We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable models to evaluating a probability generating function which contains many levels of nested high-order derivatives. We contribute faster and more stable AD algorithms for this challenging problem and a novel algorithm to compute exact gradients for learning. These contributions lead to significantly faster and more accurate learning algorithms, and are the first AD algorithms whose running time is polynomial in the number of levels of nesting.

We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the noisy sufficient statistics "as is" outperforms general-purpose differentially private learning algorithms. However, it has three limitations: it ignores knowledge about the data generating process, rests on uncertain theoretical foundations, and exhibits certain pathologies. We develop a more principled approach that applies the formalism of collective graphical models to perform inference over the true sufficient statistics within an expectation-maximization framework. We show that this learns better models than competing approaches on both synthetic data and on real human mobility data used as a case study.

Stochastic network design is a general framework for optimizing network connectivity. It has several applications in computational sustainability including spatial conservation planning, pre-disaster network preparation, and river network optimization. A common assumption in previous work has been made that network parameters (e.g., probability of species colonization) are precisely known, which is unrealistic in real- world settings. We therefore address the robust river network design problem where the goal is to optimize river connectivity for fish movement by removing barriers. We assume that fish passability probabilities are known only imprecisely, but are within some interval bounds. We then develop a planning approach that computes the policies with either high robust ratio or low regret. Empirically, our approach scales well to large river networks. We also provide insights into the solutions generated by our robust approach, which has significantly higher robust ratio than the baseline solution with mean parameter estimates.

Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained inference using Lagrangian relaxation or linear programming, collective graphical models, and forms of semi-supervised learning such as posterior regularization. We present a method to discriminatively learn broad families of inference objectives, capturing powerful non-local statistics of the latent variables, while maintaining tractable and provably fast inference using non-Euclidean projected gradient descent with a distance-generating function given by the Bethe entropy. We demonstrate the performance and flexibility of our method by (1) extracting structured citations from research papers by learning soft global constraints, (2) achieving state-of-the-art results on a widely-used handwriting recognition task using a novel learned non-convex inference procedure, and (3) providing a fast and highly scalable algorithm for the challenging problem of inference in a collective graphical model applied to bird migration.

We propose a decision making framework to optimize the resilience of road networks to natural disasters such as floods. Our model generalizes an existing one for this problem by allowing roads with a broad class of stochastic delay models. We then present a fast algorithm based on the sample average approximation (SAA) method and network design techniques to solve this problem approximately. On a small existing benchmark, our algorithm produces near-optimal solutions and the SAA method converges quickly with a small number of samples. We then apply our algorithm to a large real-world problem to optimize the resilience of a road network to failures of stream crossing structures to minimize travel times of emergency medical service vehicles. On medium-sized networks, our algorithm obtains solutions of comparable quality to a greedy baseline method but is 30–60 times faster. Our algorithm is the only existing algorithm that can scale to the full network, which has many thousands of edges.

We address the problem of robust decision making for stochastic network design. Our work is motivated by spatial conservation planning where the goal is to take management decisions within a fixed budget to maximize the expected spread of a population of species over a network of land parcels. Most previous work for this problem assumes that accurate estimates of different network parameters (edge activation probabilities, habitat suitability scores) are available, which is an unrealistic assumption. To address this shortcoming, we assume that network parameters are only partially known, specified via interval bounds. We then develop a decision making approach that computes the solution with minimax regret. We provide new theoretical results regarding the structure of the minmax regret solution which help develop a computationally efficient approach. Empirically, we show that previous approaches that work on point estimates of network parameters result in high regret on several standard benchmarks, while our approach provides significantly more robust solutions.

We address the problem of estimating the parameters of a time-homogeneous Markov chain given only noisy, aggregate data. This arises when a population of individuals behave independently according to a Markov chain, but individual sample paths cannot be observed due to limitations of the observation process or the need to protect privacy. Instead, only population-level counts of the number of individuals in each state at each time step are available. When these counts are exact, a conditional least squares (CLS) estimator is known to be consistent and asymptotically normal. We initiate the study of method of moments estimators for this problem to handle the more realistic case when observations are additionally corrupted by noise. We show that CLS can be interpreted as a simple "plug-in" method of moments estimator. However, when observations are noisy, it is not consistent because it fails to account for additional variance introduced by the noise. We develop a new, simpler method of moments estimator that bypasses this problem and is consistent under noisy observations.

We develop a fast approximation algorithm called rounded dynamic programming (RDP) for stochastic network design problems on directed trees. The underlying model describes phenomena that spread away from the root of a tree, for example, the spread of influence in a hierarchical organization or fish in a river network. Actions can be taken to intervene in the network—for some cost—to increase the probability of propagation along an edge. Our algorithm selects a set of actions to maximize the overall spread in the network under a limited budget. We prove that the algorithm is a fully polynomial-time approximation scheme (FPTAS), that is, it finds (1−ε)-optimal solutions in time polynomial in the input size and 1/ε. We apply the algorithm to the problem of allocating funds efficiently to remove barriers in a river network so fish can reach greater portions of their native range. Our experiments show that the algorithm is able to produce near-optimal solutions much faster than an existing technique.

Each volume scan consists radial velocity data. For any given pulse volume, radial of a sequence of sweeps during which the antenna velocity tells us the component of target velocity in rotates 360 degrees around a vertical axis while the direction of the radar beam, and we have no additional keeping its elevation angle fixed (figure 2). The result information about the component orthogonal of each sweep is a set of raster data products summarizing to the radar beam. However, the overall pattern of the the radar signal returned from targets within sweep often provides clear evidence about the true discrete pulse volumes, which are the portions of the target velocities. In this example, targets to the northeast atmosphere sensed at a particular antenna position (NE) of the radar station have negative radial and range from the radar. The coordinates of each velocities (dark colors), which means they are pulse volume (r, ϕ, ρ) are measured in a three-dimensional approaching the radar, and targets to the southwest polar coordinate system: r is the distance in (SW) of the radar station have positive radial velocities meters from the antenna, ϕ is the azimuth, which is (light colors), which means they are departing the angle in the horizontal plane between the antenna direction and a fixed reference direction (typically the radar station. We can infer that the targets (in this degrees clockwise from due north), and ρ is the elevation case, predominantly migrating birds) are moving uniformly angle, which is the angle between the antenna in a SW direction, as shown in panel (c). The direction and its projection onto the horizontal spiral pattern in the velocity image is due to changes plane.

The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous work has explored Markov Chain Monte Carlo (MCMC) and MAP approximations for learning and inference. This paper studies Gaussian approximations to the CGM. As the population grows large, we show that the CGM distribution converges to a multivariate Gaussian distribution (GCGM) that maintains the conditional independence properties of the original CGM. If the observations are exact marginals of the CGM or marginals that are corrupted by Gaussian noise, inference in the GCGM approximation can be computed efficiently in closed form. If the observations follow a different noise model (e.g., Poisson), then expectation propagation provides efficient and accurate approximate inference. The accuracy and speed of GCGM inference is compared to the MCMC and MAP methods on a simulated bird migration problem. The GCGM matches or exceeds the accuracy of the MAP method while being significantly faster.