arXiv subjects

John P. Cunningham

Publications and source records attributed to John P. Cunningham.

At least 37 records · Page 2Linked to original sources

arXiv2022

The Posterior Predictive Null

Bayesian model criticism is an important part of the practice of Bayesian statistics. Traditionally, model criticism methods have been based on the predictive check, an adaptation of goodness-of-fit testing to Bayesian modeling and an effective method to understand how well a model captures the distribution of the data. In modern practice, however, researchers iteratively build and develop many models, exploring a space of models to help solve the problem at hand. While classical predictive checks can help assess each one, they cannot help the researcher understand how the models relate to each other. This paper introduces the posterior predictive null check (PPN), a method for Bayesian model criticism that helps characterize the relationships between models. The idea behind the PPN is to check whether data from one model's predictive distribution can pass a predictive check designed for another model. This form of criticism complements the classical predictive check by providing a comparative tool. A collection of PPNs, which we call a PPN study, can help us understand which models are equivalent and which models provide different perspectives on the data. With mixture models, we demonstrate how a PPN study, along with traditional predictive checks, can help select the number of components by the principle of parsimony. With probabilistic factor models, we demonstrate how a PPN study can help understand relationships between different classes of models, such as linear models and models based on neural networks. Finally, we analyze data from the literature on predictive checks to show how a PPN study can improve the practice of Bayesian model criticism. Code to replicate the results in this paper is available at \url{https://github.com/gemoran/ppn-code}.

stat.ME↗

arXiv2022

Preconditioning for Scalable Gaussian Process Hyperparameter Optimization

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.

cs.LG↗

arXiv2022

Data Augmentation for Compositional Data: Advancing Predictive Models of the Microbiome

Data augmentation plays a key role in modern machine learning pipelines. While numerous augmentation strategies have been studied in the context of computer vision and natural language processing, less is known for other data modalities. Our work extends the success of data augmentation to compositional data, i.e., simplex-valued data, which is of particular interest in the context of the human microbiome. Drawing on key principles from compositional data analysis, such as the Aitchison geometry of the simplex and subcompositions, we define novel augmentation strategies for this data modality. Incorporating our data augmentations into standard supervised learning pipelines results in consistent performance gains across a wide range of standard benchmark datasets. In particular, we set a new state-of-the-art for key disease prediction tasks including colorectal cancer, type 2 diabetes, and Crohn's disease. In addition, our data augmentations enable us to define a novel contrastive learning model, which improves on previous representation learning approaches for microbiome compositional data. Our code is available at https://github.com/cunningham-lab/AugCoDa.

stat.ML↗

arXiv2022

On the Normalizing Constant of the Continuous Categorical Distribution

Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys remarkable mathematical simplicity; its density function resembles that of the Dirichlet distribution, but with a normalizing constant that can be written in closed form using elementary functions only. In spite of this mathematical simplicity, our understanding of the normalizing constant remains far from complete. In this work, we characterize the numerical behavior of the normalizing constant and we present theoretical and methodological advances that can, in turn, help to enable broader applications of the continuous categorical distribution. Our code is available at https://github.com/cunningham-lab/cb_and_cc/.

stat.ML↗

arXiv2022

Mapping Interstellar Dust with Gaussian Processes

Interstellar dust corrupts nearly every stellar observation, and accounting for it is crucial to measuring physical properties of stars. We model the dust distribution as a spatially varying latent field with a Gaussian process (GP) and develop a likelihood model and inference method that scales to millions of astronomical observations. Modeling interstellar dust is complicated by two factors. The first is integrated observations. The data come from a vantage point on Earth and each observation is an integral of the unobserved function along our line of sight, resulting in a complex likelihood and a more difficult inference problem than in classical GP inference. The second complication is scale; stellar catalogs have millions of observations. To address these challenges we develop ziggy, a scalable approach to GP inference with integrated observations based on stochastic variational inference. We study ziggy on synthetic data and the Ananke dataset, a high-fidelity mechanistic model of the Milky Way with millions of stars. ziggy reliably infers the spatial dust map with well-calibrated posterior uncertainties.

astro-ph.GA↗

arXiv2021

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

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.

cs.LG↗

arXiv2021

Rectangular Flows for Manifold Learning

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.

stat.ML↗

arXiv2021

Linear-time inference for Gaussian Processes on one dimension

Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or vector time series sampled at arbitrarily-spaced intervals), for which state-space models are popular due to their linearly-scaling computational costs. It has long been conjectured that state-space models are general, able to approximate any one-dimensional GP. We provide the first general proof of this conjecture, showing that any stationary GP on one dimension with vector-valued observations governed by a Lebesgue-integrable continuous kernel can be approximated to any desired precision using a specifically-chosen state-space model: the Latent Exponentially Generated (LEG) family. This new family offers several advantages compared to the general state-space model: it is always stable (no unbounded growth), the covariance can be computed in closed form, and its parameter space is unconstrained (allowing straightforward estimation via gradient descent). The theorem's proof also draws connections to Spectral Mixture Kernels, providing insight about this popular family of kernels. We develop parallelized algorithms for performing inference and learning in the LEG model, test the algorithm on real and synthetic data, and demonstrate scaling to datasets with billions of samples.

stat.ML↗

arXiv2021

Bias-Free Scalable Gaussian Processes via Randomized Truncations

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.

cs.LG↗

arXiv2021

Simulating time to event prediction with spatiotemporal echocardiography deep learning

Integrating methods for time-to-event prediction with diagnostic imaging modalities is of considerable interest, as accurate estimates of survival requires accounting for censoring of individuals within the observation period. New methods for time-to-event prediction have been developed by extending the cox-proportional hazards model with neural networks. In this paper, to explore the feasibility of these methods when applied to deep learning with echocardiography videos, we utilize the Stanford EchoNet-Dynamic dataset with over 10,000 echocardiograms, and generate simulated survival datasets based on the expert annotated ejection fraction readings. By training on just the simulated survival outcomes, we show that spatiotemporal convolutional neural networks yield accurate survival estimates.

cs.CV↗

arXiv2021

Medical Imaging and Machine Learning

Advances in computing power, deep learning architectures, and expert labelled datasets have spurred the development of medical imaging artificial intelligence systems that rival clinical experts in a variety of scenarios. The National Institutes of Health in 2018 identified key focus areas for the future of artificial intelligence in medical imaging, creating a foundational roadmap for research in image acquisition, algorithms, data standardization, and translatable clinical decision support systems. Among the key issues raised in the report: data availability, need for novel computing architectures and explainable AI algorithms, are still relevant despite the tremendous progress made over the past few years alone. Furthermore, translational goals of data sharing, validation of performance for regulatory approval, generalizability and mitigation of unintended bias must be accounted for early in the development process. In this perspective paper we explore challenges unique to high dimensional clinical imaging data, in addition to highlighting some of the technical and ethical considerations in developing high-dimensional, multi-modality, machine learning systems for clinical decision support.

eess.IV↗

arXiv2021

Predicting post-operative right ventricular failure using video-based deep learning

Non-invasive and cost effective in nature, the echocardiogram allows for a comprehensive assessment of the cardiac musculature and valves. Despite progressive improvements over the decades, the rich temporally resolved data in echocardiography videos remain underutilized. Human reads of echocardiograms reduce the complex patterns of cardiac wall motion, to a small list of measurements of heart function. Furthermore, all modern echocardiography artificial intelligence (AI) systems are similarly limited by design - automating measurements of the same reductionist metrics rather than utilizing the wealth of data embedded within each echo study. This underutilization is most evident in situations where clinical decision making is guided by subjective assessments of disease acuity, and tools that predict disease onset within clinically actionable timeframes are unavailable. Predicting the likelihood of developing post-operative right ventricular failure (RV failure) in the setting of mechanical circulatory support is one such clinical example. To address this, we developed a novel video AI system trained to predict post-operative right ventricular failure (RV failure), using the full spatiotemporal density of information from pre-operative echocardiography scans. We achieve an AUC of 0.729, specificity of 52% at 80% sensitivity and 46% sensitivity at 80% specificity. Furthermore, we show that our ML system significantly outperforms a team of human experts tasked with predicting RV failure on independent clinical evaluation. Finally, the methods we describe are generalizable to any cardiac clinical decision support application where treatment or patient selection is guided by qualitative echocardiography assessments.

cs.CV↗

arXiv2020

Uses and Abuses of the Cross-Entropy Loss: Case Studies in Modern Deep Learning

Modern deep learning is primarily an experimental science, in which empirical advances occasionally come at the expense of probabilistic rigor. Here we focus on one such example; namely the use of the categorical cross-entropy loss to model data that is not strictly categorical, but rather takes values on the simplex. This practice is standard in neural network architectures with label smoothing and actor-mimic reinforcement learning, amongst others. Drawing on the recently discovered continuous-categorical distribution, we propose probabilistically-inspired alternatives to these models, providing an approach that is more principled and theoretically appealing. Through careful experimentation, including an ablation study, we identify the potential for outperformance in these models, thereby highlighting the importance of a proper probabilistic treatment, as well as illustrating some of the failure modes thereof.

stat.ML↗

arXiv2020

Chronic, cortex-wide imaging of specific cell populations during behavior

Measurements of neuronal activity across brain areas are important for understanding the neural correlates of cognitive and motor processes like attention, decision-making, and action selection. However, techniques that allow cellular resolution measurements are expensive and require a high degree of technical expertise, which limits their broad use. Widefield imaging of genetically encoded indicators is a high throughput, cost effective, and flexible approach to measure activity of specific cell populations with high temporal resolution and a cortex-wide field of view. Here we outline our protocol for assembling a widefield setup, a surgical preparation to image through the intact skull, and imaging neural activity chronically in behaving, transgenic mice that express a calcium indicator in specific subpopulations of cortical neurons. Further, we highlight a processing pipeline that leverages novel, cloud-based methods to analyze large-scale imaging datasets. The protocol targets labs that are seeking to build macroscopes, optimize surgical procedures for long-term chronic imaging, and/or analyze cortex-wide neuronal recordings.

q-bio.NC↗

arXiv2020

The continuous categorical: a novel simplex-valued exponential family

Simplex-valued data appear throughout statistics and machine learning, for example in the context of transfer learning and compression of deep networks. Existing models for this class of data rely on the Dirichlet distribution or other related loss functions; here we show these standard choices suffer systematically from a number of limitations, including bias and numerical issues that frustrate the use of flexible network models upstream of these distributions. We resolve these limitations by introducing a novel exponential family of distributions for modeling simplex-valued data - the continuous categorical, which arises as a nontrivial multivariate generalization of the recently discovered continuous Bernoulli. Unlike the Dirichlet and other typical choices, the continuous categorical results in a well-behaved probabilistic loss function that produces unbiased estimators, while preserving the mathematical simplicity of the Dirichlet. As well as exploring its theoretical properties, we introduce sampling methods for this distribution that are amenable to the reparameterization trick, and evaluate their performance. Lastly, we demonstrate that the continuous categorical outperforms standard choices empirically, across a simulation study, an applied example on multi-party elections, and a neural network compression task.

stat.ML↗

arXiv2020

Paraphrase Generation with Latent Bag of Words

Paraphrase generation is a longstanding important problem in natural language processing. In addition, recent progress in deep generative models has shown promising results on discrete latent variables for text generation. Inspired by variational autoencoders with discrete latent structures, in this work, we propose a latent bag of words (BOW) model for paraphrase generation. We ground the semantics of a discrete latent variable by the BOW from the target sentences. We use this latent variable to build a fully differentiable content planning and surface realization model. Specifically, we use source words to predict their neighbors and model the target BOW with a mixture of softmax. We use Gumbel top-k reparameterization to perform differentiable subset sampling from the predicted BOW distribution. We retrieve the sampled word embeddings and use them to augment the decoder and guide its generation search space. Our latent BOW model not only enhances the decoder, but also exhibits clear interpretability. We show the model interpretability with regard to \emph{(i)} unsupervised learning of word neighbors \emph{(ii)} the step-by-step generation procedure. Extensive experiments demonstrate the transparent and effective generation process of this model.\footnote{Our code can be found at \url{https://github.com/FranxYao/dgm_latent_bow}}

cs.CL↗

arXiv2019

Deep Random Splines for Point Process Intensity Estimation of Neural Population Data

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by transforming Gaussian noise through a deep neural network whose output are the parameters of a spline. Unlike Gaussian processes, Deep Random Splines allow us to readily enforce shape constraints while inheriting the richness and tractability of deep generative models. We also present an observational model for point process data which uses Deep Random Splines to model the intensity function of each point process and apply it to neural population data to obtain a low-dimensional representation of spiking activity. Inference is performed via a variational autoencoder that uses a novel recurrent encoder architecture that can handle multiple point processes as input. We use a newly collected dataset where a primate completes a pedaling task, and observe better dimensionality reduction with our model than with competing alternatives.

stat.ML↗

arXiv2019

The continuous Bernoulli: fixing a pervasive error in variational autoencoders

Variational autoencoders (VAE) have quickly become a central tool in machine learning, applicable to a broad range of data types and latent variable models. By far the most common first step, taken by seminal papers and by core software libraries alike, is to model MNIST data using a deep network parameterizing a Bernoulli likelihood. This practice contains what appears to be and what is often set aside as a minor inconvenience: the pixel data is [0,1] valued, not {0,1} as supported by the Bernoulli likelihood. Here we show that, far from being a triviality or nuisance that is convenient to ignore, this error has profound importance to VAE, both qualitative and quantitative. We introduce and fully characterize a new [0,1]-supported, single parameter distribution: the continuous Bernoulli, which patches this pervasive bug in VAE. This distribution is not nitpicking; it produces meaningful performance improvements across a range of metrics and datasets, including sharper image samples, and suggests a broader class of performant VAE.

stat.ML↗