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Climate models are complex mathematical models designed by meteorologists, geophysicists, and climate scientists, and run as computer simulations, to predict climate. There is currently high variance among the predictions of 20 global climate models, from various laboratories around the world, that inform the Intergovernmental Panel on Climate Change (IPCC). Given temperature predictions from 20 IPCC global climate models, and over 100 years of historical temperature data, we track the changing sequence of which model predicts best at any given time. We use an algorithm due to Monteleoni and Jaakkola that models the sequence of observations using a hierarchical learner, based on a set of generalized Hidden Markov Models, where the identity of the current best climate model is the hidden variable. The transition probabilities between climate models are learned online, simultaneous to tracking the temperature predictions.On historical global mean temperature data, our online learning algorithm's average prediction loss nearly matches that of the best performing climate model in hindsight. Moreover, its performance surpasses that of the average model prediction, which is the default practice in climate science, the median prediction, and least squares linear regression. We also experimented on climate model predictions through the year 2098. Simulating labels with the predictions of any one climate model, we found significantly improved performance using our online learning algorithm with respect to the other climate models and techniques. To complement our global results, we also ran experiments on IPCC global climate model temperature predictions for the specific geographic regions of Africa, Europe, and North America. On historical data, at both annual and monthly time-scales, and in future simulations, our algorithm typically outperformed both the best climate model per region and linear regression. Notably, our algorithm consistently outperformed the average prediction over models, the current benchmark.  2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 372-392, 2011

The forecast of tropical cyclone trajectories is crucial for the protection of people and property. Although forecast dynamical models can provide high-precision short-term forecasts, they are computationally demanding, and current statistical forecasting models have much room for improvement given that the database of past hurricanes is constantly growing. Machine learning methods, that can capture non-linearities and complex relations, have only been scarcely tested for this application. We propose a neural network model fusing past trajectory data and reanalysis atmospheric images (wind and pressure 3D fields). We use a moving frame of reference that follows the storm center for the 24h tracking forecast. The network is trained to estimate the longitude and latitude displacement of tropical cyclones and depressions from a large database from both hemispheres (more than 3000 storms since 1979, sampled at a 6 hour frequency). The advantage of the fused network is demonstrated and a comparison with current forecast models shows that deep learning methods could provide a valuable and complementary prediction. Moreover, our method can give a forecast for a new storm in a few seconds, which is an important asset for real-time forecasts compared to traditional forecasts.

Abstract. We propose and analyze a fast spectral clustering algorithm with computational complexity linear in the number of data points that is directly applicable to large-scale datasets. The algorithm combines two powerful techniques in machine learning: spectral clustering algorithms and Nyström methods commonly used to obtain good quality low rank approximations of large matrices. The proposed algorithm applies the Nyström approximation to the graph Laplacian to perform clustering. We provide theoretical analysis of the performance of the algorithm and show the error bound it achieves and we discuss the conditions under which the algorithm performance is comparable to spectral clustering with the original graph Laplacian. We also present empirical results.

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