Yotam Yaniv

David J. Arnold, Dayne Fernandez, Ruizhe Jia et al.

National parks often serve as hotspots for environmental crime such as illegal deforestation and animal poaching. Previous attempts to model environmental crime were either discrete and network-based or required very restrictive assumptions on the geometry of the protected region and made heavy use of radial symmetry. We formulate a level set method to track criminals inside a protected region which uses real elevation data to determine speed of travel, does not require any assumptions of symmetry, and can be applied to regions of arbitrary shape. In doing so, we design a Hamilton-Jacobi equation to describe movement of criminals while also incorporating the effects of patrollers who attempt to deter the crime. We discuss the numerical schemes that we use to solve this Hamilton-Jacobi equation. Finally, we apply our method to Yosemite National Park and Kangaroo Island, Australia and design practical patrol strategies with the goal of minimizing the area that is affected by criminal activity.

James Chapman, Yotam Yaniv, Deanna Needell

Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different locations, which may exhibit heterogeneity. We resolve this problem by solving a modified NMF objective, Stratified-NMF, that simultaneously learns strata-dependent statistics and a shared topics matrix. We develop multiplicative update rules for this novel objective and prove convergence of the objective. Then, we experiment on synthetic data to demonstrate the efficiency and accuracy of the method. Lastly, we apply our method to three real world datasets and empirically investigate their learned features.

Aditi Gupta, Raphael A. Meyer, Yotam Yaniv et al.

To ensure high quality outputs, it is important to quantify the epistemic uncertainty of diffusion models.Existing methods are often unreliable because they mix epistemic and aleatoric uncertainty. We introduce a method based on Fisher information that explicitly isolates epistemic variance, producing more reliable plausibility scores for generated data. To make this approach scalable, we propose FLARE (Fisher-Laplace Randomized Estimator), which approximates the Fisher information using a uniformly random subset of model parameters. Empirically, FLARE improves uncertainty estimation in synthetic time-series generation tasks, achieving more accurate and reliable filtering than other methods. Theoretically, we bound the convergence rate of our randomized approximation and provide analytic and empirical evidence that last-layer Laplace approximations are insufficient for this task.

Alexander Sietsema, Zerrin Vural, James Chapman et al.

Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) decompose non-negative high-dimensional data into non-negative low-rank components. NMF and NTF methods are popular for their intrinsic interpretability and effectiveness on large-scale data. Recent work developed Stratified-NMF, which applies NMF to regimes where data may come from different sources (strata) with different underlying distributions, and seeks to recover both strata-dependent information and global topics shared across strata. Applying Stratified-NMF to multi-modal data requires flattening across modes, and therefore loses geometric structure contained implicitly within the tensor. To address this problem, we extend Stratified-NMF to the tensor setting by developing a multiplicative update rule and demonstrating the method on text and image data. We find that Stratified-NTF can identify interpretable topics with lower memory requirements than Stratified-NMF. We also introduce a regularized version of the method and demonstrate its effects on image data.