Andrew Gordon Wilson

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Assistant Professor, Cornell University

  • Exact Gaussian Processes on a Million Data Points

    Gaussian processes (GPs) are flexible models with state-of-the-art performance on many impactful applications. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. In this paper, we develop a scalable approach for exact GPs that leverages multi-GPU parallelization and methods like linear conjugate gradients, accessing the kernel matrix only through matrix multiplication. By partitioning and distributing kernel matrix multiplies, we demonstrate that an exact GP can be trained on over a million points in 3 days using 8 GPUs and can compute predictive means and variances in under a second using 1 GPU at test time. Moreover, we perform the first-ever comparison of exact GPs against state-of-the-art scalable approximations on large-scale regression datasets with 10^4-10^6 data points, showing dramatic performance improvements.

    03/19/2019 ∙ by Ke Alexander Wang, et al. ∙ 32 share

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  • A Simple Baseline for Bayesian Uncertainty in Deep Learning

    We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been shown to improve generalization in deep learning. With SWAG, we fit a Gaussian using the SWA solution as the first moment and a low rank plus diagonal covariance also derived from the SGD iterates, forming an approximate posterior distribution over neural network weights; we then sample from this Gaussian distribution to perform Bayesian model averaging. We empirically find that SWAG approximates the shape of the true posterior, in accordance with results describing the stationary distribution of SGD iterates. Moreover, we demonstrate that SWAG performs well on a wide variety of computer vision tasks, including out of sample detection, calibration, and transfer learning, in comparison to many popular alternatives including MC dropout, KFAC Laplace, and temperature scaling.

    02/07/2019 ∙ by Wesley Maddox, et al. ∙ 20 share

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  • Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning

    Bayesian optimization is popular for optimizing time-consuming black-box objectives. Nonetheless, for hyperparameter tuning in deep neural networks, the time required to evaluate the validation error for even a few hyperparameter settings remains a bottleneck. Multi-fidelity optimization promises relief using cheaper proxies to such objectives --- for example, validation error for a network trained using a subset of the training points or fewer iterations than required for convergence. We propose a highly flexible and practical approach to multi-fidelity Bayesian optimization, focused on efficiently optimizing hyperparameters for iteratively trained supervised learning models. We introduce a new acquisition function, the trace-aware knowledge-gradient, which efficiently leverages both multiple continuous fidelity controls and trace observations --- values of the objective at a sequence of fidelities, available when varying fidelity using training iterations. We provide a provably convergent method for optimizing our acquisition function and show it outperforms state-of-the-art alternatives for hyperparameter tuning of deep neural networks and large-scale kernel learning.

    03/12/2019 ∙ by Jian Wu, et al. ∙ 12 share

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  • SWALP : Stochastic Weight Averaging in Low-Precision Training

    Low precision operations can provide scalability, memory savings, portability, and energy efficiency. This paper proposes SWALP, an approach to low precision training that averages low-precision SGD iterates with a modified learning rate schedule. SWALP is easy to implement and can match the performance of full-precision SGD even with all numbers quantized down to 8 bits, including the gradient accumulators. Additionally, we show that SWALP converges arbitrarily close to the optimal solution for quadratic objectives, and to a noise ball asymptotically smaller than low precision SGD in strongly convex settings.

    04/26/2019 ∙ by Guandao Yang, et al. ∙ 10 share

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  • Change Surfaces for Expressive Multidimensional Changepoints and Counterfactual Prediction

    Identifying changes in model parameters is fundamental in machine learning and statistics. However, standard changepoint models are limited in expressiveness, often addressing unidimensional problems and assuming instantaneous changes. We introduce change surfaces as a multidimensional and highly expressive generalization of changepoints. We provide a model-agnostic formalization of change surfaces, illustrating how they can provide variable, heterogeneous, and non-monotonic rates of change across multiple dimensions. Additionally, we show how change surfaces can be used for counterfactual prediction. As a concrete instantiation of the change surface framework, we develop Gaussian Process Change Surfaces (GPCS). We demonstrate counterfactual prediction with Bayesian posterior mean and credible sets, as well as massive scalability by introducing novel methods for additive non-separable kernels. Using two large spatio-temporal datasets we employ GPCS to discover and characterize complex changes that can provide scientific and policy relevant insights. Specifically, we analyze twentieth century measles incidence across the United States and discover previously unknown heterogeneous changes after the introduction of the measles vaccine. Additionally, we apply the model to requests for lead testing kits in New York City, discovering distinct spatial and demographic patterns.

    10/28/2018 ∙ by William Herlands, et al. ∙ 8 share

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  • Simple Black-box Adversarial Attacks

    We propose an intriguingly simple method for the construction of adversarial images in the black-box setting. In constrast to the white-box scenario, constructing black-box adversarial images has the additional constraint on query budget, and efficient attacks remain an open problem to date. With only the mild assumption of continuous-valued confidence scores, our highly query-efficient algorithm utilizes the following simple iterative principle: we randomly sample a vector from a predefined orthonormal basis and either add or subtract it to the target image. Despite its simplicity, the proposed method can be used for both untargeted and targeted attacks -- resulting in previously unprecedented query efficiency in both settings. We demonstrate the efficacy and efficiency of our algorithm on several real world settings including the Google Cloud Vision API. We argue that our proposed algorithm should serve as a strong baseline for future black-box attacks, in particular because it is extremely fast and its implementation requires less than 20 lines of PyTorch code.

    05/17/2019 ∙ by Chuan Guo, et al. ∙ 7 share

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  • Scaling Gaussian Process Regression with Derivatives

    Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at n points in d dimensions requires linear solves and log determinants with an n(d+1) × n(d+1) positive definite matrix -- leading to prohibitive O(n^3d^3) computations for standard direct methods. We propose iterative solvers using fast O(nd) matrix-vector multiplications (MVMs), together with pivoted Cholesky preconditioning that cuts the iterations to convergence by several orders of magnitude, allowing for fast kernel learning and prediction. Our approaches, together with dimensionality reduction, enables Bayesian optimization with derivatives to scale to high-dimensional problems and large evaluation budgets.

    10/29/2018 ∙ by David Eriksson, et al. ∙ 6 share

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  • Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning

    The posteriors over neural network weights are high dimensional and multimodal. Each mode typically characterizes a meaningfully different representation of the data. We develop Cyclical Stochastic Gradient MCMC (SG-MCMC) to automatically explore such distributions. In particular, we propose a cyclical stepsize schedule, where larger steps discover new modes, and smaller steps characterize each mode. We prove that our proposed learning rate schedule provides faster convergence to samples from a stationary distribution than SG-MCMC with standard decaying schedules. Moreover, we provide extensive experimental results to demonstrate the effectiveness of cyclical SG-MCMC in learning complex multimodal distributions, especially for fully Bayesian inference with modern deep neural networks.

    02/11/2019 ∙ by Ruqi Zhang, et al. ∙ 6 share

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  • GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration

    Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on recent developments in machine learning hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms required for training and inference in a single call. Adapting this algorithm to complex models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM utilizes a specialized preconditioner that substantially speeds up convergence. In experiments, we show that BBMM efficiently utilizes GPU hardware, speeding up GP inference by an order of magnitude on a variety of popular GP models. Additionally, we provide GPyTorch, a new software platform for scalable Gaussian process inference via BBMM, built on PyTorch.

    09/28/2018 ∙ by Jacob R. Gardner, et al. ∙ 4 share

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  • Subspace Inference for Bayesian Deep Learning

    Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is challenging due to the high dimensionality of the parameter space. In this paper, we construct low-dimensional subspaces of parameter space, such as the first principal components of the stochastic gradient descent (SGD) trajectory, which contain diverse sets of high performing models. In these subspaces, we are able to apply elliptical slice sampling and variational inference, which struggle in the full parameter space. We show that Bayesian model averaging over the induced posterior in these subspaces produces accurate predictions and well calibrated predictive uncertainty for both regression and image classification.

    07/17/2019 ∙ by Pavel Izmailov, et al. ∙ 3 share

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  • Proceedings of NIPS 2017 Symposium on Interpretable Machine Learning

    This is the Proceedings of NIPS 2017 Symposium on Interpretable Machine Learning, held in Long Beach, California, USA on December 7, 2017

    11/27/2017 ∙ by Andrew Gordon Wilson, et al. ∙ 0 share

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