Learning Layer-wise Equivariances Automatically using Gradients

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and can not be adapted. Our goal is to allow flexible symmetry constraints that can automatically be learned from data using gradients. Learning symmetry and associated weight connectivity structures from scratch is difficult for two reasons. First, it requires efficient and flexible parameterisations of layer-wise equivariances. Secondly, symmetries act as constraints and are therefore not encouraged by training losses measuring data fit. To overcome these challenges, we improve parameterisations of soft equivariance and learn the amount of equivariance in layers by optimising the marginal likelihood, estimated using differentiable Laplace approximations. The objective balances data fit and model complexity enabling layer-wise symmetry discovery in deep networks. We demonstrate the ability to automatically learn layer-wise equivariances on image classification tasks, achieving equivalent or improved performance over baselines with hard-coded symmetry

FEWS-Waterways For Economically And Efficiently Navigating On Inland Waterways.

This paper describes the use of Delft-FEWS as part of a tool for navigating on Inland Waterways economically and efficiently. Delft-FEWS, as developed by Deltares, is an operational real time forecasting system which links data and models in real time. FEWS-Waterways forecasts water depth, , flow velocity, air clearance based on measured and forecasted hydrological and metrological data and current state of the waterway system. This feature of Delft-FEWS is used in an economy planner giving advice to ship masters with respect to: maximal cargo volume, minimum fuel consumption and the optimal ship speed in order to arrive in time at the destination, e.g. reliable Expected Time of Arrival

Analysis of Longitudinal Marginal Structural Models

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator is used as an initial estimator and the corresponding treatment-orthogonalized, one-step estimator is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. A simulation study demonstrates that the the treatment-orthogonalized, one-step estimator is superior to the IPTW estimator in terms of efficiency. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County

Low Surface Brightness Imaging of the Magellanic System: Imprints of Tidal Interactions between the Clouds in the Stellar Periphery

We present deep optical images of the Large and Small Magellanic Clouds (LMC and SMC) using a low cost telephoto lens with a wide field of view to explore stellar substructure in the outskirts of the stellar disk of the LMC (r < 10 degrees from the center). These data have higher resolution than existing star count maps, and highlight the existence of stellar arcs and multiple spiral arms in the northern periphery, with no comparable counterparts in the South. We compare these data to detailed simulations of the LMC disk outskirts, following interactions with its low mass companion, the SMC. We consider interaction in isolation and with the inclusion of the Milky Way tidal field. The simulations are used to assess the origin of the northern structures, including also the low density stellar arc recently identified in the DES data by Mackey et al. 2015 at ~ 15 degrees. We conclude that repeated close interactions with the SMC are primarily responsible for the asymmetric stellar structures seen in the periphery of the LMC. The orientation and density of these arcs can be used to constrain the LMC's interaction history with and impact parameter of the SMC. More generally, we find that such asymmetric structures should be ubiquitous about pairs of dwarfs and can persist for 1-2 Gyr even after the secondary merges entirely with the primary. As such, the lack of a companion around a Magellanic Irregular does not disprove the hypothesis that their asymmetric structures are driven by dwarf-dwarf interactions.Comment: Submitted to ApJ. Comments are welcome