Local Community-based Edge Classification in Large Online Social Networks

Relationships in online social networks often imply social connections in the real world. An accurate understanding of relationship types benefits many applications, e.g. social advertising and recommendation. Some recent attempts have been proposed to classify user relationships into predefined types with the help of pre-labeled relationships or abundant interaction features on relationships. Unfortunately, both relationship feature data and label data are very sparse in real social platforms like WeChat, rendering existing methods inapplicable. In this paper, we present an in-depth analysis of WeChat relationships to identify the major challenges for the relationship classification task. To tackle the challenges, we propose a Local Community-based Edge Classification (LoCEC) framework that classifies user relationships in a social network into real-world social connection types. LoCEC enforces a three-phase processing, namely local community detection, community classification and relationship classification, to address the sparsity issue of relationship features and relationship labels. Moreover, LoCEC is designed to handle large-scale networks by allowing parallel and distributed processing. We conduct extensive experiments on the real-world WeChat network with hundreds of billions of edges to validate the effectiveness and efficiency of LoCEC.