Estimating matrices in the symmetric positive-definite (SPD) cone is of interest for many applications ranging from computer vision to graph learning. While there exist various convex optimization-based estimators, they remain limited in expressivity due to their model-based approach. The success of deep learning has thus led many to use neural networks to learn to estimate SPD matrices in a data-driven fashion. For learning structured outputs, one promising strategy involves architectures designed by unrolling iterative algorithms, which potentially benefit from inductive bias properties. However, designing correct unrolled architectures for SPD learning is difficult: they either do not guarantee that their output has all the desired properties, rely on heavy computations, or are overly restrained to specific matrices which hinders their expressivity. In this paper, we propose a novel and generic learning module with guaranteed SPD outputs called SpodNet, that also enables learning a larger class of functions than existing approaches. Notably, it solves the challenging task of learning jointly SPD and sparse matrices. Our experiments demonstrate the versatility of SpodNet layers.

In this paper we develop a general framework that allows for both knowledge acquisition and forgetting in the Situation Calculus. Based on the Scherl and Levesque (Scherl and Levesque 1993) possible worlds approach to knowledge in the Situation Calculus, we allow for both sensing as well as explicit forgetting actions. This model of forgetting is then compared to existing frameworks. In particular we show that forgetting is well-behaved with respect to the contraction operator of the well-known AGM theory of belief revision (Alchourron, Gardenfors, and Makinson 1985) but that knowledge forgetting is distinct from the more commonly known notion of logical forgetting (Lin and Reiter 1994).

General Game Playing aims to create AI systems that can understand the rules of new games and learn to play them effectively without human intervention. The recent proposal for general game-playing robots extends this to AI systems that play games in the real world. Execution monitoring becomes a necessity when moving from a virtual to a physical environment, because in reality actions may not be executed properly and (human) opponents may make illegal game moves. We develop a formal framework for execution monitoring by which an action theory that provides an axiomatic description of a game is automatically embedded in a meta-game for a robotic player -- called the arbiter -- whose role is to monitor and correct failed actions. This allows for the seamless encoding of recovery behaviours within a meta-game, enabling a robot to recover from these unexpected events.

Records of global temperatures over the last few decades figure prominently in the debate over the climate effects of CO2 emitted by burning fossil fuels, as I discussed in my first post in this series, on What can global temperature data tell us? One recent controversy has been whether or not there has been a pause' (also referred to as a hiatus') in global warming over the last 15 to 20 years, or at least a slowdown' in the rate of warming, a question that I considered in my second post, on Has there been a pause' in global warming? As I discussed in that post, the significance of a pause in warming since around 2000, after a period of warming from about 1970 to 2000, would be to show that whatever the warming effect of CO2, other factors influencing temperatures can be large enough to counteract its effect, and hence, conversely, that such factors could also be capable of enhancing a warming trend (eg, from 1970 to 2000), perhaps giving a misleading impression that the effect of CO2 is larger than it actually is. To phrase this more technically, a pause, or substantial slowdown, in global warming would be evidence that there is a substantial degree of positive autocorrelation in global temperatures, which has the effect of rendering conclusions from apparent temperature trends more uncertain. Whether you see a pause in global temperatures may depend on which series of temperature measurements you look at, and there is controversy about which temperature series is most reliable. In my previous post, I concluded that even when looking at the satellite temperature data, for which a pause seems most visually evident, one can't conclude definitely that the trend in yearly average temperature actually slowed (ignoring short-term variation) in 2001 through 2014 compared to the period 1979 to 2000, though there is also no definite indication that the trend has not been zero in recent years. Of course, I'm not the only one to have looked at the evidence for a pause.

We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small sample sizes, and is scalable to high dimensions. We establish asymptotic bounds for Familywise Error Rate (FWER), and resultant mean square error of a linear predictor on the selected variables. We apply Predictive Correlation Screening to the following two-stage predictor design problem. An experimenter wants to learn a multivariate predictor of gene expressions based on successive biological samples assayed on mRNA arrays. She assays the whole genome on a few samples and from these assays she selects a small number of variables using Predictive Correlation Screening. To reduce assay cost, she subsequently assays only the selected variables on the remaining samples, to learn the predictor coefficients. We show superiority of Predictive Correlation Screening relative to LASSO and correlation learning (sometimes popularly referred to in the literature as marginal regression or simple thresholding) in terms of performance and computational complexity.