Enhancing Parameter-Free Frank Wolfe with an Extra Subproblem

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration, thanks to which the decision variable is updated in a prediction-correction (PC) format. Relying on no problem dependent parameters in the step sizes, the convergence rate of ExtraFW for general convex problems is shown to be ${\cal O}(\frac{1}{k})$, which is optimal in the sense of matching the lower bound on the number of solved FW subproblems. However, the merit of ExtraFW is its faster rate ${\cal O}\big(\frac{1}{k^2} \big)$ on a class of machine learning problems. Compared with other parameter-free FW variants that have faster rates on the same problems, ExtraFW has improved rates and fine-grained analysis thanks to its PC update. Numerical tests on binary classification with different sparsity-promoting constraints demonstrate that the empirical performance of ExtraFW is significantly better than FW, and even faster than Nesterov's accelerated gradient on certain datasets. For matrix completion, ExtraFW enjoys smaller optimality gap, and lower rank than FW.

Deep Learning for Cardiologist-level Myocardial Infarction Detection in Electrocardiograms

Heart disease is the leading cause of death worldwide. Amongst patients with cardiovascular diseases, myocardial infarction is the main cause of death. In order to provide adequate healthcare support to patients who may experience this clinical event, it is essential to gather supportive evidence in a timely manner to help secure a correct diagnosis. In this article, we study the feasibility of using deep learning to identify suggestive electrocardiographic (ECG) changes that may correctly classify heart conditions using the Physikalisch-Technische Bundesanstalt (PTB) database. As part of this study, we systematically quantify the contribution of each ECG lead to correctly tell apart a healthy from an unhealthy heart. For such a study we fine-tune the ConvNetQuake neural network model, which was originally designed to identify earthquakes. Our findings indicate that out of 15 ECG leads, data from the v6 and vz leads are critical to correctly identify myocardial infarction. Based on these findings, we modify ConvNetQuake to simultaneously take in raw ECG data from leads v6 and vz, achieving $99.43\%$ classification accuracy, which represents cardiologist-level performance level for myocardial infarction detection after feeding only 10 seconds of raw ECG data to our neural network model. This approach differs from others in the community in that the ECG data fed into the neural network model does not require any kind of manual feature extraction or pre-processing.

Enabling real-time multi-messenger astrophysics discoveries with deep learning

Multi-messenger astrophysics is a fast-growing, interdisciplinary field that combines data, which vary in volume and speed of data processing, from many different instruments that probe the Universe using different cosmic messengers: electromagnetic waves, cosmic rays, gravitational waves and neutrinos. In this Expert Recommendation, we review the key challenges of real-time observations of gravitational wave sources and their electromagnetic and astroparticle counterparts, and make a number of recommendations to maximize their potential for scientific discovery. These recommendations refer to the design of scalable and computationally efficient machine learning algorithms; the cyber-infrastructure to numerically simulate astrophysical sources, and to process and interpret multi-messenger astrophysics data; the management of gravitational wave detections to trigger real-time alerts for electromagnetic and astroparticle follow-ups; a vision to harness future developments of machine learning and cyber-infrastructure resources to cope with the big-data requirements; and the need to build a community of experts to realize the goals of multi-messenger astrophysics.

Be Aware of Non-Stationarity: Nearly Optimal Algorithms for Piecewise-Stationary Cascading Bandits

Cascading bandit (CB) is a variant of both the multi-armed bandit (MAB) and the cascade model (CM), where a learning agent aims to maximize the total reward by recommending $K$ out of $L$ items to a user. We focus on a common real-world scenario where the user's preference can change in a piecewise-stationary manner. Two efficient algorithms, \texttt{GLRT-CascadeUCB} and \texttt{GLRT-CascadeKL-UCB}, are developed. The key idea behind the proposed algorithms is incorporating an almost parameter-free change-point detector, the Generalized Likelihood Ratio Test (GLRT), within classical upper confidence bound (UCB) based algorithms. Gap-dependent regret upper bounds of the proposed algorithms are derived, both on the order of $\mathcal{O}(\sqrt{NLT\log{T}})$, where $N$ is the number of piecewise-stationary segments, and $T$ is the time horizon. We also derive a minimax lower bound on the order of $\mathcal{O}(\sqrt{NLT})$ for piecewise-stationary CB, showing that our proposed algorithms are optimal up to a poly-logarithmic factor $\sqrt{\log T}$. Lastly, we present numerical experiments on both synthetic and real-world datasets to show that \texttt{GLRT-CascadeUCB} and \texttt{GLRT-CascadeKL-UCB} outperform state-of-the-art algorithms in the literature.

Unsupervised Co-Learning on $\mathcal{G}$-Manifolds Across Irreducible Representations

We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism that canonically associates multiple independent vector bundles over a common base manifold, which provides multiple views for the geometry of the underlying manifold. The consistency across these fibre bundles provide a common base for performing unsupervised manifold co-learning through the redundancy created artificially across irreducible representations of the transformation group. We demonstrate the efficacy of the proposed algorithmic paradigm through drastically improved robust nearest neighbor search and community detection on rotation-invariant cryo-electron microscopy image analysis.

Multi-Frequency Vector Diffusion Maps

We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. MFVDM combines different nonlinear embeddings of the data points defined with multiple unitary irreducible representations of the alignment group that connect two nodes in the graph. We illustrate the efficacy of MFVDM on synthetic data generated according to a random graph model and cryo-electron microscopy image dataset. The new method achieves better nearest neighbor search and alignment estimation than the state-of-the-arts VDM and diffusion maps (DM) on extremely noisy data.

Representation Theoretic Patterns in Multi-Frequency Class Averaging for Three-Dimensional Cryo-Electron Microscopy

We develop in this paper a novel intrinsic classification algorithm -- multi-frequency class averaging (MFCA) -- for clustering noisy projection images obtained from three-dimensional cryo-electron microscopy (cryo-EM) by the similarity among their viewing directions. This new algorithm leverages multiple irreducible representations of the unitary group to introduce additional redundancy into the representation of the transport data, extending and outperforming the previous class averaging algorithm of Hadani and Singer [Foundations of Computational Mathematics, 11 (5), pp. 589--616 (2011)] that uses only a single representation. The formal algebraic model and representation theoretic patterns of the proposed MFCA algorithm extend the framework of Hadani and Singer to arbitrary irreducible representations of the unitary group. We conceptually establish the consistency and stability of MFCA by inspecting the spectral properties of a generalized localized parallel transport operator on the two-dimensional unit sphere through the lens of Wigner matrices. We demonstrate the efficacy of the proposed algorithm with numerical experiments.