Dmitry Storcheus
Dmitry is an Engineer at Google Research NY. He specializes in the research and implementation of scalable machine learning algorithms. He received his MSc in Mathematics from the Courant Institute at NYU, where he wrote a thesis with advisor Mehryar Mohri on Supervised Kernel PCA.
Dmitry's recent research contributions include deriving generalization guarantees for suprevized dimensionality reduction and currently he is working on implementing matrix approximation algorithms.
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Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling
Shanshan Wu
Alexandros G. Dimakis
Sujay Sanghavi
Daniel Holtmann-Rice
ICML (2019)
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Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a-priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt to data, while still performing well with the widely used ℓ1 decoder. The convex ℓ1 decoder prevents gradient propagation as needed in standard gradient-based training. Our method is based on the insight that unrolling the convex decoder into T projected subgradient steps can address this issue. Our method can be seen as a data-driven way to learn a compressed sensing measurement matrix. We compare the empirical performance of 10 algorithms over 6 sparse datasets (3 synthetic and 3 real). Our experiments show that there is indeed additional structure beyond sparsity in the real datasets. Our method is able to discover it and exploit it to create excellent reconstructions with fewer measurements (by a factor of 1.1-3x) compared to the previous state-of-the-art methods. We illustrate an application of our method in learning label embeddings for extreme multi-label classification. Our experiments show that our method is able to match or outperform the precision scores of SLEEC, which is one of the state-of-the-art embedding-based approaches for extreme multi-label learning.
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Theoretical Foundations for Learning Kernels in Supervised Kernel PCA
Modern Nonparametrics 3: Automating the Learning Pipeline, Neural Information Processing Systems, Workshop (2014)
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This paper presents a novel learning scenario which combines dimensionality reduction, supervised learning as well as kernel selection. We carefully define the hypothesis class that addresses this setting and provide an analysis of its Rademacher complexity and thereby provide generalization guarantees. The proposed algorithm uses KPCA to reduce the dimensionality of the feature space, i.e. by projecting data onto top eigenvectors of covariance operator in a kernel reproducing space. Moreover, it simultaneously learns a linear combination of base kernel functions, which defines a reproducing space, as well as the parameters of a supervised learning algorithm in order to minimize a regularized empirical loss. The bound on Rademacher complexity of our hypothesis is shown to be logarithmic in the number of base kernels, which encourages practitioners to combine as
many base kernels as possible.
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Foundations of Coupled Nonlinear Dimensionality Reduction
