Many important phenomena in scientific fields like climate, neuroscience, and epidemiology are naturally represented as spatiotemporal gridded data with complex interactions. Inferring causal relationships from these data is a challenging problem compounded by the high dimensionality of such data and the correlations between spatially proximate points. We present SPACY (SPAtiotemporal Causal discoverY), a novel framework based on variational inference, designed to model latent time series and their causal relationships from spatiotemporal data. SPACY alleviates the high-dimensional challenge by discovering causal structures in the latent space. To aggregate spatially proximate, correlated grid points, we use spatial factors, parametrized by spatial kernel functions, to map observational time series to latent representations. Theoretically, we generalize the problem to a continuous spatial domain and establish identifiability when the observations arise from a nonlinear, invertible function of the product of latent series and spatial factors. Using this approach, we avoid assumptions that are often unverifiable, including those about instantaneous effects or sufficient variability. Empirically, SPACY outperforms state-of-the-art baselines on synthetic data, even in challenging settings where existing methods struggle, while remaining scalable for large grids. SPACY also identifies key known phenomena from real-world climate data. An implementation of SPACY is available at \url{https://github.com/Rose-STL-Lab/SPACY/}

Discovering causal relationships from time series data is significant in fields such as finance, climate science, and neuroscience. However, contemporary techniques rely on the simplifying assumption that data originates from the same causal model, while in practice, data is heterogeneous and can stem from different causal models. In this work, we relax this assumption and perform causal discovery from time series data originating from *a mixture of causal models*. We propose a general variational inference-based framework called MCD to infer the underlying causal models as well as the mixing probability of each sample. Our approach employs an end-to-end training process that maximizes an evidence-lower bound for the data likelihood. We present two variants: MCD-Linear for linear relationships and independent noise, and MCD-Nonlinear for nonlinear causal relationships and history-dependent noise. We demonstrate that our method surpasses state-of-the-art benchmarks in causal discovery tasks through extensive experimentation on synthetic and real-world datasets, particularly when the data emanates from diverse underlying causal graphs. Theoretically, we prove the identifiability of such a model under some mild assumptions. Implementation is available at [https://github.com/Rose-STL-Lab/MCD](https://github.com/Rose-STL-Lab/MCD).

Multi-Agent Path Finding (MAPF) algorithms and their variants can find high-quality collision-free plans for automated warehousing under simplified assumptions about the robot dynamics. However, these simplifying assumptions pose challenging implementational issues as the robots cannot follow the plans precisely. Various robust execution frameworks, such as the Action Dependency Graph (ADG) framework, have been proposed to enable the real-world execution of MAPF plans. Under such a framework, it is unclear how the simplifying assumptions affect the performance of the robots. In this work, we first argue that the ADG framework provides the same robustness guarantees as the single-agent framework (where plans are generated independently for each robot and collisions are avoided through a reservation table), which is widely used in industry. We then improve the efficiency of the ADG framework by integrating it with the Rolling-Horizon Collision-Resolution framework to solve MAPF problems with a persistent stream of online tasks. Using the integrated framework, we compare the standard MAPF model with many of its more complex variants, such as MAPF with rotation, k-robust MAPF, and continuous-time MAPF (taking robot dynamics into account). We examine their effectiveness in improving throughput through realistic simulations of warehouse settings with the Gazebo simulator.

Generalization of machine learning models trained on a set of source domains on unseen target domains with different statistics, is a challenging problem. While many approaches have been proposed to solve this problem, they only utilize source data during training but do not take advantage of the fact that a single target example is available at the time of inference. Motivated by this, we propose a method that effectively uses the target sample during inference beyond mere classification. Our method has three components - (i) A label-preserving feature or metric transformation on source data such that the source samples are clustered in accordance with their class irrespective of their domain (ii) A generative model trained on the these features (iii) A label-preserving projection of the target point on the source-feature manifold during inference via solving an optimization problem on the input space of the generative model using the learned metric. Finally, the projected target is used in the classifier. Since the projected target feature comes from the source manifold and has the same label as the real target by design, the classifier is expected to perform better on it than the true target. We demonstrate that our method outperforms the state-of-the-art Domain Generalization methods on multiple datasets and tasks.

Several applications, like malicious URL detection and web spam detection, require classification on very high-dimensional data. In such cases anomalous data is hard to find but normal data is easily available. As such it is increasingly common to use a one-class classifier (OCC). Unfortunately, most OCC algorithms cannot scale to datasets with extremely high dimensions. In this paper, we present Fast Random projection-based One-Class Classification (FROCC), an extremely efficient, scalable and easily parallelizable method for one-class classification with provable theoretical guarantees. Our method is based on the simple idea of transforming the training data by projecting it onto a set of random unit vectors that are chosen uniformly and independently from the unit sphere, and bounding the regions based on separation of the data. FROCC can be naturally extended with kernels. We provide a new theoretical framework to prove that that FROCC generalizes well in the sense that it is stable and has low bias for some parameter settings. We then develop a fast scalable approximation of FROCC using vectorization, exploiting data sparsity and parallelism to develop a new implementation called ParDFROCC. ParDFROCC achieves up to 2 percent points better ROC than the next best baseline, with up to 12× speedup in training and test times over a range of state-of-the-art benchmarks for the OCC task.