arXiv subjects

Yuchen Wu

Publications and source records attributed to Yuchen Wu.

84 records · Page 5Linked to original sources

arXiv2023

Adversarial Examples in Random Neural Networks with General Activations

A substantial body of empirical work documents the lack of robustness in deep learning models to adversarial examples. Recent theoretical work proved that adversarial examples are ubiquitous in two-layers networks with sub-exponential width and ReLU or smooth activations, and multi-layer ReLU networks with sub-exponential width. We present a result of the same type, with no restriction on width and for general locally Lipschitz continuous activations. More precisely, given a neural network $f(\,\cdot\,;{\boldsymbol θ})$ with random weights ${\boldsymbol θ}$, and feature vector ${\boldsymbol x}$, we show that an adversarial example ${\boldsymbol x}'$ can be found with high probability along the direction of the gradient $\nabla_{\boldsymbol x}f({\boldsymbol x};{\boldsymbol θ})$. Our proof is based on a Gaussian conditioning technique. Instead of proving that $f$ is approximately linear in a neighborhood of ${\boldsymbol x}$, we characterize the joint distribution of $f({\boldsymbol x};{\boldsymbol θ})$ and $f({\boldsymbol x}';{\boldsymbol θ})$ for ${\boldsymbol x}' = {\boldsymbol x}-s({\boldsymbol x})\nabla_{\boldsymbol x}f({\boldsymbol x};{\boldsymbol θ})$.

cs.LG↗

arXiv2023

Distribution Aligned Feature Clustering for Zero-Shot Sketch-Based Image Retrieval

Zero-Shot Sketch-Based Image Retrieval (ZS-SBIR) is a challenging cross-modal retrieval task. In prior arts, the retrieval is conducted by sorting the distance between the query sketch and each image in the gallery. However, the domain gap and the zero-shot setting make neural networks hard to generalize. This paper tackles the challenges from a new perspective: utilizing gallery image features. We propose a Cluster-then-Retrieve (ClusterRetri) method that performs clustering on the gallery images and uses the cluster centroids as proxies for retrieval. Furthermore, a distribution alignment loss is proposed to align the image and sketch features with a common Gaussian distribution, reducing the domain gap. Despite its simplicity, our proposed method outperforms the state-of-the-art methods by a large margin on popular datasets, e.g., up to 31% and 39% relative improvement of mAP@all on the Sketchy and TU-Berlin datasets.

cs.CV↗

arXiv2022

Picking Up Speed: Continuous-Time Lidar-Only Odometry using Doppler Velocity Measurements

Frequency-Modulated Continuous-Wave (FMCW) lidar is a recently emerging technology that additionally enables per-return instantaneous relative radial velocity measurements via the Doppler effect. In this letter, we present the first continuous-time lidar-only odometry algorithm using these Doppler velocity measurements from an FMCW lidar to aid odometry in geometrically degenerate environments. We apply an existing continuous-time framework that efficiently estimates the vehicle trajectory using Gaussian process regression to compensate for motion distortion due to the scanning-while-moving nature of any mechanically actuated lidar (FMCW and non-FMCW). We evaluate our proposed algorithm on several real-world datasets, including publicly available ones and datasets we collected. Our algorithm outperforms the only existing method that also uses Doppler velocity measurements, and we study difficult conditions where including this extra information greatly improves performance. We additionally demonstrate state-of-the-art performance of lidar-only odometry with and without using Doppler velocity measurements in nominal conditions. Code for this project can be found at: https://github.com/utiasASRL/steam_icp.

cs.RO↗

arXiv2022

Along Similar Lines: Local Obstacle Avoidance for Long-term Autonomous Path Following

Visual Teach and Repeat 3 (VT&R3), a generalization of stereo VT&R, achieves long-term autonomous path-following using topometric mapping and localization from a single rich sensor stream. In this paper, we improve the capabilities of a LiDAR implementation of VT&R3 to reliably detect and avoid obstacles in changing environments. Our architecture simplifies the obstacle-perception problem to that of place-dependent change detection. We then extend the behaviour of generic sample-based motion planners to better suit the teach-and-repeat problem structure by introducing a new edge-cost metric paired with a curvilinear planning space. The resulting planner generates naturally smooth paths that avoid local obstacles while minimizing lateral path deviation to best exploit prior terrain knowledge. While we use the method with VT&R, it can be generalized to suit arbitrary path-following applications. Experimental results from online run-time analysis, unit testing, and qualitative experiments on a differential drive robot show the promise of the technique for reliable long-term autonomous operation in complex unstructured environments.

cs.RO↗

arXiv2022

Fundamental Limits of Low-Rank Matrix Estimation with Diverging Aspect Ratios

We consider the problem of estimating the factors of a low-rank $n \times d$ matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances. Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal. Here, we characterize the asymptotics of the minimum estimation error under the assumption that the distribution of the entries is known to the statistician. Our results apply to the high-dimensional regime $n, d \to \infty$ and $d / n \to \infty$ (or $d / n \to 0$) and generalize earlier work that focused on the proportional asymptotics $n, d \to \infty$, $d / n \to δ\in (0, \infty)$. We outline an interesting signal strength regime in which $d / n \to \infty$ and partial recovery is possible for the left singular vectors while impossible for the right singular vectors. We illustrate the general theory by deriving consequences for Gaussian mixture clustering and carrying out a numerical study on genomics data.

math.ST↗

arXiv2022

Statistically Optimal First Order Algorithms: A Proof via Orthogonalization

We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ (and possibly some labels ${\boldsymbol y}\in{\mathbb R}^n$) and would like to estimate a coefficient vector ${\boldsymbol θ}\in{\mathbb R}^d$ (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g., sparse regression). First order methods proceed by iteratively multiplying current estimates by ${\boldsymbol X}$ or its transpose. Examples include gradient descent or its accelerated variants. Celentano, Montanari, Wu proved that for any constant number of iterations (matrix vector multiplications), the optimal first order algorithm is a specific approximate message passing algorithm (known as `Bayes AMP'). The error of this estimator can be characterized in the high-dimensional asymptotics $n,d\to\infty$, $n/d\toδ$, and provides a lower bound to the estimation error of any first order algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of first order algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof technique does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications.

stat.CO↗

arXiv2021

Scalable Hierarchical Agglomerative Clustering

The applicability of agglomerative clustering, for inferring both hierarchical and flat clustering, is limited by its scalability. Existing scalable hierarchical clustering methods sacrifice quality for speed and often lead to over-merging of clusters. In this paper, we present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points. We perform a detailed theoretical analysis, showing that under mild separability conditions our algorithm can not only recover the optimal flat partition, but also provide a two-approximation to non-parametric DP-Means objective. This introduces a novel application of hierarchical clustering as an approximation algorithm for the non-parametric clustering objective. We additionally relate our algorithm to the classic hierarchical agglomerative clustering method. We perform extensive empirical experiments in both hierarchical and flat clustering settings and show that our proposed approach achieves state-of-the-art results on publicly available clustering benchmarks. Finally, we demonstrate our method's scalability by applying it to a dataset of 30 billion queries. Human evaluation of the discovered clusters show that our method finds better quality of clusters than the current state-of-the-art.

cs.LG↗

arXiv2021

Streaming Belief Propagation for Community Detection

The community detection problem requires to cluster the nodes of a network into a small number of well-connected "communities". There has been substantial recent progress in characterizing the fundamental statistical limits of community detection under simple stochastic block models. However, in real-world applications, the network structure is typically dynamic, with nodes that join over time. In this setting, we would like a detection algorithm to perform only a limited number of updates at each node arrival. While standard voting approaches satisfy this constraint, it is unclear whether they exploit the network information optimally. We introduce a simple model for networks growing over time which we refer to as streaming stochastic block model (StSBM). Within this model, we prove that voting algorithms have fundamental limitations. We also develop a streaming belief-propagation (StreamBP) approach, for which we prove optimality in certain regimes. We validate our theoretical findings on synthetic and real data.

stat.ML↗

arXiv2020

Shaping Rewards for Reinforcement Learning with Imperfect Demonstrations using Generative Models

The potential benefits of model-free reinforcement learning to real robotics systems are limited by its uninformed exploration that leads to slow convergence, lack of data-efficiency, and unnecessary interactions with the environment. To address these drawbacks we propose a method that combines reinforcement and imitation learning by shaping the reward function with a state-and-action-dependent potential that is trained from demonstration data, using a generative model. We show that this accelerates policy learning by specifying high-value areas of the state and action space that are worth exploring first. Unlike the majority of existing methods that assume optimal demonstrations and incorporate the demonstration data as hard constraints on policy optimization, we instead incorporate demonstration data as advice in the form of a reward shaping potential trained as a generative model of states and actions. In particular, we examine both normalizing flows and Generative Adversarial Networks to represent these potentials. We show that, unlike many existing approaches that incorporate demonstrations as hard constraints, our approach is unbiased even in the case of suboptimal and noisy demonstrations. We present an extensive range of simulations, as well as experiments on the Franka Emika 7DOF arm, to demonstrate the practicality of our method.

cs.RO↗

arXiv2020

The estimation error of general first order methods

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are the fundamental limits to these approaches? This question is well understood from an optimization viewpoint when the underlying objective is convex. Work in this area characterizes the gap to global optimality as a function of the number of iterations. However, these results have only indirect implications in terms of the gap to statistical optimality. Here we consider two families of high-dimensional estimation problems: high-dimensional regression and low-rank matrix estimation, and introduce a class of `general first order methods' that aim at efficiently estimating the underlying parameters. This class of algorithms is broad enough to include classical first order optimization (for convex and non-convex objectives), but also other types of algorithms. Under a random design assumption, we derive lower bounds on the estimation error that hold in the high-dimensional asymptotics in which both the number of observations and the number of parameters diverge. These lower bounds are optimal in the sense that there exist algorithms whose estimation error matches the lower bounds up to asymptotically negligible terms. We illustrate our general results through applications to sparse phase retrieval and sparse principal component analysis.

stat.ML↗

arXiv2016

The Effect of Pets on Happiness: A Data-Driven Approach via Large-Scale Social Media

Psychologists have demonstrated that pets have a positive impact on owners' happiness. For example, lonely people are often advised to have a dog or cat to quell their social isolation. Conventional psychological research methods of analyzing this phenomenon are mostly based on surveys or self-reported questionnaires, which are time-consuming and lack of scalability. Utilizing social media as an alternative and complimentary resource could potentially address both issues and provide different perspectives on this psychological investigation. In this paper, we propose a novel and effective approach that exploits social media to study the effect of pets on owners' happiness. The proposed framework includes three major components: 1) collecting user-level data from Instagram consisting of about 300,000 images from 2905 users; 2) constructing a convolutional neural network (CNN) for pets classification, and combined with timeline information, further identifying pet owners and the control group; 3) measuring the confidence score of happiness by detecting and analyzing selfie images. Furthermore, various factors of demographics are employed to analyze the fine-grained effects of pets on happiness. Our experimental results demonstrate the effectiveness of the proposed approach and we believe that this approach can be applied to other related domains as a large-scale, high-confidence methodology of user activity analysis through social media.

cs.SI↗

arXiv2016

Higher-Order Kullback-Leibler Aggregation of Markov Chains

We consider the problem of reducing a first-order Markov chain on a large alphabet to a higher-order Markov chain on a small alphabet. We present information-theoretic cost functions that are related to predictability and lumpability, show relations between these cost functions, and discuss heuristics to minimize them. Our experiments suggest that the generalization to higher orders is useful for model reduction in reliability analysis and natural language processing.

cs.IT↗