Related papers: Approximation with Error Bounds in Spark

This report describes a technical methodology to render the Apache Spark execution engine adaptive. It presents the engineering solutions, which specifically target to adaptively reorder predicates in data streams with evolving statistics.…

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For…

Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…

In recent years, with the rapid development of sensing technology and the Internet of Things (IoT), sensors play increasingly important roles in traffic control, medical monitoring, industrial production and etc. They generated high volume…

Deep learning models in large-scale machine learning systems are often continuously trained with enormous data from production environments. The sheer volume of streaming training data poses a significant challenge to real-time training…

This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…

Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…

Real-world data streams can change unpredictably due to distribution shifts, feedback loops and adversarial actors, which challenges the validity of forecasts. We present a forecasting framework ensuring valid uncertainty estimates…

Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN,…

Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing…

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically…

Diffusion and flow-matching have emerged as powerful methodologies for generative modeling, with remarkable success in capturing complex data distributions and enabling flexible guidance at inference time. Many downstream applications,…

We study sampling problems associated with potentials that lack smoothness. The potentials can be either convex or non-convex. Departing from the standard smooth setting, the potentials are only assumed to be weakly smooth or non-smooth, or…

Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…

We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…