Sibling Regression for Generalized Linear Models

Field observations form the basis of many scientific studies, especially in ecological and social sciences. Despite efforts to conduct such surveys in a standardized way, observations can be prone to systematic measurement errors. The removal of systematic variability introduced by the observation process, if possible, can greatly increase the value of this data. Existing non-parametric techniques for correcting such errors assume linear additive noise models. This leads to biased estimates when applied to generalized linear models (GLM). We present an approach based on residual functions to address this limitation. We then demonstrate its effectiveness on synthetic data and show it reduces systematic detection variability in moth surveys.

The Spatio-Temporal Poisson Point Process: A Simple Model for the Alignment of Event Camera Data

Event cameras, inspired by biological vision systems, provide a natural and data efficient representation of visual information. Visual information is acquired in the form of events that are triggered by local brightness changes. Each pixel location of the camera's sensor records events asynchronously and independently with very high temporal resolution. However, because most brightness changes are triggered by relative motion of the camera and the scene, the events recorded at a single sensor location seldom correspond to the same world point. To extract meaningful information from event cameras, it is helpful to register events that were triggered by the same underlying world point. In this work we propose a new model of event data that captures its natural spatio-temporal structure. We start by developing a model for aligned event data. That is, we develop a model for the data as though it has been perfectly registered already. In particular, we model the aligned data as a spatio-temporal Poisson point process. Based on this model, we develop a maximum likelihood approach to registering events that are not yet aligned. That is, we find transformations of the observed events that make them as likely as possible under our model. In particular we extract the camera rotation that leads to the best event alignment. We show new state of the art accuracy for rotational velocity estimation on the DAVIS 240C dataset. In addition, our method is also faster and has lower computational complexity than several competing methods.

Faster Kernel Interpolation for Gaussian Processes

A key challenge in scaling Gaussian Process (GP) regression to massive datasets is that exact inference requires computation with a dense n x n kernel matrix, where n is the number of data points. Significant work focuses on approximating the kernel matrix via interpolation using a smaller set of m inducing points. Structured kernel interpolation (SKI) is among the most scalable methods: by placing inducing points on a dense grid and using structured matrix algebra, SKI achieves per-iteration time of O(n + m log m) for approximate inference. This linear scaling in n enables inference for very large data sets; however the cost is per-iteration, which remains a limitation for extremely large n. We show that the SKI per-iteration time can be reduced to O(m log m) after a single O(n) time precomputation step by reframing SKI as solving a natural Bayesian linear regression problem with a fixed set of m compact basis functions. With per-iteration complexity independent of the dataset size n for a fixed grid, our method scales to truly massive data sets. We demonstrate speedups in practice for a wide range of m and n and apply the method to GP inference on a three-dimensional weather radar dataset with over 100 million points.

Three-quarter Sibling Regression for Denoising Observational Data

Many ecological studies and conservation policies are based on field observations of species, which can be affected by systematic variability introduced by the observation process. A recently introduced causal modeling technique called 'half-sibling regression' can detect and correct for systematic errors in measurements of multiple independent random variables. However, it will remove intrinsic variability if the variables are dependent, and therefore does not apply to many situations, including modeling of species counts that are controlled by common causes. We present a technique called 'three-quarter sibling regression' to partially overcome this limitation. It can filter the effect of systematic noise when the latent variables have observed common causes. We provide theoretical justification of this approach, demonstrate its effectiveness on synthetic data, and show that it reduces systematic detection variability due to moon brightness in moth surveys.

Normalizing Flows Across Dimensions

Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data representations. Unfortunately, a popular generative model, normalizing flows, cannot take advantage of this. Normalizing flows are based on successive variable transformations that are, by design, incapable of learning lower-dimensional representations. In this paper we introduce noisy injective flows (NIF), a generalization of normalizing flows that can go across dimensions. NIF explicitly map the latent space to a learnable manifold in a high-dimensional data space using injective transformations. We further employ an additive noise model to account for deviations from the manifold and identify a stochastic inverse of the generative process. Empirically, we demonstrate that a simple application of our method to existing flow architectures can significantly improve sample quality and yield separable data embeddings.

Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimization

Recent research has seen several advances relevant to black-box VI, but the current state of automatic posterior inference is unclear. One such advance is the use of normalizing flows to define flexible posterior densities for deep latent variable models. Another direction is the integration of Monte-Carlo methods to serve two purposes; first, to obtain tighter variational objectives for optimization, and second, to define enriched variational families through sampling. However, both flows and variational Monte-Carlo methods remain relatively unexplored for black-box VI. Moreover, on a pragmatic front, there are several optimization considerations like step-size scheme, parameter initialization, and choice of gradient estimators, for which there are no clear guidance in the existing literature. In this paper, we postulate that black-box VI is best addressed through a careful combination of numerous algorithmic components. We evaluate components relating to optimization, flows, and Monte-Carlo methods on a benchmark of 30 models from the Stan model library. The combination of these algorithmic components significantly advances the state-of-the-art "out of the box" variational inference.

General-Purpose Differentially-Private Confidence Intervals

One of the most common statistical goals is to estimate a population parameter and quantify uncertainty by constructing a confidence interval. However, the field of differential privacy lacks easy-to-use and general methods for doing so. We partially fill this gap by developing two broadly applicable methods for private confidence-interval construction. The first is based on asymptotics: for two widely used model classes, exponential families and linear regression, a simple private estimator has the same asymptotic normal distribution as the corresponding non-private estimator, so confidence intervals can be constructed using quantiles of the normal distribution. These are computationally cheap and accurate for large data sets, but do not have good coverage for small data sets. The second approach is based on the parametric bootstrap. It applies "out of the box" to a wide class of private estimators and has good coverage at small sample sizes, but with increased computational cost. Both methods are based on post-processing the private estimator and do not consume additional privacy budget.

Detecting and Tracking Communal Bird Roosts in Weather Radar Data

The US weather radar archive holds detailed information about biological phenomena in the atmosphere over the last 20 years. Communally roosting birds congregate in large numbers at nighttime roosting locations, and their morning exodus from the roost is often visible as a distinctive pattern in radar images. This paper describes a machine learning system to detect and track roost signatures in weather radar data. A significant challenge is that labels were collected opportunistically from previous research studies and there are systematic differences in labeling style. We contribute a latent variable model and EM algorithm to learn a detection model together with models of labeling styles for individual annotators. By properly accounting for these variations we learn a significantly more accurate detector. The resulting system detects previously unknown roosting locations and provides comprehensive spatio-temporal data about roosts across the US. This data will provide biologists important information about the poorly understood phenomena of broad-scale habitat use and movements of communally roosting birds during the non-breeding season.

Differentially Private Bayesian Linear Regression

Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regression coefficients. We investigate the problem of Bayesian linear regression, with the goal of computing posterior distributions that correctly quantify uncertainty given privately released statistics. We show that a naive approach that ignores the noise injected by the privacy mechanism does a poor job in realistic data settings. We then develop noise-aware methods that perform inference over the privacy mechanism and produce correct posteriors across a wide range of scenarios.

Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation

Recent work in variational inference (VI) uses ideas from Monte Carlo estimation to tighten the lower bounds on the log-likelihood that are used as objectives. However, there is no systematic understanding of how optimizing different objectives relates to approximating the posterior distribution. Developing such a connection is important if the ideas are to be applied to inference-i.e., applications that require an approximate posterior and not just an approximation of the log-likelihood. Given a VI objective defined by a Monte Carlo estimator of the likelihood, we use a "divide and couple" procedure to identify augmented proposal and target distributions. The divergence between these is equal to the gap between the VI objective and the log-likelihood. Thus, after maximizing the VI objective, the augmented variational distribution may be used to approximate the posterior distribution.