A Logical Characterization of Constraint-Based Causal Discovery

We present a novel approach to constraint-based causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed (in)dependencies. It is both sound and complete, in the sense that all invariant features of the corresponding partial ancestral graph (PAG) are identified, even in the presence of latent variables and selection bias. The approach shows that every identifiable causal relation corresponds to one of just two fundamental forms. More importantly, as the basic building blocks of the method do not rely on the detailed (graphical) structure of the corresponding PAG, it opens up a range of new opportunities, including more robust inference, detailed accountability, and application to large models

A Fused Elastic Net Logistic Regression Model for Multi-Task Binary Classification

Multi-task learning has shown to significantly enhance the performance of multiple related learning tasks in a variety of situations. We present the fused logistic regression, a sparse multi-task learning approach for binary classification. Specifically, we introduce sparsity inducing penalties over parameter differences of related logistic regression models to encode similarity across related tasks. The resulting joint learning task is cast into a form that lends itself to be efficiently optimized with a recursive variant of the alternating direction method of multipliers. We show results on synthetic data and describe the regime of settings where our multi-task approach achieves significant improvements over the single task learning approach and discuss the implications on applying the fused logistic regression in different real world settings.Comment: 17 page

Markov Network Structure Learning via Ensemble-of-Forests Models

Real world systems typically feature a variety of different dependency types and topologies that complicate model selection for probabilistic graphical models. We introduce the ensemble-of-forests model, a generalization of the ensemble-of-trees model. Our model enables structure learning of Markov random fields (MRF) with multiple connected components and arbitrary potentials. We present two approximate inference techniques for this model and demonstrate their performance on synthetic data. Our results suggest that the ensemble-of-forests approach can accurately recover sparse, possibly disconnected MRF topologies, even in presence of non-Gaussian dependencies and/or low sample size. We applied the ensemble-of-forests model to learn the structure of perturbed signaling networks of immune cells and found that these frequently exhibit non-Gaussian dependencies with disconnected MRF topologies. In summary, we expect that the ensemble-of-forests model will enable MRF structure learning in other high dimensional real world settings that are governed by non-trivial dependencies.Comment: 13 pages, 6 figure

Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles

While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying causal discovery algorithms designed for the acyclic setting on data generated by a system that involves feedback, one would not expect to obtain correct results. In this work, we show that---surprisingly---the output of the Fast Causal Inference (FCI) algorithm is correct if it is applied to observational data generated by a system that involves feedback. More specifically, we prove that for observational data generated by a simple and $\sigma$-faithful Structural Causal Model (SCM), FCI is sound and complete, and can be used to consistently estimate (i) the presence and absence of causal relations, (ii) the presence and absence of direct causal relations, (iii) the absence of confounders, and (iv) the absence of specific cycles in the causal graph of the SCM. We extend these results to constraint-based causal discovery algorithms that exploit certain forms of background knowledge, including the causally sufficient setting (e.g., the PC algorithm) and the Joint Causal Inference setting (e.g., the FCI-JCI algorithm).Comment: Major revision. To appear in Proceedings of the 36 th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR volume 124, 202

AGRICULTURAL LAND USE CHOICE: A DISCRETE CHOICE APPROACH

A discrete choice model and site-specific data are used to analyze land use choices between crop production and pasture in the Corn Belt. The results show that conversion probabilities depend on relative returns, land quality, and government policy. In general it is found that landowners are less inclined to remove land from crop production than to convert land to crop production.Land Economics/Use,

Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schr\"odinger Equations

We consider the existence and stability of real-valued, spatially antiperiodic standing wave solutions to a family of nonlinear Schr\"odinger equations with fractional dispersion and power-law nonlinearity. As a key technical result, we demonstrate that the associated linearized operator is nondegenerate when restricted to antiperiodic perturbations, i.e. that its kernel is generated by the translational and gauge symmetries of the governing evolution equation. In the process, we provide a characterization of the antiperiodic ground state eigenfunctions for linear fractional Schr\"odinger operators on $\mathbb{R}$ with real-valued, periodic potentials as well as a Sturm-Liouville type oscillation theory for the higher antiperiodic eigenfunctions.Comment: 46 pages, 2 figure

Greening Income Support and Supporting Green

A multitude of design decisions influence the performance of voluntary conservation programs. This Economic Brief is one of a set of five exploring the implications of decisions policymakers and program managers must make about who is eligible to receive payments, how much can be received, for what action, and the means by which applicants are selected. In particular, this Brief focuses on potential tradeoffs in combining income support and environmental objectives in a single program.Agricultural and Food Policy, Environmental Economics and Policy,

A system concept for wide swath constant incident angle coverage

Multiple beam approach readily overcomes radar ambiguity constraints associated with orbital systems and therefore permits imagery over swaths much wider than 100 kilometers. Furthermore, the antenna technique permits imagery at nearly constant incident angles. When frequency scanning is employed, the center angle may be programmed. The redundant use of the antenna aperture during reception results in lower transmitted power and in shorter antenna lengths in comparison to conventional designs. Compatibility of the approach with passive imagery is also considered