arXiv subjects

Yuxin Chen

Publications and source records attributed to Yuxin Chen.

At least 271 records · Page 15Linked to original sources

arXiv2019

Inference and Uncertainty Quantification for Noisy Matrix Completion

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained estimates and how to perform statistical inference on the unknown matrix (e.g.~constructing a valid and short confidence interval for an unseen entry). This paper takes a step towards inference and uncertainty quantification for noisy matrix completion. We develop a simple procedure to compensate for the bias of the widely used convex and nonconvex estimators. The resulting de-biased estimators admit nearly precise non-asymptotic distributional characterizations, which in turn enable optimal construction of confidence intervals\,/\,regions for, say, the missing entries and the low-rank factors. Our inferential procedures do not rely on sample splitting, thus avoiding unnecessary loss of data efficiency. As a byproduct, we obtain a sharp characterization of the estimation accuracy of our de-biased estimators, which, to the best of our knowledge, are the first tractable algorithms that provably achieve full statistical efficiency (including the preconstant). The analysis herein is built upon the intimate link between convex and nonconvex optimization --- an appealing feature recently discovered by \cite{chen2019noisy}.

stat.ML↗

arXiv2019

Landmark Ordinal Embedding

In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form "item j is closer to item i than item k". Existing approaches for this "ordinal embedding" problem require expensive optimization procedures, which cannot scale to handle increasingly larger datasets. To address this issue, we propose a landmark-based strategy, which we call Landmark Ordinal Embedding (LOE). Our approach trades off statistical efficiency for computational efficiency by exploiting the low-dimensionality of the latent embedding. We derive bounds establishing the statistical consistency of LOE under the popular Bradley-Terry-Luce noise model. Through a rigorous analysis of the computational complexity, we show that LOE is significantly more efficient than conventional ordinal embedding approaches as the number of items grows. We validate these characterizations empirically on both synthetic and real datasets. We also present a practical approach that achieves the "best of both worlds", by using LOE to warm-start existing methods that are more statistically efficient but computationally expensive.

cs.LG↗

arXiv2019

Teaching Multiple Concepts to a Forgetful Learner

How can we help a forgetful learner learn multiple concepts within a limited time frame? While there have been extensive studies in designing optimal schedules for teaching a single concept given a learner's memory model, existing approaches for teaching multiple concepts are typically based on heuristic scheduling techniques without theoretical guarantees. In this paper, we look at the problem from the perspective of discrete optimization and introduce a novel algorithmic framework for teaching multiple concepts with strong performance guarantees. Our framework is both generic, allowing the design of teaching schedules for different memory models, and also interactive, allowing the teacher to adapt the schedule to the underlying forgetting mechanisms of the learner. Furthermore, for a well-known memory model, we are able to identify a regime of model parameters where our framework is guaranteed to achieve high performance. We perform extensive evaluations using simulations along with real user studies in two concrete applications: (i) an educational app for online vocabulary teaching; and (ii) an app for teaching novices how to recognize animal species from images. Our results demonstrate the effectiveness of our algorithm compared to popular heuristic approaches.

cs.AI↗

arXiv2019

Preference-Based Batch and Sequential Teaching: Towards a Unified View of Models

Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis. In a quest to lower teaching complexity and to achieve more natural teacher-learner interactions, several teaching models and complexity measures have been proposed for both the batch settings (e.g., worst-case, recursive, preference-based, and non-clashing models) as well as the sequential settings (e.g., local preference-based model). To better understand the connections between these different batch and sequential models, we develop a novel framework which captures the teaching process via preference functions $Σ$. In our framework, each function $σ\in Σ$ induces a teacher-learner pair with teaching complexity as $\TD(σ)$. We show that the above-mentioned teaching models are equivalent to specific types/families of preference functions in our framework. This equivalence, in turn, allows us to study the differences between two important teaching models, namely $σ$ functions inducing the strongest batch (i.e., non-clashing) model and $σ$ functions inducing a weak sequential (i.e., local preference-based) model. Finally, we identify preference functions inducing a novel family of sequential models with teaching complexity linear in the VC dimension of the hypothesis class: this is in contrast to the best known complexity result for the batch models which is quadratic in the VC dimension.

cs.LG↗

arXiv2019

RDMA vs. RPC for Implementing Distributed Data Structures

Distributed data structures are key to implementing scalable applications for scientific simulations and data analysis. In this paper we look at two implementation styles for distributed data structures: remote direct memory access (RDMA) and remote procedure call (RPC). We focus on operations that require individual accesses to remote portions of a distributed data structure, e.g., accessing a hash table bucket or distributed queue, rather than global operations in which all processors collectively exchange information. We look at the trade-offs between the two styles through microbenchmarks and a performance model that approximates the cost of each. The RDMA operations have direct hardware support in the network and therefore lower latency and overhead, while the RPC operations are more expressive but higher cost and can suffer from lack of attentiveness from the remote side. We also run experiments to compare the real-world performance of RDMA- and RPC-based data structure operations with the predicted performance to evaluate the accuracy of our model, and show that while the model does not always precisely predict running time, it allows us to choose the best implementation in the examples shown. We believe this analysis will assist developers in designing data structures that will perform well on current network architectures, as well as network architects in providing better support for this class of distributed data structures.

cs.DC↗

arXiv2019

Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle this problem is convex relaxation, which achieves remarkable efficacy in practice. However, the theoretical support of this approach is still far from optimal in the noisy setting, falling short of explaining its empirical success. We make progress towards demystifying the practical efficacy of convex relaxation vis-à-vis random noise. When the rank and the condition number of the unknown matrix are bounded by a constant, we demonstrate that the convex programming approach achieves near-optimal estimation errors --- in terms of the Euclidean loss, the entrywise loss, and the spectral norm loss --- for a wide range of noise levels. All of this is enabled by bridging convex relaxation with the nonconvex Burer-Monteiro approach, a seemingly distinct algorithmic paradigm that is provably robust against noise. More specifically, we show that an approximate critical point of the nonconvex formulation serves as an extremely tight approximation of the convex solution, thus allowing us to transfer the desired statistical guarantees of the nonconvex approach to its convex counterpart.

stat.ML↗

arXiv2019

Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.

cs.LG↗

arXiv2019

Nailed It: Autonomous Roofing with a Nailgun-Equipped Octocopter

This paper presents the first demonstration of autonomous roofing with a multicopter. A DJI S1000 octocopter equipped with an off-the-shelf nailgun and an adjustableslope roof mock-up were used. The nailgun was modified to allow triggering from the vehicle and tooltip compression feedback. A mount was designed to adjust the angle to match representative roof slopes. An open-source octocopter autopilot facilitated controller adaptation for the roofing application. A state machine managed autonomous nailing sequences using smooth trajectories designed to apply prescribed contact forces for reliable nail deployment. Experimental results showed that the system is capable of nailing within a required three centimeter gap on the shingle. Extensions to achieve a complete autonomous roofing system are discussed as future work.

cs.RO↗

arXiv2019

Augmenting Monte Carlo Dropout Classification Models with Unsupervised Learning Tasks for Detecting and Diagnosing Out-of-Distribution Faults

The Monte Carlo dropout method has proved to be a scalable and easy-to-use approach for estimating the uncertainty of deep neural network predictions. This approach was recently applied to Fault Detection and Di-agnosis (FDD) applications to improve the classification performance on incipient faults. In this paper, we propose a novel approach of augmenting the classification model with an additional unsupervised learning task. We justify our choice of algorithm design via an information-theoretical analysis. Our experimental results on three datasets from diverse application domains show that the proposed method leads to improved fault detection and diagnosis performance, especially on out-of-distribution examples including both incipient and unknown faults.

cs.LG↗

arXiv2019

Barrier Certificates for Assured Machine Teaching

Machine teaching can be viewed as optimal control for learning. Given a learner's model, machine teaching aims to determine the optimal training data to steer the learner towards a target hypothesis. In this paper, we are interested in providing assurances for machine teaching algorithms using control theory. In particular, we study a well-established learner's model in the machine teaching literature that is captured by the local preference over a version space. We interpret the problem of teaching a preference-based learner as solving a partially observable Markov decision process (POMDP). We then show that the POMDP formulation can be cast as a special hybrid system, i.e., a discrete-time switched system. Subsequently, we use barrier certificates to verify set-theoric properties of this special hybrid system. We show how the computation of the barrier certificate can be decomposed and numerically implemented as the solution to a sum-of-squares (SOS) program. For illustration, we show how the proposed framework based on control theory can be used to verify the teaching performance of two well-known machine teaching methods.

eess.SY↗

arXiv2019

Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often require proper regularization (e.g. trimming, regularized cost, projection) in order to guarantee fast convergence. For vanilla procedures such as gradient descent, however, prior theory either recommends highly conservative learning rates to avoid overshooting, or completely lacks performance guarantees. This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models. In fact, gradient descent follows a trajectory staying within a basin that enjoys nice geometry, consisting of points incoherent with the sampling mechanism. This "implicit regularization" feature allows gradient descent to proceed in a far more aggressive fashion without overshooting, which in turn results in substantial computational savings. Focusing on three fundamental statistical estimation problems, i.e. phase retrieval, low-rank matrix completion, and blind deconvolution, we establish that gradient descent achieves near-optimal statistical and computational guarantees without explicit regularization. In particular, by marrying statistical modeling with generic optimization theory, we develop a general recipe for analyzing the trajectories of iterative algorithms via a leave-one-out perturbation argument. As a byproduct, for noisy matrix completion, we demonstrate that gradient descent achieves near-optimal error control --- measured entrywise and by the spectral norm --- which might be of independent interest.

cs.LG↗

arXiv2019

An Encoder-Decoder Based Approach for Anomaly Detection with Application in Additive Manufacturing

We present a novel unsupervised deep learning approach that utilizes the encoder-decoder architecture for detecting anomalies in sequential sensor data collected during industrial manufacturing. Our approach is designed not only to detect whether there exists an anomaly at a given time step, but also to predict what will happen next in the (sequential) process. We demonstrate our approach on a dataset collected from a real-world testbed. The dataset contains images collected under both normal conditions and synthetic anomalies. We show that the encoder-decoder model is able to identify the injected anomalies in a modern manufacturing process in an unsupervised fashion. In addition, it also gives hints about the temperature non-uniformity of the testbed during manufacturing, which is what we are not aware of before doing the experiment.

cs.LG↗

arXiv2019

Batched Stochastic Bayesian Optimization via Combinatorial Constraints Design

In many high-throughput experimental design settings, such as those common in biochemical engineering, batched queries are more cost effective than one-by-one sequential queries. Furthermore, it is often not possible to directly choose items to query. Instead, the experimenter specifies a set of constraints that generates a library of possible items, which are then selected stochastically. Motivated by these considerations, we investigate \emph{Batched Stochastic Bayesian Optimization} (BSBO), a novel Bayesian optimization scheme for choosing the constraints in order to guide exploration towards items with greater utility. We focus on \emph{site-saturation mutagenesis}, a prototypical setting of BSBO in biochemical engineering, and propose a natural objective function for this problem. Importantly, we show that our objective function can be efficiently decomposed as a difference of submodular functions (DS), which allows us to employ DS optimization tools to greedily identify sets of constraints that increase the likelihood of finding items with high utility. Our experimental results show that our algorithm outperforms common heuristics on both synthetic and two real protein datasets.

cs.LG↗

arXiv2019

Understanding the Effectiveness of Ultrasonic Microphone Jammer

Recent works have explained the principle of using ultrasonic transmissions to jam nearby microphones. These signals are inaudible to nearby users, but leverage "hardware nonlinearity" to induce a jamming signal inside microphones that disrupts voice recordings. This has great implications on audio privacy protection. In this work, we gain a deeper understanding on the effectiveness of ultrasonic jammer under practical scenarios, with the goal of disabling both visible and hidden microphones in the surrounding area. We first experiment with existing jammer designs (both commercial products and that proposed by recent papers), and find that they all offer limited angular coverage, and can only target microphones in a particular direction. We overcome this limitation by building a circular transducer array as a wearable bracelet. It emits ultrasonic signals simultaneously from many directions, targeting surrounding microphones without needing to point at any. More importantly, as the bracelet moves with the wearer, its motion increases jamming coverage and diminishes blind spots (the fundamental problem facing any transducer array). We evaluate the jammer bracelet under practical scenarios, confirming that it can effectively disrupt visible and hidden microphones in the surrounding areas, preventing recognition of recorded speech. We also identify limitations and areas for improvement.

cs.CR↗

arXiv2019

Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval

This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples $y_{i}=(\mathbf{a}_{i}^{\top}\mathbf{x}^{\natural})^{2}$, $1\leq i\leq m$. This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficiency of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descent --- when randomly initialized --- yields an $ε$-accurate solution in $O\big(\log n+\log(1/ε)\big)$ iterations given nearly minimal samples, thus achieving near-optimal computational and sample complexities at once. This provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes. All of these are achieved by exploiting the statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain statistical dependency between the gradient descent iterates and the data.

stat.ML↗

arXiv2019

AED-Net: An Abnormal Event Detection Network

It is challenging to detect the anomaly in crowded scenes for quite a long time. In this paper, a self-supervised framework, abnormal event detection network (AED-Net), which is composed of PCAnet and kernel principal component analysis (kPCA), is proposed to address this problem. Using surveillance video sequences of different scenes as raw data, PCAnet is trained to extract high-level semantics of crowd's situation. Next, kPCA,a one-class classifier, is trained to determine anomaly of the scene. In contrast to some prevailing deep learning methods,the framework is completely self-supervised because it utilizes only video sequences in a normal situation. Experiments of global and local abnormal event detection are carried out on UMN and UCSD datasets, and competitive results with higher EER and AUC compared to other state-of-the-art methods are observed. Furthermore, by adding local response normalization (LRN) layer, we propose an improvement to original AED-Net. And it is proved to perform better by promoting the framework's generalization capacity according to the experiments.

cs.CV↗

arXiv2019

A One-Class Support Vector Machine Calibration Method for Time Series Change Point Detection

It is important to identify the change point of a system's health status, which usually signifies an incipient fault under development. The One-Class Support Vector Machine (OC-SVM) is a popular machine learning model for anomaly detection and hence could be used for identifying change points; however, it is sometimes difficult to obtain a good OC-SVM model that can be used on sensor measurement time series to identify the change points in system health status. In this paper, we propose a novel approach for calibrating OC-SVM models. The approach uses a heuristic search method to find a good set of input data and hyperparameters that yield a well-performing model. Our results on the C-MAPSS dataset demonstrate that OC-SVM can also achieve satisfactory accuracy in detecting change point in time series with fewer training data, compared to state-of-the-art deep learning approaches. In our case study, the OC-SVM calibrated by the proposed model is shown to be useful especially in scenarios with limited amount of training data.

cs.LG↗

arXiv2018

Understanding the Role of Adaptivity in Machine Teaching: The Case of Version Space Learners

In real-world applications of education, an effective teacher adaptively chooses the next example to teach based on the learner's current state. However, most existing work in algorithmic machine teaching focuses on the batch setting, where adaptivity plays no role. In this paper, we study the case of teaching consistent, version space learners in an interactive setting. At any time step, the teacher provides an example, the learner performs an update, and the teacher observes the learner's new state. We highlight that adaptivity does not speed up the teaching process when considering existing models of version space learners, such as "worst-case" (the learner picks the next hypothesis randomly from the version space) and "preference-based" (the learner picks hypothesis according to some global preference). Inspired by human teaching, we propose a new model where the learner picks hypotheses according to some local preference defined by the current hypothesis. We show that our model exhibits several desirable properties, e.g., adaptivity plays a key role, and the learner's transitions over hypotheses are smooth/interpretable. We develop efficient teaching algorithms and demonstrate our results via simulation and user studies.

cs.LG↗