arXiv subjects

Yotam Yaniv

Publications and source records attributed to Yotam Yaniv.

9 recordsLinked to original sources

arXiv2026

Quantifying Epistemic Uncertainty in Diffusion Models

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.

stat.ML↗

arXiv2025

Tackling Parallelization Challenges of Randomized Preconditioners With Dependency Tracking

Incomplete Cholesky (IC) preconditioners are the standard black-box, memory-efficient first resort for large graph Laplacian systems, but classical IC can break down on irregular graphs. Approximate Cholesky (AC) addresses this with randomized dropping that is provably breakdown-free. Its stochastic fill-in pattern, however, resists static parallelization, creating a "setup bottleneck." We present ParAC, which parallelizes the sequential rchol algorithm on CPUs and GPUs using dynamic dependency tracking and architecture-aware memory management, without altering its numerics. Total time-to-solution speedups over deterministic IC reach $57.3\times$ on CPU and $52.2\times$ on GPU. Algebraic multigrid (AMG) remains preferable on structured PDE discretizations; on irregular graph Laplacians where AMG struggles, ParAC attains up to $7.2\times$ and $6.0\times$. On 200 adversarial SDD systems, ParAC converges on every instance, whereas the AMG solvers fail on 15 and 19, on CPU and GPU, respectively.

cs.DC↗

arXiv2025

Construction of Hierarchically Semi-Separable matrix Representation using Adaptive Johnson-Lindenstrauss Sketching

We present an extension of an adaptive, partially matrix-free, Hierarchically Semi-Separable (HSS) matrix construction algorithm by Gorman et al. [SIAM J. Sci. Comput. 41(5), 2019] which uses Gaussian sketching operators to a broader class of Johnson--Lindenstrauss (JL) sketching operators. We develop theoretical work which justifies this extension. In particular, we extend the earlier concentration bounds to all JL sketching operators and examine this bound for specific classes of such operators including the original Gaussian sketching operators, subsampled randomized Hadamard transform (SRHT) and the sparse Johnson--Lindenstrauss transform (SJLT). We discuss the implementation details of applying SJLT and SRHT efficiently. Then we demonstrate experimentally that using SJLT or SRHT instead of Gaussian sketching operators leads to up to 2.5x speedups of the serial HSS construction implementation in the STRUMPACK C++ library. Additionally, we discuss the implementation of a parallel distributed HSS construction that leverages Gaussian or SJLT sketching operators. We observe a performance improvement of up to 35x when using SJLT sketching operators over Gaussian sketching operators. The generalized algorithm allows users to select their own JL sketching operators with theoretical lower bounds on the size of the operators which may lead to faster run time with similar HSS construction accuracy.

math.NA↗

arXiv2024

Stratified Non-Negative Tensor Factorization

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.

cs.LG↗

arXiv2023

Stratified-NMF for Heterogeneous Data

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.

cs.LG↗

arXiv2022

Multi-Randomized Kaczmarz for Latent Class Regression

Linear regression is effective at identifying interpretable trends in a data set, but averages out potentially different effects on subgroups within data. We propose an iterative algorithm based on the randomized Kaczmarz (RK) method to automatically identify subgroups in data and perform linear regression on these groups simultaneously. We prove almost sure convergence for this method, as well as linear convergence in expectation under certain conditions. The result is an interpretable collection of different weight vectors for the regressor variables that capture the different trends within data. Furthermore, we experimentally validate our convergence results by demonstrating the method can successfully identify two trends within simulated data.

math.NA↗

arXiv2022

Online Signal Recovery via Heavy Ball Kaczmarz

Recovering a signal $x^\ast \in \mathbb{R}^n$ from a sequence of linear measurements is an important problem in areas such as computerized tomography and compressed sensing. In this work, we consider an online setting in which measurements are sampled one-by-one from some source distribution. We propose solving this problem with a variant of the Kaczmarz method with an additional heavy ball momentum term. A popular technique for solving systems of linear equations, recent work has shown that the Kaczmarz method also enjoys linear convergence when applied to random measurement models, however convergence may be slowed when successive measurements are highly coherent. We demonstrate that the addition of heavy ball momentum may accelerate the convergence of the Kaczmarz method when data is coherent, and provide a theoretical analysis of the method culminating in a linear convergence guarantee for a wide class of source distributions.

math.NA↗

arXiv2022

Selectable Set Randomized Kaczmarz

The Randomized Kaczmarz method (RK) is a stochastic iterative method for solving linear systems that has recently grown in popularity due to its speed and low memory requirement. Selectable Set Randomized Kaczmarz (SSRK) is an variant of RK that leverages existing information about the Kaczmarz iterate to identify an adaptive "selectable set" and thus yields an improved convergence guarantee. In this paper, we propose a general perspective for selectable set approaches and prove a convergence result for that framework. In addition, we define two specific selectable set sampling strategies that have competitive convergence guarantees to those of other variants of RK. One selectable set sampling strategy leverages information about the previous iterate, while the other leverages the orthogonality structure of the problem via the Gramian matrix. We complement our theoretical results with numerical experiments that compare our proposed rules with those existing in the literature.

math.NA↗

arXiv2018

Modeling Environmental Crime in Protected Areas Using the Level Set Method

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.

math.NA↗