Abstract:

The study of theoretical properties of wide and deep neural networks is a growing body of research that complements their empirical success. In this paper, we study the partial derivatives of a random, wide, fully connected neural network w.r.t. each individual feature, which we refer to as the feature sensitivities of that neural network. Under a set of general conditions, as the network widens, we show that these sensitivities are consistent around their mean. Moreover, we show that these sensitivities, as a random function of the features, converge in distribution to Gaussian processes under proper scaling. We discuss the ramifications of such behavior and how this can be leveraged to obtain robust estimates of feature importance and pruning strategies.

Abstract:

A number of studies have shown that the frequency and intensity of extreme precipitation events has increased across the contiguous United States (CONUS) over the previous century, and that this trend is projected to continue. The increasing frequency of these extreme precipitation events is attributable to climate change and will likely increase the frequency of flooding events across CONUS, resulting in a potentially heavy socioeconomic burden.
However, the results of analyzing 1-day precipitation events in isolation may not accurately reflect trends in flood risk, since flooding events are associated with a variety other factors. One of the most important such factors is groundwater level, since the true risk of flooding is related to the ability of precipitation to drain away into unsaturated soil.
In our statistical analysis, we derive a processed count dataset from NOAA’s Physical Sciences Laboratory’s Twentieth Century Reanalysis dataset that accounts for both extreme precipitation and 30-day preceding precipitation, which serves as a proxy for groundwater level. We then apply our spatial spline-based Poisson model to this dataset with an intensity parameter λ that varies in space and time.
Our analysis finds a statistically significant increase in flood risk across almost all regions of CONUS, and that the spatial distribution of the magnitude of this increase differs from that for extreme precipitation events.