Xingguo Li — Research
Deep Learning
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The deep neural networks have exceptional performance in a wide range of applications, but their theoretical understanding is still largely missing. Our goal is to provide fundamental justification for the theoretical properties of deep neural networks, including computational convergence, generalization, etc. We are also interested in studying new network architectures and optimization procedures that enable superior learning process than the state-of-the-art. |
Statistical Learning & Optimization
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Nonconvex regularization and constraints are widely used in solving modern machine learning problems, such as in sparsity-inducing high-dimensional learning and data factorization. They can effectively reduce the estimation bias, and make the obtained estimator attain significantly better statistical performance in parameter estimation with favored computational properties than the convex counterpart. Our goal is to establish statistical guarantees with underlying statistical models, which can provide us new insights on developing computational guarantees and geometric properties for nonconvex optimization algorithms. |
Data Sketching & Robust PCA
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Modern data science and machine learning problems often exhibit in magnificent scales, leading to massive computational burden using traditional dimension reduction techniques. Our goal is to propose novel data sketching and inference approach that intelligently subsamples the original array in a judicious way to effectively reduce its overall size while preserving the latent geometric features and being robust to undesired outliers. Several orders of speedup is achieved in practice, such as in saliency detection. Extension to more challenging multi-way array data (or tensor) is also plausible, which allows extensively more modeling flexibility. |
Scalable Software
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Beyond the theoretical investigation, we also make efforts in developing high performance R software for new algorithms in solving high-dimensional sparse learning problems. Existing R software for nonconvex and nonsmooth sparse learning has significantly worse scalability than the convex and smooth counterpart. Using efficient computational techniques, such as homotopy scheme and novel active set update strategies, we developed scalable software for addressing a broad class of nonconvex and nonsmooth sparse learning problems. They achieved significant improvement on running time and scalability performance over existing competitors. |