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We develop a rigorous approach for using a set of arbitrarily correlated weak supervision sources in order to solve a multiclass classification task when only a very small set of labeled data is available. Our learning algorithm provably converges to a model that has minimum empirical risk with respect to an adversarial choice over feasible labelings for a set of unlabeled data, where the feasibility of a labeling is computed through constraints defined by rigorously estimated statistics of the weak supervision sources. We show theoretical guarantees for this approach that depend on the information provided by the weak supervision sources. Notably, this method does not require the weak supervision sources to have the same labeling space as the multiclass classification task. We demonstrate the effectiveness of our approach with experiments on various image classification tasks. 

Recent works apply Graph Neural Networks (GNNs) to graph matching tasks and show promising results. Considering that model outputs are complex matchings, we devise several techniques to improve the learning of GNNs and obtain a new model, Stochastic Iterative Graph MAtching (SIGMA). Our model predicts a distribution of matchings, instead of a single matching, for a graph pair so the model can explore several probable matchings. We further introduce a novel multi-step matching procedure, which learns how to refine a graph pair’s matching results incrementally. The model also includes dummy nodes so that the model does not have to find matchings for nodes without correspondence. We fit this model to data via scalable stochastic optimization. We conduct extensive experiments across synthetic graph datasets as well as biochemistry and computer vision applications. Across all tasks, our results show that SIGMA can produce significantly improved graph matching results compared to state-of-the-art models. Ablation studies verify that each of our components (stochastic training, iterative matching, and dummy nodes) offers noticeable improvement. 

Unsupervised learning of the Dawid-Skene (D&S) model from noisy, incomplete and crowdsourced annotations has been a long-standing challenge, and is a critical step towards reliably labeling massive data. A recent work takes a coupled nonnegative matrix factorization (CNMF) perspective, and shows appealing features: It ensures the identifiability of the D&S model and enjoys low sample complexity, as only the estimates of the co-occurrences of annotator labels are involved. However, the identifiability holds only when certain somewhat restrictive conditions are met in the context of crowdsourcing. Optimizing the CNMF criterion is also costly—and convergence assurances are elusive. This work recasts the pairwise co-occurrence based D&S model learning problem as a symmetric NMF (SymNMF) problem—which offers enhanced identifiability relative to CNMF. In practice, the SymNMF model is often (largely) incomplete, due to the lack of co-labeled items by some annotators. Two lightweight algorithms are proposed for co-occurrence imputation. Then, a low-complexity shifted rectified linear unit (ReLU)-empowered SymNMF algorithm is proposed to identify the D&S model. Various performance characterizations (e.g., missing co-occurrence recoverability, stability, and convergence) and evaluations are also presented. 

The label noise transition matrix, characterizing the probabilities of a training instance being wrongly annotated, is crucial to designing popular solutions to learning with noisy labels. Existing works heavily rely on finding “anchor points” or their approximates, defined as instances belonging to a particular class almost surely. Nonetheless, finding anchor points remains a non-trivial task, and the estimation accuracy is also often throttled by the number of available anchor points. In this paper, we propose an alternative option to the above task. Our main contribution is the discovery of an efficient estimation procedure based on a clusterability condition. We prove that with clusterable representations of features, using up to third-order consensuses of noisy labels among neighbor representations is sufficient to estimate a unique transition matrix. Compared with methods using anchor points, our approach uses substantially more instances and benefits from a much better sample complexity. We demonstrate the estimation accuracy and advantages of our estimates using both synthetic noisy labels (on CIFAR-10/100) and real human-level noisy labels (on Clothing1M and our self-collected human-annotated CIFAR-10). Our code and human-level noisy CIFAR-10 labels are available at https://github.com/UCSC-REAL/HOC. 

Incorporating graph side information into recommender systems has been widely used to better predict ratings, but relatively few works have focused on theoretical guarantees. Ahn et al. (2018) firstly characterized the optimal sample complexity in the presence of graph side information, but the results are limited due to strict, unrealistic assumptions made on the unknown latent preference matrix and the structure of user clusters. In this work, we propose a new model in which 1) the unknown latent preference matrix can have any discrete values, and 2) users can be clustered into multiple clusters, thereby relaxing the assumptions made in prior work. Under this new model, we fully characterize the optimal sample complexity and develop a computationally-efficient algorithm that matches the optimal sample complexity. Our algorithm is robust to model errors and outperforms the existing algorithms in terms of prediction performance on both synthetic and real data. 

Inspired by the demands of real-time climate and weather forecasting, we develop optimistic online learning algorithms that require no parameter tuning and have optimal regret guarantees under delayed feedback. Our algorithms—DORM, DORM+, and AdaHedgeD—arise from a novel reduction of delayed online learning to optimistic online learning that reveals how optimistic hints can mitigate the regret penalty caused by delay. We pair this delay-as-optimism perspective with a new analysis of optimistic learning that exposes its robustness to hinting errors and a new meta-algorithm for learning effective hinting strategies in the presence of delay. We conclude by benchmarking our algorithms on four subseasonal climate forecasting tasks, demonstrating low regret relative to state-of-the-art forecasting models. 

Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the best of our knowledge, the theoretical guarantees of FL concerning neural networks with explicit forms and multi-step updates are unexplored. Nevertheless, training analysis of neural networks in FL is non-trivial for two reasons: first, the objective loss function we are optimizing is non-smooth and non-convex, and second, we are even not updating in the gradient direction. Existing convergence results for gradient descent-based methods heavily rely on the fact that the gradient direction is used for updating. The current paper presents a new class of convergence analysis for FL, Federated Neural Tangent Kernel (FL-NTK), which corresponds to overparamterized ReLU neural networks trained by gradient descent in FL and is inspired by the analysis in Neural Tangent Kernel (NTK). Theoretically, FL-NTK converges to a global-optimal solution at a linear rate with properly tuned learning parameters. Furthermore, with proper distributional assumptions, FL-NTK can also achieve good generalization. The proposed theoretical analysis scheme can be generalized to more complex neural networks. 

Black-box variational inference algorithms use stochastic sampling to analyze diverse statistical models, like those expressed in probabilistic programming languages, without model-specific derivations. While the popular score-function estimator computes unbiased gradient estimates, its variance is often unacceptably large, especially in models with discrete latent variables. We propose a stochastic natural gradient estimator that is as broadly applicable and unbiased, but improves efficiency by exploiting the curvature of the variational bound, and provably reduces variance by marginalizing discrete latent variables. Our marginalized stochastic natural gradients have intriguing connections to classic coordinate ascent variational inference, but allow parallel updates of variational parameters, and provide superior convergence guarantees relative to naive Monte Carlo approximations. We integrate our method with the probabilistic programming language Pyro and evaluate real-world models of documents, images, networks, and crowd-sourcing. Compared to score-function estimators, we require far fewer Monte Carlo samples and consistently convergence orders of magnitude faster. 

Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for tuning the step sizes have been proposed, ranging from coordinate-wise approaches (a.k.a. “adaptive” step sizes) to sophisticated heuristics to change the step size in each iteration. In this paper, we study two step size schedules whose power has been repeatedly confirmed in practice: the exponential and the cosine step sizes. For the first time, we provide theoretical support for them proving convergence rates for smooth non-convex functions, with and without the Polyak-Łojasiewicz (PL) condition. Moreover, we show the surprising property that these two strategies are adaptive to the noise level in the stochastic gradients of PL functions. That is, contrary to polynomial step sizes, they achieve almost optimal performance without needing to know the noise level nor tuning their hyperparameters based on it. Finally, we conduct a fair and comprehensive empirical evaluation of real-world datasets with deep learning architectures. Results show that, even if only requiring at most two hyperparameters to tune, these two strategies best or match the performance of various finely-tuned state-of-the-art strategies. 

Transfer in reinforcement learning is based on the idea that it is possible to use what is learned in one task to improve the learning process in another task. For transfer between tasks which share transition dynamics but differ in reward function, successor features have been shown to be a useful representation which allows for efficient computation of action-value functions for previously-learned policies in new tasks. These functions induce policies in the new tasks, so an agent may not need to learn a new policy for each new task it encounters, especially if it is allowed some amount of suboptimality in those tasks. We present new bounds for the performance of optimal policies in a new task, as well as an approach to use these bounds to decide, when presented with a new task, whether to use cached policies or learn a new policy.