Andrew C. Miller, Nick Foti, Ryan P. Adams
preprint [arxiv]
Early version appearing in Advances in Approximate Bayesian Inference 2016 (NIPS Workshop)
We present a black-box variational inference (BBVI) method to approximate intractable posterior distributions with an increasingly rich approximating class. Using mixture distributions as the approximating class, we first describe how to apply the re-parameterization trick and existing BBVI methods to mixtures. We then describe a method, termed Variational Boosting, that iteratively refines an existing approximation by defining and solving a sequence of optimization problems, allowing the practitioner to trade computation time for increased accuracy.
Andrew C. Miller, Luke Bornn
in submission
We develop a novel measure of similarity be- tween two dynamic point clouds, where a dynamic point cloud is a collection of spatiotemporal trajectories representing multiple agents moving and interacting. Certain types of vari- ation in trajectory data make this challenging; two dynamic point clouds may describe the same joint action, but sub-actions may occur at different speeds, spatial locations, or may be performed by different agents. As such, for the purposes of clustering and classifica- tion, known similarity measures fail. To solve this problem we construct a similarity measure in two parts. We first construct a novel distance metric between two sets of points (i.e. static point clouds). We then integrate this distance metric into dynamic time warping, yielding a similarity measure between dynamic point clouds. The resulting simi- larity measure is invariant to permutation of the agents and robust to spatiotemporal variation. Importantly, we describe how to differentiate through dynamic time warping in order to learn a similarity measure specific to an objective function. We use our method to describe the similarity of basketball sequences using player-tracking data from the National Basketball Association.
Scott W. Linderman, Andrew C. Miller, Ryan P. Adams, David M. Blei, Liam Paninski, Matthew J. Johnson
in submission [arxiv]
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dynamical systems (SLDS), we present a new model class that not only discovers these dynamical units, but also explains how their switching behavior depends on observations or continuous latent states. These "recurrent" switching linear dynamical systems provide further insight by discovering the conditions under which each unit is deployed, something that traditional SLDS models fail to do. We leverage recent algorithmic advances in approximate inference to make Bayesian inference in these models easy, fast, and scalable.
Andrew Miller, Albert Wu, Jeffrey Regier, Jon McAuliffe, Dustin Lang, Mr Prabhat, David Schlegel, Ryan Adams
Neural Information Processing Systems 2015 [pdf]
We propose a method for combining two sources of astronomical data, spectroscopy and photometry, which carry information about sources of light (e.g., stars, galaxies, and quasars) at extremely different spectral resolutions. Our model treats the spectral energy distribution (SED) of the radiation from a source as a latent variable, hierarchically generating both photometric and spectroscopic observations. We place a flexible, nonparametric prior over the SED of a light source that admits a physically interpretable decomposition, and allows us to tractably perform inference. We use our model to predict the distribution of the redshift of a quasar from five-band (low spectral resolution) photometric data, the so called "photo-z" problem. Our method shows that tools from machine learning and Bayesian statistics allow us to leverage multiple resolutions of information to make accurate predictions with well-characterized uncertainties.
Vasileios Lampos, Andrew Miller, Steve Crossan, and Christian Stefansen
Scientific Reports [pdf]
This paper presents an improvement on the Google Flu Trends model, an epidemiological surveillance tool for measuring the current rate of influenza like illness (ILI) in the population. These methods relate patterns in user search queries to historical influenza estimates to obtain real-time ILI estimates. We develop a non-linear model based on Gaussian processes and a family of autoregressive models. We compare it to many already proposed methods, assessing predictive performance over five years of flu seasons, 2008-2013, and show that it obtains state of the art predictive performance.
Jeffrey Regier, Andrew Miller, Jon McAuliffe, Ryan Adams, Matt Hoffman, Dustin Lang, David Schlegel, Mr Prabhat
Proceedings of The 32nd International Conference on Machine Learning, pp. 2095–2103, 2015 [link]
We present a new, fully generative model of optical telescope image sets, along with a variational procedure for inference. Each pixel intensity is treated as a Poisson random variable, with a rate parameter dependent on latent properties of stars and galaxies. Key latent properties are themselves random, with scientific prior distributions constructed from large ancillary data sets. We check our approach on synthetic images. We also run it on images from a major sky survey, where it exceeds the performance of the current state-of-the-art method for locating celestial bodies and measuring their colors.
Alexander Franks, Andrew Miller, Luke Bornn, and Kirk Goldsberry
The Annals of Applied Statistics, [AoAS] [arxiv]
We develop a spatial model to analyze the defensive ability of professional basketball players. We first define two preprocessing steps to find a representation of players and posessions, and then we define a parametric model with effects that correspond to interpretable defensive ability.
Alexander Franks*, Andrew Miller*, Luke Bornn, and Kirk Goldsberry
MIT Sloan Sports Analytics Conference, 2015 [pdf] [talk]
best paper award. press:
This paper describes some advanced defensive metrics for NBA basketball, derived from player tracking data. We use the who's guarding whom model from this paper to define a new suite of metrics designed to measure how suppressive and disruptive players are on average, and throughout the entire possession.
Andrew Miller, Luke Bornn, Ryan Adams and Kirk Goldsberry
International Conference on Machine Learning (ICML), 2014 [arxiv]
We develop a dimensionality reduction method that can be applied to collections of point processes on a common space. Using this representation, we analyze the shooting habits of professional basketball players, create a new characterization of offensive player types and model shooting efficiency.
Andrew Miller, Vishal Jain and Joseph L. Mundy
IEEE Transactions on Parallel and Distributed Systems (submitted for review)
This paper presents a scalable system of multiple GPUs and CPUs to reconstruct dense 3-d models. This is a continuation Miller 2011 (which constructed models of size ~ 1 billion voxels) that extends the system to models in the 50-100 billion voxel range. Results are shown for building a 3-d model of an area of about 2 square kilometers (< 1 meter resolution) represented by 50 billion voxels over 4 GPUs in near real-time.
Vishal Jain, Andrew Miller and Joseph L. Mundy
2013 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) pdf
This paper presents a system that fuses both optical and infrared imagery to build a volumetric model. We develop a technique to tightly register multiple volumetric models, and show the benefits of the multi-modal datasource by developing classifiers to label high level features of the landscape (road, sidewalk, pavement, buildings, etc.).
Andrew Miller, Vishal Jain and Joseph L. Mundy
Proceedings of the Fourth Workshop on General Purpose Processing on Graphics Processing Units, ASPLOS 2011 pdf
We develop and optimize a parallel ray tracing-inspired algorithm for both constructing and rendering a high fidelity 3-d volumetric model from aerial imagery. This paper goes over the engineering effort to gain an 800x speedup over serial implementations using a single gpu.
Simple, lightweight dynamic time warping implementation (and visualization) in numpy/python/cython.
A python module for astronomical source discovery and classification.
Sampyl is a package for sampling from probability distributions using MCMC methods. Similar to PyMC3 using theano to compute gradients, Sampyl uses autograd to compute gradients. However, you are free to write your own gradient functions, autograd is not necessary. This project was started as a way to use MCMC samplers by defining models purely with Python and numpy.