Abstract We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or require carefully increasing the batch size over the course of the algorithm’s execution, which leads to computing full gradients. In contrast, the proposed method, equipped with a stochastic average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques. In applications we put special emphasis on problems with a large number of separable constraints. Such problems are prevalent among semidefinite programming (SDP) formulations arising in machine learning and theoretical computer science. We provide numerical experiments on matrix completion, unsupervised clustering, and sparsest-cut SDPs.

Authors Gideon Dresdner, Maria-Luiza Vladarean, Gunnar Rätsch, Francesco Locatello, Volkan Cevher, Alp Yurtsever

Submitted Proceedings of The 25th International Conference on Artificial Intelligence and Statistics (AISTATS-22)

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Abstract Intensive care units (ICU) are increasingly looking towards machine learning for methods to provide online monitoring of critically ill patients. In machine learning, online monitoring is often formulated as a supervised learning problem. Recently, contrastive learning approaches have demonstrated promising improvements over competitive supervised benchmarks. These methods rely on well-understood data augmentation techniques developed for image data which do not apply to online monitoring. In this work, we overcome this limitation by supplementing time-series data augmentation techniques with a novel contrastive learning objective which we call neighborhood contrastive learning (NCL). Our objective explicitly groups together contiguous time segments from each patient while maintaining state-specific information. Our experiments demonstrate a marked improvement over existing work applying contrastive methods to medical time-series.

Authors Hugo Yèche, Gideon Dresdner, Francesco Locatello, Matthias Hüser, Gunnar Rätsch

Submitted ICML 2021

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Abstract Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature impacts time and memory consumption, address the problem with the notion of local curvature, and provide a novel approximate backtracking algorithm for estimating local curvature. We give new theoretical convergence rates for our algorithms and provide experimental validation on synthetic and real-world datasets.

Authors Gideon Dresdner, Saurav Shekhar, Fabian Pedregosa, Francesco Locatello, Gunnar Rätsch

Submitted International Joint Conference on Artificial Intelligence (IJCAI-21)

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Abstract We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization with sparse, low-rank, or other structured constraints. The proposed method is simple to implement, does not require step-size tuning, and has a constant per-iteration cost that is independent of the dataset size. Furthermore, as a byproduct of the method we obtain a stochastic estimator of the Frank-Wolfe gap that can be used as a stopping criterion. Depending on the setting, the proposed method matches or improves on the best computational guarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several datasets highlight different regimes in which the proposed method exhibits a faster empirical convergence than related methods. Finally, we provide an implementation of all considered methods in an open-source package.

Authors Geoffrey Négiar, Gideon Dresdner, Alicia Tsai, Laurent El Ghaoui, Francesco Locatello, Robert M. Freund, Fabian Pedregosa

Submitted ICML 2020

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Abstract Kernel methods on discrete domains have shown great promise for many challenging tasks, e.g., on biological sequence data as well as on molecular structures. Scalable kernel methods like support vector machines offer good predictive performances but they often do not provide uncertainty estimates. In contrast, probabilistic kernel methods like Gaussian Processes offer uncertainty estimates in addition to good predictive performance but fall short in terms of scalability. We present the first sparse Gaussian Process approximation framework on discrete input domains. Our framework achieves good predictive performance as well as uncertainty estimates using different discrete optimization techniques. We present competitive results comparing our framework to support vector machine and full Gaussian Process baselines on synthetic data as well as on challenging real-world DNA sequence data.

Authors Vincent Fortuin, Gideon Dresdner, Heiko Strathmann, Gunnar Rätsch

Submitted IEEE Access

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Abstract Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with a greedily constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions.

Authors Francesco Locatello, Gideon Dresdner, Rajiv Khanna, Isabel Valera, Gunnar Rätsch

Submitted NeurIPS 2018 (spotlight)

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