arXiv subjects

Pavel Izmailov

Publications and source records attributed to Pavel Izmailov.

39 records · Page 3Linked to original sources

arXiv2018

Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model. We achieve improved performance compared to the recent state-of-the-art Snapshot Ensembles, on CIFAR-10, CIFAR-100, and ImageNet.

stat.ML↗

arXiv2018

Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition

We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure exploiting algebra. The key idea of our method is to use Tensor Train decomposition for variational parameters, which allows us to train GPs with billions of inducing inputs and achieve state-of-the-art results on several benchmarks. Further, our approach allows for training kernels based on deep neural networks without any modifications to the underlying GP model. A neural network learns a multidimensional embedding for the data, which is used by the GP to make the final prediction. We train GP and neural network parameters end-to-end without pretraining, through maximization of GP marginal likelihood. We show the efficiency of the proposed approach on several regression and classification benchmark datasets including MNIST, CIFAR-10, and Airline.

cs.LG↗

arXiv2016

Faster variational inducing input Gaussian process classification

Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider the classification problem only. The complexity of standard methods for GP-classification scales cubically with the size of the training dataset. This complexity makes them inapplicable to big data problems. Therefore, a variety of methods were introduced to overcome this limitation. In the paper we focus on methods based on so called inducing inputs. This approach is based on variational inference and proposes a particular lower bound for marginal likelihood (evidence). This bound is then maximized w.r.t. parameters of kernel function of the Gaussian process, thus fitting the model to data. The computational complexity of this method is $O(nm^2)$, where $m$ is the number of inducing inputs used by the model and is assumed to be substantially smaller than the size of the dataset $n$. Recently, a new evidence lower bound for GP-classification problem was introduced. It allows using stochastic optimization, which makes it suitable for big data problems. However, the new lower bound depends on $O(m^2)$ variational parameter, which makes optimization challenging in case of big m. In this work we develop a new approach for training inducing input GP models for classification problems. Here we use quadratic approximation of several terms in the aforementioned evidence lower bound, obtaining analytical expressions for optimal values of most of the parameters in the optimization, thus sufficiently reducing the dimension of optimization space. In our experiments we achieve as well or better results, compared to the existing method. Moreover, our method doesn't require the user to manually set the learning rate, making it more practical, than the existing method.

cs.LG↗