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Subseasonal climate forecasting is the task of predicting climate variables, such as temperature and precipitation, in a two-week to two-month time horizon. The primary predictors for such prediction problem are spatio-temporal satellite and ground measurements of a variety of climate variables in the atmosphere, ocean, and land, which however have rather limited predictive signal at the subseasonal time horizon. We propose a carefully constructed spatial hierarchical Bayesian regression model that makes use of the inherent spatial structure of the subseasonal climate prediction task. We use our Bayesian model to then derive decision-theoretically optimal point estimates with respect to various performance measures of interest to climate science. As we show, our approach handily improves on various off-the-shelf ML baselines. Since our method is based on a Bayesian frame- work, we are also able to quantify the uncertainty in our predictions, which is particularly crucial for difficult tasks such as the subseasonal prediction, where we expect any model to have considerable uncertainty at different test locations under differ- ent scenarios. 

We study the problem of learning Ising models in a setting where some of the samples from the underlying distribution can be arbitrarily corrupted. In such a setup, we aim to design statistically optimal estimators in a high-dimensional scaling in which the number of nodes p, the number of edges k and the maximal node degree d are allowed to increase to infinity as a function of the sample size n. Our analysis is based on exploiting moments of the underlying distribution, coupled with novel reductions to univariate estimation. Our proposed estimators achieve an optimal dimension independent dependence on the fraction of corrupted data in the contaminated setting, while also simultaneously achieving high-probability error guarantees with optimal sample-complexity. We corroborate our theoretical results by simulations.