Conservation science depends on an accurate understanding of what’s happening in a given ecosystem. How many species live there? What is the makeup of the population? How is that changing over time? Species Distribution Modeling (SDM) seeks to predict the spatial (and sometimes temporal) patterns of species occurrence, i.e. where a species is likely to be found. The last few years have seen a surge of interest in applying powerful machine learning tools to challenging problems in ecology [2, 5, 8]. Despite its considerable importance, SDM has received relatively little attention from the computer science community. Our goal in this work is to provide computer scientists with the necessary background to read the SDM literature and develop ecologically useful ML-based SDM algorithms. In particular, we introduce key SDM concepts and terminology, review standard models, discuss data availability, and highlight technical challenges and pitfalls.

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.

Graphical models with latent count variables arise in a number of areas. However, standard inference algorithms do not apply to these models due to the infinite support of the latent variables. Winner and Sheldon (2016) recently developed a new technique using probability generating functions (PGFs) to perform efficient, exact inference for certain Poisson latent variable models. However, the method relies on symbolic manipulation of PGFs, and it is unclear whether this can be extended to more general models. In this paper we introduce a new approach for inference with PGFs: instead of manipulating PGFs symbolically, we adapt techniques from the autodiff literature to compute the higher-order derivatives necessary for inference. This substantially generalizes the class of models for which efficient, exact inference algorithms are available. Specifically, our results apply to a class of models that includes branching processes, which are widely used in applied mathematics and population ecology, and autoregressive models for integer data. Experiments show that our techniques are more scalable than existing approximate methods and enable new applications.

Graphical models with latent count variables arise in a number of fields. Standard exact inference techniques such as variable elimination and belief propagation do not apply to these models because the latent variables have countably infinite support. As a result, approximations such as truncation or MCMC are employed. We present the first exact inference algorithms for a class of models with latent count variables by developing a novel representation of countably infinite factors as probability generating functions, and then performing variable elimination with generating functions. Our approach is exact, runs in pseudo-polynomial time, and is much faster than existing approximate techniques. It leads to better parameter estimates for problems in population ecology by avoiding error introduced by approximate likelihood computations.

We consider the problem of inference in a probabilistic model for transient populations where we wish to learn about arrivals, departures, and population size over all time, but the only available data are periodic counts of the population size at specific observation times. The underlying model arises in queueing theory (as an M/G/inf queue) and also in ecological models for short-lived animals such as insects. Our work applies to both systems. Previous work in the ecology literature focused on maximum likelihood estimation and made a simplifying independence assumption that prevents inference over unobserved random variables such as arrivals and departures. The contribution of this paper is to formulate a latent variable model and develop a novel Gibbs sampler based on Markov bases to perform inference using the correct, but intractable, likelihood function. We empirically validate the convergence behavior of our sampler and demonstrate the ability of our model to make much finer-grained inferences than the previous approach.