Search for: All records

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr ́echet mean. In this work, we equip a set of graph with the pseudometric defined by the l2 norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Fr ́echet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric. 

Rapid advancement in inverse modeling methods have brought into light their susceptibility to imperfect data. This has made it imperative to obtain more explainable and trustworthy estimates from these models. In hydrology, basin characteristics can be noisy or missing, impacting streamflow prediction. We propose a probabilistic inverse model framework that can reconstruct robust hydrology basin characteristics from dynamic input weather driver and streamflow response data. We address two aspects of building more explainable inverse models, uncertainty estimation (uncertainty due to imperfect data and imperfect model) and robustness. This can help improve the trust of water managers, handling of noisy data and reduce costs. We also propose an uncertainty based loss regularization that offers removal of 17% of temporal artifacts in reconstructions, 36% reduction in uncertainty and 4% higher coverage rate for basin characteristics. The forward model performance (streamflow estimation) is also improved by 6% using these uncertainty learning based reconstructions. 

In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to minibatch training, temporal relationships between training segments within the batch (intra-batch) as well as between batches (inter-batch) are not considered, which can lead to limited performance. Stateful RNNs aim to address this issue by passing hidden states between batches. Since Stateful RNNs ignore intra-batch temporal dependency, there exists a trade-off between training stability and capturing temporal dependency. In this paper, we provide a quantitative comparison of different Stateful RNN modeling strategies, and propose two strategies to enforce both intra- and inter-batch temporal dependency. First, we extend Stateful RNNs by defining a batch as a temporally ordered set of training segments, which enables intra-batch sharing of temporal information. While this approach significantly improves the performance, it leads to much larger training times due to highly sequential training. To address this issue, we further propose a new strategy which augments a training segment with an initial value of the target variable from the timestep right before the starting of the training segment. In other words, we provide an initial value of the target variable as additional input so that the network can focus on learning changes relative to that initial value. By using this strategy, samples can be passed in any order (mini-batch training) which significantly reduces the training time while maintaining the performance. In demonstrating the utility of our approach in hydrological modeling, we observe that the most significant gains in predictive accuracy occur when these methods are applied to state variables whose values change more slowly, such as soil water and snowpack, rather than continuously moving flux variables such as streamflow. 

Creating separable representations via representation learning and clustering is critical in analyzing large unstructured datasets with only a few labels. Separable representations can lead to supervised models with better classification capabilities and additionally aid in generating new labeled samples. Most unsupervised and semisupervised methods to analyze large datasets do not leverage the existing small amounts of labels to get better representations. In this paper, we propose a spatiotemporal clustering paradigm that uses spatial and temporal features combined with a constrained loss to produce separable representations. We show the working of this method on the newly published dataset ReaLSAT, a dataset of surface water dynamics for over 680,000 lakes across the world, making it an essential dataset in terms of ecology and sustainability. Using this large unlabelled dataset, we first show how a spatiotemporal representation is better compared to just spatial or temporal representation. We then show how we can learn even better representations using a constrained loss with few labels. We conclude by showing how our method, using few labels, can pick out new labeled samples from the unlabeled data, which can be used to augment supervised methods leading to better classification.