arXiv subjects

Roman Garnett

Publications and source records attributed to Roman Garnett.

At least 37 records · Page 2Linked to original sources

arXiv2020

Detecting Multiple DLAs per Spectrum in SDSS DR12 with Gaussian Processes

We present a revised version of our automated technique using Gaussian processes (GPs) to detect Damped Lyman-$α$ absorbers (DLAs) along quasar (QSO) sightlines. The main improvement is to allow our Gaussian process pipeline to detect multiple DLAs along a single sightline. Our DLA detections are regularised by an improved model for the absorption from the Lyman-$α$ forest which improves performance at high redshift. We also introduce a model for unresolved sub-DLAs which reduces mis-classifications of absorbers without detectable damping wings. We compare our results to those of two different large-scale DLA catalogues and provide a catalogue of the processed results of our Gaussian process pipeline using 158 825 Lyman-$α$ spectra from SDSS data release 12. We present updated estimates for the statistical properties of DLAs, including the column density distribution function (CDDF), line density ($dN/dX$), and neutral hydrogen density ($Ω_{\textrm{DLA}}$).

astro-ph.CO↗

arXiv2020

GPIRT: A Gaussian Process Model for Item Response Theory

The goal of item response theoretic (IRT) models is to provide estimates of latent traits from binary observed indicators and at the same time to learn the item response functions (IRFs) that map from latent trait to observed response. However, in many cases observed behavior can deviate significantly from the parametric assumptions of traditional IRT models. Nonparametric IRT models overcome these challenges by relaxing assumptions about the form of the IRFs, but standard tools are unable to simultaneously estimate flexible IRFs and recover ability estimates for respondents. We propose a Bayesian nonparametric model that solves this problem by placing Gaussian process priors on the latent functions defining the IRFs. This allows us to simultaneously relax assumptions about the shape of the IRFs while preserving the ability to estimate latent traits. This in turn allows us to easily extend the model to further tasks such as active learning. GPIRT therefore provides a simple and intuitive solution to several longstanding problems in the IRT literature.

stat.ML↗

arXiv2020

BINOCULARS for Efficient, Nonmyopic Sequential Experimental Design

Finite-horizon sequential experimental design (SED) arises naturally in many contexts, including hyperparameter tuning in machine learning among more traditional settings. Computing the optimal policy for such problems requires solving Bellman equations, which are generally intractable. Most existing work resorts to severely myopic approximations by limiting the decision horizon to only a single time-step, which can underweight exploration in favor of exploitation. We present BINOCULARS: Batch-Informed NOnmyopic Choices, Using Long-horizons for Adaptive, Rapid SED, a general framework for deriving efficient, nonmyopic approximations to the optimal experimental policy. Our key idea is simple and surprisingly effective: we first compute a one-step optimal batch of experiments, then select a single point from this batch to evaluate. We realize BINOCULARS for Bayesian optimization and Bayesian quadrature -- two notable SED problems with radically different objectives -- and demonstrate that BINOCULARS significantly outperforms myopic alternatives in real-world scenarios.

cs.LG↗

arXiv2019

D-VAE: A Variational Autoencoder for Directed Acyclic Graphs

Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.

cs.LG↗

arXiv2019

Automated Model Selection with Bayesian Quadrature

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Previous research has shown that BQ offers sample efficiency superior to Monte Carlo in computing the evidence of an individual model. However, applying BQ directly to model comparison may waste computation producing an overly-accurate estimate for the evidence of a clearly poor model. We propose an automated and efficient algorithm for computing the most-relevant quantity for model selection: the posterior probability of a model. Our technique maximizes the mutual information between this quantity and observations of the models' likelihoods, yielding efficient acquisition of samples across disparate model spaces when likelihood observations are limited. Our method produces more-accurate model posterior estimates using fewer model likelihood evaluations than standard Bayesian quadrature and Monte Carlo estimators, as we demonstrate on synthetic and real-world examples.

cs.LG↗

arXiv2019

Improving Quadrature for Constrained Integrands

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the range of the function of interest, such as nonnegativity or boundedness. Although our framework is general, we derive explicit approximation schemes for these constraints, and argue for the use of a log transformation for functions with high dynamic range such as likelihood surfaces. We propose a novel method for optimizing hyperparameters in this framework: we optimize the marginal likelihood in the original space, as opposed to in the transformed space. The result is a model that better explains the actual data. Experiments on synthetic and real-world data demonstrate our framework achieves superior estimates using less wall-clock time than existing Bayesian quadrature procedures.

cs.LG↗

arXiv2018

Efficient nonmyopic active search with applications in drug and materials discovery

Active search is a learning paradigm for actively identifying as many members of a given class as possible. A critical target scenario is high-throughput screening for scientific discovery, such as drug or materials discovery. In this paper, we approach this problem in Bayesian decision framework. We first derive the Bayesian optimal policy under a natural utility, and establish a theoretical hardness of active search, proving that the optimal policy can not be approximated for any constant ratio. We also study the batch setting for the first time, where a batch of $b>1$ points can be queried at each iteration. We give an asymptotic lower bound, linear in batch size, on the adaptivity gap: how much we could lose if we query $b$ points at a time for $t$ iterations, instead of one point at a time for $bt$ iterations. We then introduce a novel approach to nonmyopic approximations of the optimal policy that admits efficient computation. Our proposed policy can automatically trade off exploration and exploitation, without relying on any tuning parameters. We also generalize our policy to batch setting, and propose two approaches to tackle the combinatorial search challenge. We evaluate our proposed policies on a large database of drug discovery and materials science. Results demonstrate the superior performance of our proposed policy in both sequential and batch setting; the nonmyopic behavior is also illustrated in various aspects.

cs.LG↗

arXiv2018

Learning and Anticipating Future Actions During Exploratory Data Analysis

The goal of visual analytics is to create a symbiosis between human and computer by leveraging their unique strengths. While this model has demonstrated immense success, we are yet to realize the full potential of such a human-computer partnership. In a perfect collaborative mixed-initiative system, the computer must possess skills for learning and anticipating the users' needs. Addressing this gap, we propose a framework for inferring focus areas from passive observations of the user's actions, thereby allowing accurate predictions of future events. We evaluate this technique with a crime map and demonstrate that users' clicks appear in our prediction set 95% - 97% of the time. Further analysis shows that we can achieve high prediction accuracy typically after three clicks. Altogether, we show that passive observations of interaction data can reveal valuable information that will allow the system to learn and anticipate future events, laying the foundation for next-generation tools.

cs.HC↗

arXiv2018

Detecting Damped Lyman-$α$ Absorbers with Gaussian Processes

We develop an automated technique for detecting damped Lyman-$α$ absorbers (DLAs) along spectroscopic lines of sight to quasi-stellar objects (QSOs or quasars). The detection of DLAs in large-scale spectroscopic surveys such as SDSS-III sheds light on galaxy formation at high redshift, showing the nucleation of galaxies from diffuse gas. We use nearly 50 000 QSO spectra to learn a novel tailored Gaussian process model for quasar emission spectra, which we apply to the DLA detection problem via Bayesian model selection. We propose models for identifying an arbitrary number of DLAs along a given line of sight. We demonstrate our method's effectiveness using a large-scale validation experiment, with excellent performance. We also provide a catalog of our results applied to 162 858 spectra from SDSS-III data release 12.

astro-ph.CO↗

arXiv2018

Exact Sampling from Determinantal Point Processes

Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on regular grids, applicable to a general set of spaces. This is helpful whenever an algorithm explores to reduce uncertainty, such as in active learning, Bayesian optimization, reinforcement learning, and marginalization in graphical models. To draw samples from a DPP in practice, existing literature focuses on approximate schemes of low cost, or comparably inefficient exact algorithms like rejection sampling. We point out that, for many settings of relevance to machine learning, it is also possible to draw exact samples from DPPs on continuous domains. We start from an intuitive example on the real line, which is then generalized to multivariate real vector spaces. We also compare to previously studied approximations, showing that exact sampling, despite higher cost, can be preferable where precision is needed.

cs.LG↗

arXiv2016

Statistical properties of damped Lyman-alpha systems from Sloan Digital Sky Survey DR12

We present new estimates for the statistical properties of damped Lyman-$α$ absorbers (DLAs). We compute the column density distribution function at $z>2$, the line density, $\mathrm{d}N/\mathrm{d}X$, and the neutral hydrogen density, $Ω_\mathrm{DLA}$. Our estimates are derived from the DLA catalogue of Garnett 2016, which uses the SDSS-III DR12 quasar spectroscopic survey. This catalogue provides a probability that a given spectrum contains a DLA, allowing us to use even the noisiest data without biasing our results and thus substantially increase our sample size. We measure a non-zero column density distribution function at $95\%$ confidence for all column densities $N_\mathrm{HI} < 5\times 10^{22}$ cm$^{-2}$. We make the first measurements from SDSS of $\mathrm{d}N/\mathrm{d}X$ and $Ω_\mathrm{DLA}$ at $z>4$. We show that our results are insensitive to the signal-to-noise ratio of the spectra, but that there is a residual dependence on quasar redshift for $z<2.5$, which may be due to remaining systematics in our analysis.

astro-ph.GA↗

arXiv2016

Active Search for Sparse Signals with Region Sensing

Autonomous systems can be used to search for sparse signals in a large space; e.g., aerial robots can be deployed to localize threats, detect gas leaks, or respond to distress calls. Intuitively, search algorithms may increase efficiency by collecting aggregate measurements summarizing large contiguous regions. However, most existing search methods either ignore the possibility of such region observations (e.g., Bayesian optimization and multi-armed bandits) or make strong assumptions about the sensing mechanism that allow each measurement to arbitrarily encode all signals in the entire environment (e.g., compressive sensing). We propose an algorithm that actively collects data to search for sparse signals using only noisy measurements of the average values on rectangular regions (including single points), based on the greedy maximization of information gain. We analyze our algorithm in 1d and show that it requires $\tilde{O}(\frac{n}{μ^2}+k^2)$ measurements to recover all of $k$ signal locations with small Bayes error, where $μ$ and $n$ are the signal strength and the size of the search space, respectively. We also show that active designs can be fundamentally more efficient than passive designs with region sensing, contrasting with the results of Arias-Castro, Candes, and Davenport (2013). We demonstrate the empirical performance of our algorithm on a search problem using satellite image data and in high dimensions.

stat.ML↗

arXiv2015

Anomaly Detection and Removal Using Non-Stationary Gaussian Processes

This paper proposes a novel Gaussian process approach to fault removal in time-series data. Fault removal does not delete the faulty signal data but, instead, massages the fault from the data. We assume that only one fault occurs at any one time and model the signal by two separate non-parametric Gaussian process models for both the physical phenomenon and the fault. In order to facilitate fault removal we introduce the Markov Region Link kernel for handling non-stationary Gaussian processes. This kernel is piece-wise stationary but guarantees that functions generated by it and their derivatives (when required) are everywhere continuous. We apply this kernel to the removal of drift and bias errors in faulty sensor data and also to the recovery of EOG artifact corrupted EEG signals.

stat.ML↗

arXiv2015

Differentially Private Bayesian Optimization

Bayesian optimization is a powerful tool for fine-tuning the hyper-parameters of a wide variety of machine learning models. The success of machine learning has led practitioners in diverse real-world settings to learn classifiers for practical problems. As machine learning becomes commonplace, Bayesian optimization becomes an attractive method for practitioners to automate the process of classifier hyper-parameter tuning. A key observation is that the data used for tuning models in these settings is often sensitive. Certain data such as genetic predisposition, personal email statistics, and car accident history, if not properly private, may be at risk of being inferred from Bayesian optimization outputs. To address this, we introduce methods for releasing the best hyper-parameters and classifier accuracy privately. Leveraging the strong theoretical guarantees of differential privacy and known Bayesian optimization convergence bounds, we prove that under a GP assumption these private quantities are also near-optimal. Finally, even if this assumption is not satisfied, we can use different smoothness guarantees to protect privacy.

stat.ML↗

arXiv2014

Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature

We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in probabilistic inference is numerical integration, to average over ensembles of models or unknown (hyper-)parameters (for example to compute the marginal likelihood or a partition function). MCMC has provided approaches to numerical integration that deliver state-of-the-art inference, but can suffer from sample inefficiency and poor convergence diagnostics. Bayesian quadrature techniques offer a model-based solution to such problems, but their uptake has been hindered by prohibitive computation costs. We introduce a warped model for probabilistic integrands (likelihoods) that are known to be non-negative, permitting a cheap active learning scheme to optimally select sample locations. Our algorithm is demonstrated to offer faster convergence (in seconds) relative to simple Monte Carlo and annealed importance sampling on both synthetic and real-world examples.

stat.ML↗

arXiv2014

Propagation Kernels

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage early-stage distributions from propagation schemes such as random walks to capture structural information encoded in node labels, attributes, and edge information. This has two benefits. First, off-the-shelf propagation schemes can be used to naturally construct kernels for many graph types, including labeled, partially labeled, unlabeled, directed, and attributed graphs. Second, by leveraging existing efficient and informative propagation schemes, propagation kernels can be considerably faster than state-of-the-art approaches without sacrificing predictive performance. We will also show that if the graphs at hand have a regular structure, for instance when modeling image or video data, one can exploit this regularity to scale the kernel computation to large databases of graphs with thousands of nodes. We support our contributions by exhaustive experiments on a number of real-world graphs from a variety of application domains.

stat.ML↗

arXiv2014

The entropic basis of collective behaviour

In this paper, we identify a radically new viewpoint on the collective behaviour of groups of intelligent agents. We first develop a highly general abstract model for the possible future lives that these agents may encounter as a result of their decisions. In the context of these possible futures, we show that the causal entropic principle, whereby agents follow behavioural rules that maximise their entropy over all paths through the future, predicts many of the observed features of social interactions between individuals in both human and animal groups. Our results indicate that agents are often able to maximise their future path entropy by remaining cohesive as a group, and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of future paths that are possible. We derive social interaction rules that are consistent with maximum-entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Weber's law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus-response mechanism, and providing a novel basis for the common assumption of linearly additive 'social forces' in simulation studies of collective behaviour.

q-bio.OT↗

arXiv2013

Active Learning of Linear Embeddings for Gaussian Processes

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical difficulties. We further introduce a novel technique for approximately marginalizing GP hyperparameters, yielding marginal predictions robust to hyperparameter mis-specification. Our method offers an efficient means of performing GP regression, quadrature, or Bayesian optimization in high-dimensional spaces.

stat.ML↗