Near Input Sparsity Time Kernel Embeddings via Adaptive Sampling

Jul 12, 2020

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To accelerate kernel methods, we propose a near input sparsity time method for sampling the high-dimensional space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for subsampling the feature space of a degree q tensoring of data points in almost input sparsity time, improving the recent oblivious sketching of (Ahle et al., 2020) by a factor of q^5/2/ϵ^2. This leads to a subspace embedding for the polynomial kernel as well as the Gaussian kernel with a target dimension that is only linearly dependent on the statistical dimension of the kernel and in time which is only linearly dependent on the sparsity of the input dataset. We show how our spectral matrix approximation bounds imply new statistical guarantees for kernel ridge regression. Furthermore, we empirically show that in large-scale regression tasks, our algorithm outperforms state-of-the-art kernel approximation methods.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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