Goto

Collaborating Authors

Zhang, Yuchen


On Localized Discrepancy for Domain Adaptation

arXiv.org Machine Learning

We propose the discrepancy-based generalization theories for unsupervised domain adaptation. Previous theories introduced distribution discrepancies defined as the supremum over complete hypothesis space. The hypothesis space may contain hypotheses that lead to unnecessary overestimation of the risk bound. This paper studies the localized discrepancies defined on the hypothesis space after localization. First, we show that these discrepancies have desirable properties. They could be significantly smaller than the pervious discrepancies. Their values will be different if we exchange the two domains, thus can reveal asymmetric transfer difficulties. Next, we derive improved generalization bounds with these discrepancies. We show that the discrepancies could influence the rate of the sample complexity. Finally, we further extend the localized discrepancies for achieving super transfer and derive generalization bounds that could be even more sample-efficient on source domain.


Information-theoretic lower bounds for distributed statistical estimation with communication constraints

Neural Information Processing Systems

We establish minimax risk lower bounds for distributed statistical estimation given a budget $B$ of the total number of bits that may be communicated. Such lower bounds in turn reveal the minimum amount of communication required by any procedure to achieve the classical optimal rate for statistical estimation. We study two classes of protocols in which machines send messages either independently or interactively. The lower bounds are established for a variety of problems, from estimating the mean of a population to estimating parameters in linear regression or binary classification. Papers published at the Neural Information Processing Systems Conference.


Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences

Neural Information Processing Systems

We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with $M \geq 3$ components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians. We prove that the log-likelihood value of these bad local maxima can be arbitrarily worse than that of any global optimum, thereby resolving an open question of Srebro (2007). Our second main result shows that the EM algorithm (or a first-order variant of it) with random initialization will converge to bad critical points with probability at least $1-e {-\Omega(M)}$. We further establish that a first-order variant of EM will not converge to strict saddle points almost surely, indicating that the poor performance of the first-order method can be attributed to the existence of bad local maxima rather than bad saddle points.


Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing

Neural Information Processing Systems

The Dawid-Skene estimator has been widely used for inferring the true labels from the noisy labels provided by non-expert crowdsourcing workers. However, since the estimator maximizes a non-convex log-likelihood function, it is hard to theoretically justify its performance. In this paper, we propose a two-stage efficient algorithm for multi-class crowd labeling problems. The first stage uses the spectral method to obtain an initial estimate of parameters. We show that our algorithm achieves the optimal convergence rate up to a logarithmic factor.


HPC AI500: A Benchmark Suite for HPC AI Systems

arXiv.org Artificial Intelligence

In recent years, with the trend of applying deep learning (DL) in high performance scientific computing, the unique characteristics of emerging DL workloads in HPC raise great challenges in designing, implementing HPC AI systems. The community needs a new yard stick for evaluating the future HPC systems. In this paper, we propose HPC AI500 --- a benchmark suite for evaluating HPC systems that running scientific DL workloads. Covering the most representative scientific fields, each workload from HPC AI500 is based on real-world scientific DL applications. Currently, we choose 14 scientific DL benchmarks from perspectives of application scenarios, data sets, and software stack. We propose a set of metrics for comprehensively evaluating the HPC AI systems, considering both accuracy, performance as well as power and cost. We provide a scalable reference implementation of HPC AI500. HPC AI500 is a part of the open-source AIBench project, the specification and source code are publicly available from \url{http://www.benchcouncil.org/AIBench/index.html}.


Bridging Theory and Algorithm for Domain Adaptation

arXiv.org Machine Learning

This paper addresses the problem of unsupervised domain adaption from theoretical and algorithmic perspectives. Existing domain adaptation theories naturally imply minimax optimization algorithms, which connect well with the adversarial-learning based domain adaptation methods. However, several disconnections still form the gap between theory and algorithm. We extend previous theories (Ben-David et al., 2010; Mansour et al., 2009c) to multiclass classification in domain adaptation, where classifiers based on scoring functions and margin loss are standard algorithmic choices. We introduce a novel measurement, margin disparity discrepancy, that is tailored both to distribution comparison with asymmetric margin loss, and to minimax optimization for easier training. Using this discrepancy, we derive new generalization bounds in terms of Rademacher complexity. Our theory can be seamlessly transformed into an adversarial learning algorithm for domain adaptation, successfully bridging the gap between theory and algorithm. A series of empirical studies show that our algorithm achieves the state-of-the-art accuracies on challenging domain adaptation tasks.


Defending against Whitebox Adversarial Attacks via Randomized Discretization

arXiv.org Machine Learning

Adversarial perturbations dramatically decrease the accuracy of state-of-the-art image classifiers. In this paper, we propose and analyze a simple and computationally efficient defense strategy: inject random Gaussian noise, discretize each pixel, and then feed the result into any pre-trained classifier. Theoretically, we show that our randomized discretization strategy reduces the KL divergence between original and adversarial inputs, leading to a lower bound on the classification accuracy of any classifier against any (potentially whitebox) $\ell_\infty$-bounded adversarial attack. Empirically, we evaluate our defense on adversarial examples generated by a strong iterative PGD attack. On ImageNet, our defense is more robust than adversarially-trained networks and the winning defenses of the NIPS 2017 Adversarial Attacks & Defenses competition.


A Hitting Time Analysis of Stochastic Gradient Langevin Dynamics

arXiv.org Machine Learning

We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for non-convex optimization. The algorithm performs stochastic gradient descent, where in each step it injects appropriately scaled Gaussian noise to the update. We analyze the algorithm's hitting time to an arbitrary subset of the parameter space. Two results follow from our general theory: First, we prove that for empirical risk minimization, if the empirical risk is point-wise close to the (smooth) population risk, then the algorithm achieves an approximate local minimum of the population risk in polynomial time, escaping suboptimal local minima that only exist in the empirical risk. Second, we show that SGLD improves on one of the best known learnability results for learning linear classifiers under the zero-one loss.


Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences

Neural Information Processing Systems

We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with $M \geq 3$ components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians. We prove that the log-likelihood value of these bad local maxima can be arbitrarily worse than that of any global optimum, thereby resolving an open question of Srebro (2007). Our second main result shows that the EM algorithm (or a first-order variant of it) with random initialization will converge to bad critical points with probability at least $1-e^{-\Omega(M)}$. We further establish that a first-order variant of EM will not converge to strict saddle points almost surely, indicating that the poor performance of the first-order method can be attributed to the existence of bad local maxima rather than bad saddle points. Overall, our results highlight the necessity of careful initialization when using the EM algorithm in practice, even when applied in highly favorable settings.


Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences

arXiv.org Machine Learning

We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with $M \geq 3$ components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians. We prove that the log-likelihood value of these bad local maxima can be arbitrarily worse than that of any global optimum, thereby resolving an open question of Srebro (2007). Our second main result shows that the EM algorithm (or a first-order variant of it) with random initialization will converge to bad critical points with probability at least $1-e^{-\Omega(M)}$. We further establish that a first-order variant of EM will not converge to strict saddle points almost surely, indicating that the poor performance of the first-order method can be attributed to the existence of bad local maxima rather than bad saddle points. Overall, our results highlight the necessity of careful initialization when using the EM algorithm in practice, even when applied in highly favorable settings.