We are interested in a framework of online learning with kernels for low-dimensional, but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge regression. Despite its simplicity, the algorithm we study is the first to achieve the optimal regret for a wide range of kernels with a per-round complexity of order $n^\alpha$ with $\alpha < 2$. The algorithm we consider is based on approximating the kernel with the linear span of basis functions. Our contributions are twofold: 1) For the Gaussian kernel, we propose to build the basis beforehand (independently of the data) through Taylor expansion. For $d$-dimensional inputs, we provide a (close to) optimal regret of order $O((\log n)^{d+1})$ with per-round time complexity and space complexity $O((\log n)^{2d})$. This makes the algorithm a suitable choice as soon as $n \gg e^d$ which is likely to happen in a scenario with small dimensional and large-scale dataset; 2) For general kernels with low effective dimension, the basis functions are updated sequentially, adapting to the data, by sampling Nyström points. In this case, our algorithm improves the computational trade-off known for online kernel regression.

We are interested in a framework of online learning with kernels for low-dimensional, but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge regression. Despite its simplicity, the algorithm we study is the first to achieve the optimal regret for a wide range of kernels with a per-round complexity of order n \alpha with \alpha 2 . The algorithm we consider is based on approximating the kernel with the linear span of basis functions. Our contributions are twofold: 1) For the Gaussian kernel, we propose to build the basis beforehand (independently of the data) through Taylor expansion.

Support Vector Machines (SVMs) are currently the state-of-the-art models for many classification problems but they suffer from the complexity of their train(cid:173) ing algorithm which is at least quadratic with respect to the number of examples. Hence, it is hopeless to try to solve real-life problems having more than a few hundreds of thousands examples with SVMs. The present paper proposes a new mixture of SVMs that can be easily implemented in parallel and where each SVM is trained on a small subset of the whole dataset. Experiments on a large benchmark dataset (Forest) as well as a difficult speech database, yielded significant time improvement (time complexity appears empirically to locally grow linearly with the number of examples) . In addition, and that is a surprise, a significant improvement in generalization was observed on Forest.

We are interested in a framework of online learning with kernels for low-dimensional, but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge regression. Despite its simplicity, the algorithm we study is the first to achieve the optimal regret for a wide range of kernels with a per-round complexity of order $n \alpha$ with $\alpha 2$. The algorithm we consider is based on approximating the kernel with the linear span of basis functions. Our contributions are twofold: 1) For the Gaussian kernel, we propose to build the basis beforehand (independently of the data) through Taylor expansion.

Minimum qualifications: BA/BS degree in Computer Science or related technical field or equivalent practical experience. 2 years of work or educational experience in Machine Learning or Artificial Intelligence. 1 year of relevant work experience, including software development. Experience with one or more general purpose programming languages including but not limited to: Java, C/C or Python. Preferred qualifications: MS or PhD degree in Computer Science, Artificial Intelligence, Machine Learning, or related technical field. About the job Google's software engineers develop the next-generation technologies that change how billions of users connect, explore, and interact with information and one another. Our products need to handle information at massive scale, and extend well beyond web search.