arXiv subjects

Yuxin Chen

Publications and source records attributed to Yuxin Chen.

At least 253 records · Page 14Linked to original sources

arXiv2021

Learning Mixtures of Low-Rank Models

We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings -- low-rank matrix sensing and mixed linear regression -- by bringing latent variables (i.e. unknown labels) and structural priors (i.e. low-rank structures) into consideration. To cope with the non-convexity issues arising from unlabelled heterogeneous data and low-complexity structure, we develop a three-stage meta-algorithm that is guaranteed to recover the unknown matrices with near-optimal sample and computational complexities under Gaussian designs. In addition, the proposed algorithm is provably stable against random noise. We complement the theoretical studies with empirical evidence that confirms the efficacy of our algorithm.

stat.ML↗

arXiv2021

Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Data

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as robust principal component analysis (robust PCA), finds applications in various domains. Despite the wide applicability of convex relaxation, the available statistical support (particularly the stability analysis vis-à-vis random noise) remains highly suboptimal, which we strengthen in this paper. When the unknown matrix is well-conditioned, incoherent, and of constant rank, we demonstrate that a principled convex program achieves near-optimal statistical accuracy, in terms of both the Euclidean loss and the $\ell_{\infty}$ loss. All of this happens even when nearly a constant fraction of observations are corrupted by outliers with arbitrary magnitudes. The key analysis idea lies in bridging the convex program in use and an auxiliary nonconvex optimization algorithm, and hence the title of this paper.

stat.ML↗

arXiv2021

The Teaching Dimension of Kernel Perceptron

Algorithmic machine teaching has been studied under the linear setting where exact teaching is possible. However, little is known for teaching nonlinear learners. Here, we establish the sample complexity of teaching, aka teaching dimension, for kernelized perceptrons for different families of feature maps. As a warm-up, we show that the teaching complexity is $Θ(d)$ for the exact teaching of linear perceptrons in $\mathbb{R}^d$, and $Θ(d^k)$ for kernel perceptron with a polynomial kernel of order $k$. Furthermore, under certain smooth assumptions on the data distribution, we establish a rigorous bound on the complexity for approximately teaching a Gaussian kernel perceptron. We provide numerical examples of the optimal (approximate) teaching set under several canonical settings for linear, polynomial and Gaussian kernel perceptrons.

cs.LG↗

arXiv2020

Subspace Estimation from Unbalanced and Incomplete Data Matrices: $\ell_{2,\infty}$ Statistical Guarantees

This paper is concerned with estimating the column space of an unknown low-rank matrix $\boldsymbol{A}^{\star}\in\mathbb{R}^{d_{1}\times d_{2}}$, given noisy and partial observations of its entries. There is no shortage of scenarios where the observations -- while being too noisy to support faithful recovery of the entire matrix -- still convey sufficient information to enable reliable estimation of the column space of interest. This is particularly evident and crucial for the highly unbalanced case where the column dimension $d_{2}$ far exceeds the row dimension $d_{1}$, which is the focal point of the current paper. We investigate an efficient spectral method, which operates upon the sample Gram matrix with diagonal deletion. While this algorithmic idea has been studied before, we establish new statistical guarantees for this method in terms of both $\ell_{2}$ and $\ell_{2,\infty}$ estimation accuracy, which improve upon prior results if $d_{2}$ is substantially larger than $d_{1}$. To illustrate the effectiveness of our findings, we derive matching minimax lower bounds with respect to the noise levels, and develop consequences of our general theory for three applications of practical importance: (1) tensor completion from noisy data, (2) covariance estimation / principal component analysis with missing data, and (3) community recovery in bipartite graphs. Our theory leads to improved performance guarantees for all three cases.

math.ST↗

arXiv2020

Average-case Complexity of Teaching Convex Polytopes via Halfspace Queries

We examine the task of locating a target region among those induced by intersections of $n$ halfspaces in $\mathbb{R}^d$. This generic task connects to fundamental machine learning problems, such as training a perceptron and learning a $ϕ$-separable dichotomy. We investigate the average teaching complexity of the task, i.e., the minimal number of samples (halfspace queries) required by a teacher to help a version-space learner in locating a randomly selected target. As our main result, we show that the average-case teaching complexity is $Θ(d)$, which is in sharp contrast to the worst-case teaching complexity of $Θ(n)$. If instead, we consider the average-case learning complexity, the bounds have a dependency on $n$ as $Θ(n)$ for \tt{i.i.d.} queries and $Θ(d \log(n))$ for actively chosen queries by the learner. Our proof techniques are based on novel insights from computational geometry, which allow us to count the number of convex polytopes and faces in a Euclidean space depending on the arrangement of halfspaces. Our insights allow us to establish a tight bound on the average-case complexity for $ϕ$-separable dichotomies, which generalizes the known $\mathcal{O}(d)$ bound on the average number of "extreme patterns" in the classical computational geometry literature (Cover, 1965).

cs.LG↗

arXiv2020

Preference-Based Batch and Sequential Teaching

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, 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) and the sequential settings (e.g., local preference-based model). To better understand the connections between these models, we develop a novel framework that 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. We analyze several properties of the teaching complexity parameter $TD(σ)$ associated with different families of the preference functions, e.g., comparison to the VC dimension of the hypothesis class and additivity/sub-additivity of $TD(σ)$ over disjoint domains. Finally, we identify preference functions inducing a novel family of sequential models with teaching complexity linear in the VC dimension: this is in contrast to the best-known complexity result for the batch models, which is quadratic in the VC dimension.

cs.LG↗

arXiv2020

Communication-Efficient Distributed Optimization in Networks with Gradient Tracking and Variance Reduction

There is growing interest in large-scale machine learning and optimization over decentralized networks, e.g. in the context of multi-agent learning and federated learning. Due to the imminent need to alleviate the communication burden, the investigation of communication-efficient distributed optimization algorithms - particularly for empirical risk minimization - has flourished in recent years. A large fraction of these algorithms have been developed for the master/slave setting, relying on a central parameter server that can communicate with all agents. This paper focuses on distributed optimization over networks, or decentralized optimization, where each agent is only allowed to aggregate information from its neighbors. By properly adjusting the global gradient estimate via local averaging in conjunction with proper correction, we develop a communication-efficient approximate Newton-type method Network-DANE, which generalizes DANE to the decentralized scenarios. Our key ideas can be applied in a systematic manner to obtain decentralized versions of other master/slave distributed algorithms. A notable development is Network-SVRG/SARAH, which employs variance reduction to further accelerate local computation. We establish linear convergence of Network-DANE and Network-SVRG for strongly convex losses, and Network-SARAH for quadratic losses, which shed light on the impacts of data homogeneity, network connectivity, and local averaging upon the rate of convergence. We further extend Network-DANE to composite optimization by allowing a nonsmooth penalty term. Numerical evidence is provided to demonstrate the appealing performance of our algorithms over competitive baselines, in terms of both communication and computation efficiency. Our work suggests that performing a certain amount of local communications and computations per iteration can substantially improve the overall efficiency.

stat.ML↗

arXiv2020

Using Ensemble Classifiers to Detect Incipient Anomalies

Incipient anomalies present milder symptoms compared to severe ones, and are more difficult to detect and diagnose due to their close resemblance to normal operating conditions. The lack of incipient anomaly examples in the training data can pose severe risks to anomaly detection methods that are built upon Machine Learning (ML) techniques, because these anomalies can be easily mistaken as normal operating conditions. To address this challenge, we propose to utilize the uncertainty information available from ensemble learning to identify potential misclassified incipient anomalies. We show in this paper that ensemble learning methods can give improved performance on incipient anomalies and identify common pitfalls in these models through extensive experiments on two real-world datasets. Then, we discuss how to design more effective ensemble models for detecting incipient anomalies.

cs.LG↗

arXiv2020

Exploiting Uncertainties from Ensemble Learners to Improve Decision-Making in Healthcare AI

Ensemble learning is widely applied in Machine Learning (ML) to improve model performance and to mitigate decision risks. In this approach, predictions from a diverse set of learners are combined to obtain a joint decision. Recently, various methods have been explored in literature for estimating decision uncertainties using ensemble learning; however, determining which metrics are a better fit for certain decision-making applications remains a challenging task. In this paper, we study the following key research question in the selection of uncertainty metrics: when does an uncertainty metric outperforms another? We answer this question via a rigorous analysis of two commonly used uncertainty metrics in ensemble learning, namely ensemble mean and ensemble variance. We show that, under mild assumptions on the ensemble learners, ensemble mean is preferable with respect to ensemble variance as an uncertainty metric for decision making. We empirically validate our assumptions and theoretical results via an extensive case study: the diagnosis of referable diabetic retinopathy.

cs.LG↗

arXiv2020

Are Ensemble Classifiers Powerful Enough for the Detection and Diagnosis of Intermediate-Severity Faults?

Intermediate-Severity (IS) faults present milder symptoms compared to severe faults, and are more difficult to detect and diagnose due to their close resemblance to normal operating conditions. The lack of IS fault examples in the training data can pose severe risks to Fault Detection and Diagnosis (FDD) methods that are built upon Machine Learning (ML) techniques, because these faults can be easily mistaken as normal operating conditions. Ensemble models are widely applied in ML and are considered promising methods for detecting out-of-distribution (OOD) data. We identify common pitfalls in these models through extensive experiments with several popular ensemble models on two real-world datasets. Then, we discuss how to design more effective ensemble models for detecting and diagnosing IS faults.

cs.LG↗

arXiv2020

Modeling, Simulation and Implementation of a Bird-Inspired Morphing Wing Aircraft

We present a design of a bird-inspired morphing wing aircraft, including bionic research, modeling, simulation and flight experiments. Inspired by birds and activated by a planar linkage, our proposed aircraft has three key states: gliding, descending and high-maneuverability. We build the aerodynamic model of the aircraft and analyze its mechanisms to find out a group of optimized parameters. Furthermore, we validate our design by Computational Fluid Dynamics (CFD) simulation based on Lattice-Boltzmann technology and determine three phases of the planar linkage for the three states. Lastly, we manufacture a prototype and conduct flight experiments to test the performance of the aircraft.

eess.SY↗

arXiv2020

Uncertainty quantification for nonconvex tensor completion: Confidence intervals, heteroscedasticity and optimality

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion -- the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation algorithm proposed by Cai et al. (2019), we characterize the distribution of this nonconvex estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and the unknown tensor factors. The proposed inferential procedure enjoys several important features: (1) it is fully adaptive to noise heteroscedasticity, and (2) it is data-driven and automatically adapts to unknown noise distributions. Furthermore, our findings unveil the statistical optimality of nonconvex tensor completion: it attains un-improvable $\ell_{2}$ accuracy -- including both the rates and the pre-constants -- when estimating both the unknown tensor and the underlying tensor factors.

stat.ML↗

arXiv2020

Understanding the Power and Limitations of Teaching with Imperfect Knowledge

Machine teaching studies the interaction between a teacher and a student/learner where the teacher selects training examples for the learner to learn a specific task. The typical assumption is that the teacher has perfect knowledge of the task---this knowledge comprises knowing the desired learning target, having the exact task representation used by the learner, and knowing the parameters capturing the learning dynamics of the learner. Inspired by real-world applications of machine teaching in education, we consider the setting where teacher's knowledge is limited and noisy, and the key research question we study is the following: When does a teacher succeed or fail in effectively teaching a learner using its imperfect knowledge? We answer this question by showing connections to how imperfect knowledge affects the teacher's solution of the corresponding machine teaching problem when constructing optimal teaching sets. Our results have important implications for designing robust teaching algorithms for real-world applications.

cs.LG↗

arXiv2020

Asymmetry Helps: Eigenvalue and Eigenvector Analyses of Asymmetrically Perturbed Low-Rank Matrices

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\mathbf{M}$ is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\star}$ is composed of zero-mean independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise, for example, when we have two independent samples for each entry of $\mathbf{M}^{\star}$ and arrange them into an {\em asymmetric} data matrix $\mathbf{M}$. The aim is to estimate the leading eigenvalue and eigenvector of $\mathbf{M}^{\star}$. We demonstrate that the leading eigenvalue of the data matrix $\mathbf{M}$ can be $O(\sqrt{n})$ times more accurate --- up to some log factor --- than its (unadjusted) leading singular value in eigenvalue estimation. Further, the perturbation of any linear form of the leading eigenvector of $\mathbf{M}$ --- say, entrywise eigenvector perturbation --- is provably well-controlled. This eigen-decomposition approach is fully adaptive to heteroscedasticity of noise without the need of careful bias correction or any prior knowledge about the noise variance. We also provide partial theory for the more general rank-$r$ case. The takeaway message is this: arranging the data samples in an asymmetric manner and performing eigen-decomposition could sometimes be beneficial.

math.ST↗

arXiv2020

A Financial Service Chatbot based on Deep Bidirectional Transformers

We develop a chatbot using Deep Bidirectional Transformer models (BERT) to handle client questions in financial investment customer service. The bot can recognize 381 intents, and decides when to say "I don't know" and escalates irrelevant/uncertain questions to human operators. Our main novel contribution is the discussion about uncertainty measure for BERT, where three different approaches are systematically compared on real problems. We investigated two uncertainty metrics, information entropy and variance of dropout sampling in BERT, followed by mixed-integer programming to optimize decision thresholds. Another novel contribution is the usage of BERT as a language model in automatic spelling correction. Inputs with accidental spelling errors can significantly decrease intent classification performance. The proposed approach combines probabilities from masked language model and word edit distances to find the best corrections for misspelled words. The chatbot and the entire conversational AI system are developed using open-source tools, and deployed within our company's intranet. The proposed approach can be useful for industries seeking similar in-house solutions in their specific business domains. We share all our code and a sample chatbot built on a public dataset on Github.

cs.CL↗

arXiv2020

Adaptive Teaching of Temporal Logic Formulas to Learners with Preferences

Machine teaching is an algorithmic framework for teaching a target hypothesis via a sequence of examples or demonstrations. We investigate machine teaching for temporal logic formulas -- a novel and expressive hypothesis class amenable to time-related task specifications. In the context of teaching temporal logic formulas, an exhaustive search even for a myopic solution takes exponential time (with respect to the time span of the task). We propose an efficient approach for teaching parametric linear temporal logic formulas. Concretely, we derive a necessary condition for the minimal time length of a demonstration to eliminate a set of hypotheses. Utilizing this condition, we propose a myopic teaching algorithm by solving a sequence of integer programming problems. We further show that, under two notions of teaching complexity, the proposed algorithm has near-optimal performance. The results strictly generalize the previous results on teaching preference-based version space learners. We evaluate our algorithm extensively under a variety of learner types (i.e., learners with different preference models) and interactive protocols (e.g., batched and adaptive). The results show that the proposed algorithms can efficiently teach a given target temporal logic formula under various settings, and that there are significant gains of teaching efficacy when the teacher adapts to the learner's current hypotheses or uses oracles.

cs.AI↗

arXiv2020

Et Tu Alexa? When Commodity WiFi Devices Turn into Adversarial Motion Sensors

Our work demonstrates a new set of silent reconnaissance attacks, which leverages the presence of commodity WiFi devices to track users inside private homes and offices, without compromising any WiFi network, data packets, or devices. We show that just by sniffing existing WiFi signals, an adversary can accurately detect and track movements of users inside a building. This is made possible by our new signal model that links together human motion near WiFi transmitters and variance of multipath signal propagation seen by the attacker sniffer outside of the property. The resulting attacks are cheap, highly effective, and yet difficult to detect. We implement the attack using a single commodity smartphone, deploy it in 11 real-world offices and residential apartments, and show it is highly effective. Finally, we evaluate potential defenses, and propose a practical and effective defense based on AP signal obfuscation.

cs.CR↗

arXiv2019

Pixel Level Data Augmentation for Semantic Image Segmentation using Generative Adversarial Networks

Semantic segmentation is one of the basic topics in computer vision, it aims to assign semantic labels to every pixel of an image. Unbalanced semantic label distribution could have a negative influence on segmentation accuracy. In this paper, we investigate using data augmentation approach to balance the semantic label distribution in order to improve segmentation performance. We propose using generative adversarial networks (GANs) to generate realistic images for improving the performance of semantic segmentation networks. Experimental results show that the proposed method can not only improve segmentation performance on those classes with low accuracy, but also obtain 1.3% to 2.1% increase in average segmentation accuracy. It shows that this augmentation method can boost accuracy and be easily applicable to any other segmentation models.

cs.CV↗