Here,weproposea spatio-translational embeddingmodel,called BoxE,that simultaneously addresses all these limitations.

Social science research often hinges on the relationship between categorical variables and outcomes. We introduce CAVIAR, a novel method for embedding categorical variables that assume values in a high-dimensional ambient space but are sampled from an underlying manifold. Our theoretical and numerical analyses outline challenges posed by such categorical variables in causal inference. Specifically, dynamically varying and sparse levels can lead to violations of the Donsker conditions and a failure of the estimation functionals to converge to a tight Gaussian process. Traditional approaches, including the exclusion of rare categorical levels and principled variable selection models like LASSO, fall short. CAVIAR embeds the data into a lower-dimensional global coordinate system. The mapping can be derived from both structured and unstructured data, and ensures stable and robust estimates through dimensionality reduction. In a dataset of direct-to-consumer apparel sales, we illustrate how high-dimensional categorical variables, such as zip codes, can be succinctly represented, facilitating inference and analysis.

Neural network representation learning for spatial data is a common need for geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in representation learning for points, polylines, and networks, whereas little progress has been made for polygons, especially complex polygonal geometries. In this work, we focus on developing a general-purpose polygon encoding model, which can encode a polygonal geometry (with or without holes, single or multipolygons) into an embedding space. The result embeddings can be leveraged directly (or finetuned) for downstream tasks such as shape classification, spatial relation prediction, and so on. To achieve model generalizability guarantees, we identify a few desirable properties: loop origin invariance, trivial vertex invariance, part permutation invariance, and topology awareness. We explore two different designs for the encoder: one derives all representations in the spatial domain; the other leverages spectral domain representations. For the spatial domain approach, we propose ResNet1D, a 1D CNN-based polygon encoder, which uses circular padding to achieve loop origin invariance on simple polygons. For the spectral domain approach, we develop NUFTspec based on Non-Uniform Fourier Transformation (NUFT), which naturally satisfies all the desired properties. We conduct experiments on two tasks: 1) shape classification based on MNIST; 2) spatial relation prediction based on two new datasets - DBSR-46K and DBSR-cplx46K. Our results show that NUFTspec and ResNet1D outperform multiple existing baselines with significant margins. While ResNet1D suffers from model performance degradation after shape-invariance geometry modifications, NUFTspec is very robust to these modifications due to the nature of the NUFT.

Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-translational embedding model, called BoxE, that simultaneously addresses all these limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a detailed experimental analysis, and show that BoxE achieves state-of-the-art performance, both on benchmark knowledge graphs and on more general KBs, and we empirically show the power of integrating logical rules.

Today, Google announced a plethora of new hardware. Just now, at the event, I got to spend a little bit of hands-on time with the Pixel Phones, Google Home, and the Daydream VR viewer. The first thing I noticed when I started playing with the Pixel Phone is that it's fast. I didn't experience anything resembling lag, no matter how many apps I opened. Google is claiming that the Pixel has the best smartphone camera ever.

The Modified Antarctic Mapping Mission MAMM) was conducted from September to November 2000 onboard RADARSAT. The mission plan consisted of more than 2400 synthetic aperture radar data acquisitions of Antarctica that achieved the scientific objectives and obeyed RADARSAT's resource and operational constraints. Mission planning is a time- and knowledge-intensive effort. It required over a workyear to manually develop a comparable plan for AMM-1, the precursor mission to MAMM. This article describes the design and use of the automated mission planning system for MAMM, which dramatically reduced mission-planning costs to just a few workweeks and enabled rapid generation of what-if scenarios for evaluating alternative mission designs.