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Geoff Pleiss

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26 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Asymmetric Duos: Sidekicks Improve Uncertainty

Tim G. Zhou
Evan Shelhamer
Geoff Pleiss

The go-to strategy to apply deep networks in settings where uncertainty informs decisions—ensembling multiple training runs with random initializations—is ill-suited for the extremely large-scale models and practical fine-tuning workflows of today. We introduce a new cost-effective strategy for improving the uncertainty quantification and downstream decisions of a large model (e. g. a fine-tuned ViT-B): coupling it with a less accurate but much smaller "sidekick" (e. g. a fine-tuned ResNet-34) with a fraction of the computational cost. We propose aggregating the predictions of this *Asymmetric Duo* by simple learned weighted averaging. Surprisingly, despite their inherent asymmetry, the sidekick model almost never harms the performance of the larger model. In fact, across five image classification benchmarks, and a variety of model architectures and training schemes (including soups), Asymmetric Duos significantly improve accuracy, uncertainty quantification, and selective classification metrics with only ${\sim}10-20$% more computation. Code is available at: https: //github. com/timgzhou/asymmetric-duos

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ICML Conference 2025 Conference Paper

Theoretical Limitations of Ensembles in the Age of Overparameterization

Niclas Dern
John P. Cunningham
Geoff Pleiss

Classic ensembles generalize better than any single component model. In contrast, recent empirical studies find that modern ensembles of (overparameterized) neural networks may not provide any inherent generalization advantage over single but larger neural networks. This paper clarifies how modern overparameterized ensembles differ from their classic underparameterized counterparts, using ensembles of random feature (RF) regressors as a basis for developing theory. In contrast to the underparameterized regime, where ensembling typically induces regularization and increases generalization, we prove with minimal assumptions that infinite ensembles of overparameterized RF regressors become pointwise equivalent to (single) infinite-width RF regressors, and finite width ensembles rapidly converge to single models with the same parameter budget. These results, which are exact for ridgeless models and approximate for small ridge penalties, imply that overparameterized ensembles and single large models exhibit nearly identical generalization. We further characterize the predictive variance amongst ensemble members, demonstrating that it quantifies the expected effects of increasing capacity rather than capturing any conventional notion of uncertainty. Our results challenge common assumptions about the advantages of ensembles in overparameterized settings, prompting a reconsideration of how well intuitions from underparameterized ensembles transfer to deep ensembles and the overparameterized regime.

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ICML Conference 2024 Conference Paper

A Sober Look at LLMs for Material Discovery: Are They Actually Good for Bayesian Optimization Over Molecules?

Agustinus Kristiadi
Felix Strieth-Kalthoff
Marta Skreta
Pascal Poupart
Alán Aspuru-Guzik
Geoff Pleiss

Automation is one of the cornerstones of contemporary material discovery. Bayesian optimization (BO) is an essential part of such workflows, enabling scientists to leverage prior domain knowledge into efficient exploration of a large molecular space. While such prior knowledge can take many forms, there has been significant fanfare around the ancillary scientific knowledge encapsulated in large language models (LLMs). However, existing work thus far has only explored LLMs for heuristic materials searches. Indeed, recent work obtains the uncertainty estimate—an integral part of BO—from point-estimated, non-Bayesian LLMs. In this work, we study the question of whether LLMs are actually useful to accelerate principled Bayesian optimization in the molecular space. We take a sober, dispassionate stance in answering this question. This is done by carefully (i) viewing LLMs as fixed feature extractors for standard but principled BO surrogate models and by (ii) leveraging parameter-efficient finetuning methods and Bayesian neural networks to obtain the posterior of the LLM surrogate. Our extensive experiments with real-world chemistry problems show that LLMs can be useful for BO over molecules, but only if they have been pretrained or finetuned with domain-specific data.

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NeurIPS Conference 2024 Conference Paper

Approximation-Aware Bayesian Optimization

Natalie Maus
Kyurae Kim
Geoff Pleiss
David Eriksson
John P. Cunningham
Jacob R. Gardner

High-dimensional Bayesian optimization (BO) tasks such as molecular design often require $>10, $$000$ function evaluations before obtaining meaningful results. While methods like sparse variational Gaussian processes (SVGPs) reduce computational requirements in these settings, the underlying approximations result in suboptimal data acquisitions that slow the progress of optimization. In this paper we modify SVGPs to better align with the goals of BO: targeting informed data acquisition over global posterior fidelity. Using the framework of utility-calibrated variational inference (Lacoste–Julien et al. , 2011), we unify GP approximation and data acquisition into a joint optimization problem, thereby ensuring optimal decisions under a limited computational budget. Our approach can be used with any decision-theoretic acquisition function and is readily compatible with trust region methods like TuRBO (Eriksson et al. , 2019). We derive efficient joint objectives for the expected improvement (EI) and knowledge gradient (KG) acquisition functions in both the standard and batch BO settings. On a variety of recent high dimensional benchmark tasks in control and molecular design, our approach significantly outperforms standard SVGPs and is capable of achieving comparable rewards with up to $10\times$ fewer function evaluations.

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NeurIPS Conference 2024 Conference Paper

Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference

Jonathan Wenger
Kaiwen Wu
Philipp Hennig
Jacob R. Gardner
Geoff Pleiss
John P. Cunningham

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the form of computational uncertainty, which enables---at the cost of quadratic complexity---an explicit tradeoff between computational efficiency and precision. Here we extend this development to model selection, which requires significant enhancements to the existing approach, including linear-time scaling in the size of the dataset. We propose a novel training loss for hyperparameter optimization and demonstrate empirically that the resulting method can outperform SGPR, CGGP and SVGP, state-of-the-art methods for GP model selection, on medium to large-scale datasets. Our experiments show that model selection for computation-aware GPs trained on 1. 8 million data points can be done within a few hours on a single GPU. As a result of this work, Gaussian processes can be trained on large-scale datasets without significantly compromising their ability to quantify uncertainty---a fundamental prerequisite for optimal decision-making.

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ICML Conference 2024 Conference Paper

Layerwise Proximal Replay: A Proximal Point Method for Online Continual Learning

Jinsoo Yoo
Yunpeng Liu 0007
Frank Wood
Geoff Pleiss

In online continual learning, a neural network incrementally learns from a non-i. i. d. data stream. Nearly all online continual learning methods employ experience replay to simultaneously prevent catastrophic forgetting and underfitting on past data. Our work demonstrates a limitation of this approach: neural networks trained with experience replay tend to have unstable optimization trajectories, impeding their overall accuracy. Surprisingly, these instabilities persist even when the replay buffer stores all previous training examples, suggesting that this issue is orthogonal to catastrophic forgetting. We minimize these instabilities through a simple modification of the optimization geometry. Our solution, Layerwise Proximal Replay (LPR), balances learning from new and replay data while only allowing for gradual changes in the hidden activation of past data. We demonstrate that LPR consistently improves replay-based online continual learning across multiple problem settings, regardless of the amount of available replay memory.

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TMLR Journal 2024 Journal Article

Pathologies of Predictive Diversity in Deep Ensembles

Taiga Abe
E. Kelly Buchanan
Geoff Pleiss
John Patrick Cunningham

Classic results establish that encouraging predictive diversity improves performance in ensembles of low-capacity models, e.g. through bagging or boosting. Here we demonstrate that these intuitions do not apply to high-capacity neural network ensembles (deep ensembles), and in fact the opposite is often true. In a large scale study of nearly 600 neural network classification ensembles, we examine a variety of interventions that trade off component model performance for predictive diversity. While such interventions can improve the performance of small neural network ensembles (in line with standard intuitions), they harm the performance of the large neural network ensembles most often used in practice. Surprisingly, we also find that discouraging predictive diversity is often benign in large-network ensembles, fully inverting standard intuitions. Even when diversity-promoting interventions do not sacrifice component model performance (e.g. using heterogeneous architectures and training paradigms), we observe an opportunity cost associated with pursuing increased predictive diversity. Examining over 1000 ensembles, we observe that the performance benefits of diverse architectures/training procedures are easily dwarfed by the benefits of simply using higher-capacity models, despite the fact that such higher capacity models often yield significantly less predictive diversity. Overall, our findings demonstrate that standard intuitions around predictive diversity, originally developed for low-capacity ensembles, do not directly apply to modern high-capacity deep ensembles. This work clarifies fundamental challenges to the goal of improving deep ensembles by making them more diverse, while suggesting an alternative path: simply forming ensembles from ever more powerful (and less diverse) component models.

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NeurIPS Conference 2023 Conference Paper

CoLA: Exploiting Compositional Structure for Automatic and Efficient Numerical Linear Algebra

Andres Potapczynski
Marc Finzi
Geoff Pleiss
Andrew G. Wilson

Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker, convolutional, block diagonal, sum, or product structure. In this paper, we propose a simple but general framework for large-scale linear algebra problems in machine learning, named CoLA (Compositional Linear Algebra). By combining a linear operator abstraction with compositional dispatch rules, CoLA automatically constructs memory and runtime efficient numerical algorithms. Moreover, CoLA provides memory efficient automatic differentiation, low precision computation, and GPU acceleration in both JAX and PyTorch, while also accommodating new objects, operations, and rules in downstream packages via multiple dispatch. CoLA can accelerate many algebraic operations, while making it easy to prototype matrix structures and algorithms, providing an appealing drop-in tool for virtually any computational effort that requires linear algebra. We showcase its efficacy across a broad range of applications, including partial differential equations, Gaussian processes, equivariant model construction, and unsupervised learning.

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NeurIPS Conference 2023 Conference Paper

Sharp Calibrated Gaussian Processes

Alexandre Capone
Sandra Hirche
Geoff Pleiss

While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance, which yields confidence intervals that are potentially too coarse. To remedy this, we present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance but using a different set of hyperparameters chosen to satisfy an empirical calibration constraint. This results in a calibration approach that is considerably more flexible than existing approaches, which we optimize to yield tight predictive quantiles. Our approach is shown to yield a calibrated model under reasonable assumptions. Furthermore, it outperforms existing approaches in sharpness when employed for calibrated regression.

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NeurIPS Conference 2022 Conference Paper

Deep Ensembles Work, But Are They Necessary?

Taiga Abe
Estefany Kelly Buchanan
Geoff Pleiss
Richard Zemel
John P. Cunningham

Ensembling neural networks is an effective way to increase accuracy, and can often match the performance of individual larger models. This observation poses a natural question: given the choice between a deep ensemble and a single neural network with similar accuracy, is one preferable over the other? Recent work suggests that deep ensembles may offer distinct benefits beyond predictive power: namely, uncertainty quantification and robustness to dataset shift. In this work, we demonstrate limitations to these purported benefits, and show that a single (but larger) neural network can replicate these qualities. First, we show that ensemble diversity, by any metric, does not meaningfully contribute to an ensemble's ability to detect out-of-distribution (OOD) data, but is instead highly correlated with the relative improvement of a single larger model. Second, we show that the OOD performance afforded by ensembles is strongly determined by their in-distribution (InD) performance, and - in this sense - is not indicative of any "effective robustness. " While deep ensembles are a practical way to achieve improvements to predictive power, uncertainty quantification, and robustness, our results show that these improvements can be replicated by a (larger) single model.

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NeurIPS Conference 2022 Conference Paper

Posterior and Computational Uncertainty in Gaussian Processes

Jonathan Wenger
Geoff Pleiss
Marvin Pförtner
Philipp Hennig
John P. Cunningham

Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited computation, is entirely ignored when using the approximate posterior. Therefore in practice, GP models are often as much about the approximation method as they are about the data. Here, we develop a new class of methods that provides consistent estimation of the combined uncertainty arising from both the finite number of data observed and the finite amount of computation expended. The most common GP approximations map to an instance in this class, such as methods based on the Cholesky factorization, conjugate gradients, and inducing points. For any method in this class, we prove (i) convergence of its posterior mean in the associated RKHS, (ii) decomposability of its combined posterior covariance into mathematical and computational covariances, and (iii) that the combined variance is a tight worst-case bound for the squared error between the method's posterior mean and the latent function. Finally, we empirically demonstrate the consequences of ignoring computational uncertainty and show how implicitly modeling it improves generalization performance on benchmark datasets.

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ICML Conference 2022 Conference Paper

Preconditioning for Scalable Gaussian Process Hyperparameter Optimization

Jonathan Wenger
Geoff Pleiss
Philipp Hennig
John P. Cunningham
Jacob R. Gardner

Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient method (CG) for the linear solves and stochastic trace estimation for the log-determinant. This work introduces new algorithmic and theoretical insights for preconditioning these computations. While preconditioning is well understood in the context of CG, we demonstrate that it can also accelerate convergence and reduce variance of the estimates for the log-determinant and its derivative. We prove general probabilistic error bounds for the preconditioned computation of the log-determinant, log-marginal likelihood and its derivatives. Additionally, we derive specific rates for a range of kernel-preconditioner combinations, showing that up to exponential convergence can be achieved. Our theoretical results enable provably efficient optimization of kernel hyperparameters, which we validate empirically on large-scale benchmark problems. There our approach accelerates training by up to an order of magnitude.

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ICML Conference 2022 Conference Paper

Variational nearest neighbor Gaussian process

Luhuan Wu
Geoff Pleiss
John P. Cunningham

Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix. We propose variational nearest neighbor Gaussian process (VNNGP), which introduces a prior that only retains correlations within $K$ nearest-neighboring observations, thereby inducing sparse precision structure. Using the variational framework, VNNGP’s objective can be factorized over both observations and inducing points, enabling stochastic optimization with a time complexity of $O(K^3)$. Hence, we can arbitrarily scale the inducing point size, even to the point of putting inducing points at every observed location. We compare VNNGP to other scalable GPs through various experiments, and demonstrate that VNNGP (1) can dramatically outperform low-rank methods, and (2) is less prone to overfitting than other nearest neighbor methods.

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ICML Conference 2021 Conference Paper

Bias-Free Scalable Gaussian Processes via Randomized Truncations

Andres Potapczynski
Luhuan Wu
Dan Biderman
Geoff Pleiss
John P. Cunningham

Scalable Gaussian Process methods are computationally attractive, yet introduce modeling biases that require rigorous study. This paper analyzes two common techniques: early truncated conjugate gradients (CG) and random Fourier features (RFF). We find that both methods introduce a systematic bias on the learned hyperparameters: CG tends to underfit while RFF tends to overfit. We address these issues using randomized truncation estimators that eliminate bias in exchange for increased variance. In the case of RFF, we show that the bias-to-variance conversion is indeed a trade-off: the additional variance proves detrimental to optimization. However, in the case of CG, our unbiased learning procedure meaningfully outperforms its biased counterpart with minimal additional computation. Our code is available at https: //github. com/ cunningham-lab/RTGPS.

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NeurIPS Conference 2021 Conference Paper

Rectangular Flows for Manifold Learning

Anthony L. Caterini
Gabriel Loaiza-Ganem
Geoff Pleiss
John P. Cunningham

Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live in some (often unknown) low-dimensional manifold embedded in a high-dimensional ambient space. The result is a modelling mismatch since -- by construction -- the invertibility requirement implies high-dimensional support of the learned distribution. Injective flows, mappings from low- to high-dimensional spaces, aim to fix this discrepancy by learning distributions on manifolds, but the resulting volume-change term becomes more challenging to evaluate. Current approaches either avoid computing this term entirely using various heuristics, or assume the manifold is known beforehand and therefore are not widely applicable. Instead, we propose two methods to tractably calculate the gradient of this term with respect to the parameters of the model, relying on careful use of automatic differentiation and techniques from numerical linear algebra. Both approaches perform end-to-end nonlinear manifold learning and density estimation for data projected onto this manifold. We study the trade-offs between our proposed methods, empirically verify that we outperform approaches ignoring the volume-change term by more accurately learning manifolds and the corresponding distributions on them, and show promising results on out-of-distribution detection. Our code is available at https: //github. com/layer6ai-labs/rectangular-flows.

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NeurIPS Conference 2021 Conference Paper

The Limitations of Large Width in Neural Networks: A Deep Gaussian Process Perspective

Geoff Pleiss
John P. Cunningham

Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain representational power with width, potentially masking any negative effects. Our analysis in this paper decouples capacity and width via the generalization of neural networks to Deep Gaussian Processes (Deep GP), a class of nonparametric hierarchical models that subsume neural nets. In doing so, we aim to understand how width affects (standard) neural networks once they have sufficient capacity for a given modeling task. Our theoretical and empirical results on Deep GP suggest that large width can be detrimental to hierarchical models. Surprisingly, we prove that even nonparametric Deep GP converge to Gaussian processes, effectively becoming shallower without any increase in representational power. The posterior, which corresponds to a mixture of data-adaptable basis functions, becomes less data-dependent with width. Our tail analysis demonstrates that width and depth have opposite effects: depth accentuates a model’s non-Gaussianity, while width makes models increasingly Gaussian. We find there is a “sweet spot” that maximizes test performance before the limiting GP behavior prevents adaptability, occurring at width = 1 or width = 2 for nonparametric Deep GP. These results make strong predictions about the same phenomenon in conventional neural networks trained with L2 regularization (analogous to a Gaussian prior on parameters): we show that such neural networks may need up to 500 − 1000 hidden units for sufficient capacity - depending on the dataset - but further width degrades performance.

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UAI Conference 2020 Conference Paper

Deep Sigma Point Processes

Martin Jankowiak
Geoff Pleiss
Jacob R. Gardner

We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational) DGPs, including mini-batch training and predictive uncertainty that is controlled by kernel basis functions. Importantly, since DSPPs admit a simple maximum likelihood inference procedure, the resulting predictive distributions are not degraded by any posterior approximations. In an extensive empirical comparison on univariate and multivariate regression tasks we find that the resulting predictive distributions are significantly better calibrated than those obtained with other probabilistic methods for scalable regression, including variational DGPs–often by as much as a nat per datapoint.

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NeurIPS Conference 2020 Conference Paper

Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization

Geoff Pleiss
Martin Jankowiak
David Eriksson
Anil Damle
Jacob Gardner

Matrix square roots and their inverses arise frequently in machine learning, e. g. , when sampling from high-dimensional Gaussians N(0, K) or “whitening” a vector b against covariance matrix K. While existing methods typically require O(N^3) computation, we introduce a highly-efficient quadratic-time algorithm for computing K^{1/2}b, K^{-1/2}b, and their derivatives through matrix-vector multiplication (MVMs). Our method combines Krylov subspace methods with a rational approximation and typically achieves 4 decimal places of accuracy with fewer than 100 MVMs. Moreover, the backward pass requires little additional computation. We demonstrate our method's applicability on matrices as large as 50, 000 by 50, 000 - well beyond traditional methods - with little approximation error. Applying this increased scalability to variational Gaussian processes, Bayesian optimization, and Gibbs sampling results in more powerful models with higher accuracy. In particular, we perform variational GP inference with up to 10, 000 inducing points and perform Gibbs sampling on a 25, 000-dimensional problem.

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NeurIPS Conference 2020 Conference Paper

Identifying Mislabeled Data using the Area Under the Margin Ranking

Geoff Pleiss
Tianyi Zhang
Ethan Elenberg
Kilian Q. Weinberger

Not all data in a typical training set help with generalization; some samples can be overly ambiguous or outrightly mislabeled. This paper introduces a new method to identify such samples and mitigate their impact when training neural networks. At the heart of our algorithm is the Area Under the Margin (AUM) statistic, which exploits differences in the training dynamics of clean and mislabeled samples. A simple procedure - adding an extra class populated with purposefully mislabeled threshold samples - learns a AUM upper bound that isolates mislabeled data. This approach consistently improves upon prior work on synthetic and real-world datasets. On the WebVision50 classification task our method removes 17% of training data, yielding a 1. 6% (absolute) improvement in test error. On CIFAR100 removing 13% of the data leads to a 1. 2% drop in error.

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ICML Conference 2020 Conference Paper

Parametric Gaussian Process Regressors

Martin Jankowiak
Geoff Pleiss
Jacob R. Gardner

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially underestimated uncertainties. Notably, in the regression case the predictive variance is typically dominated by observation noise, yielding uncertainty estimates that make little use of the input-dependent function uncertainty that makes GP priors attractive. In this work we propose two simple methods for scalable GP regression that address this issue and thus yield substantially improved predictive uncertainties. The first applies variational inference to FITC (Fully Independent Training Conditional; Snelson et. al. 2006). The second bypasses posterior approximations and instead directly targets the posterior predictive distribution. In an extensive empirical comparison with a number of alternative methods for scalable GP regression, we find that the resulting predictive distributions exhibit significantly better calibrated uncertainties and higher log likelihoods–often by as much as half a nat per datapoint.

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ICLR Conference 2020 Conference Paper

Pseudo-LiDAR++: Accurate Depth for 3D Object Detection in Autonomous Driving

Yurong You
Yan Wang 0051
Wei-Lun Chao
Divyansh Garg
Geoff Pleiss
Bharath Hariharan
Mark E. Campbell
Kilian Q. Weinberger

Detecting objects such as cars and pedestrians in 3D plays an indispensable role in autonomous driving. Existing approaches largely rely on expensive LiDAR sensors for accurate depth information. While recently pseudo-LiDAR has been introduced as a promising alternative, at a much lower cost based solely on stereo images, there is still a notable performance gap. In this paper we provide substantial advances to the pseudo-LiDAR framework through improvements in stereo depth estimation. Concretely, we adapt the stereo network architecture and loss function to be more aligned with accurate depth estimation of faraway objects --- currently the primary weakness of pseudo-LiDAR. Further, we explore the idea to leverage cheaper but extremely sparse LiDAR sensors, which alone provide insufficient information for 3D detection, to de-bias our depth estimation. We propose a depth-propagation algorithm, guided by the initial depth estimates, to diffuse these few exact measurements across the entire depth map. We show on the KITTI object detection benchmark that our combined approach yields substantial improvements in depth estimation and stereo-based 3D object detection --- outperforming the previous state-of-the-art detection accuracy for faraway objects by 40%. Our code is available at https://github.com/mileyan/Pseudo_Lidar_V2.

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NeurIPS Conference 2019 Conference Paper

Exact Gaussian Processes on a Million Data Points

Ke Wang
Geoff Pleiss
Jacob Gardner
Stephen Tyree
Kilian Weinberger
Andrew Gordon Wilson

Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. 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, a task previously thought to be impossible with current computing hardware. Moreover, our approach is generally applicable, without constraints to grid data or specific kernel classes. Enabled by this scalability, we perform the first-ever comparison of exact GPs against scalable GP approximations on datasets with $10^4 \! -\! 10^6$ data points, showing dramatic performance improvements.

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ICML Conference 2018 Conference Paper

Constant-Time Predictive Distributions for Gaussian Processes

Geoff Pleiss
Jacob R. Gardner
Kilian Q. Weinberger
Andrew Gordon Wilson

One of the most compelling features of Gaussian process (GP) regression is its ability to provide well-calibrated posterior distributions. Recent advances in inducing point methods have sped up GP marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining computational bottlenecks. In this paper we address these shortcomings by using the Lanczos algorithm to rapidly approximate the predictive covariance matrix. Our approach, which we refer to as LOVE (LanczOs Variance Estimates), substantially improves time and space complexity. In our experiments, LOVE computes covariances up to 2, 000 times faster and draws samples 18, 000 times faster than existing methods, all without sacrificing accuracy.

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NeurIPS Conference 2018 Conference Paper

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

Jacob Gardner
Geoff Pleiss
Kilian Weinberger
David Bindel
Andrew Wilson

Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing 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 for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from O(n^3) to O(n^2). Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.

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ICML Conference 2017 Conference Paper

On Calibration of Modern Neural Networks

Chuan Guo 0001
Geoff Pleiss
Yu Sun 0020
Kilian Q. Weinberger

Confidence calibration – the problem of predicting probability estimates representative of the true correctness likelihood – is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling – a single-parameter variant of Platt Scaling – is surprisingly effective at calibrating predictions.

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NeurIPS Conference 2017 Conference Paper

On Fairness and Calibration

Geoff Pleiss
Manish Raghavan
Felix Wu
Jon Kleinberg
Kilian Weinberger

The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be "fair. " In this paper, we investigate the tension between minimizing error disparity across different population groups while maintaining calibrated probability estimates. We show that calibration is compatible only with a single error constraint (i. e. equal false-negatives rates across groups), and show that any algorithm that satisfies this relaxation is no better than randomizing a percentage of predictions for an existing classifier. These unsettling findings, which extend and generalize existing results, are empirically confirmed on several datasets.

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