Related papers: Bug Hunting By Computing Range Reduction
The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique…
The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR…
Recent studies in Retrieval-Augmented Generation (RAG) have investigated extracting evidence from retrieved passages to reduce computational costs and enhance the final RAG performance, yet it remains challenging. Existing methods heavily…
This article proposes an PQR search method for probabilistic objects. The main idea of our method is to use a strategy called \textit{pre-approximation} that can reduce the initial problem to a highly simplified version, implying that it…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the…
Recent advances in computer vision have made training object detectors more efficient and effective; however, assessing their performance in real-world applications still relies on costly manual annotation. To address this limitation, we…
Bounded Model Checking is one the most successful techniques for finding bugs in program. However, model checkers are resource hungry and are often unable to verify programs with loops iterating over large arrays.We present a transformation…
Controlled branching processes are stochastic growth population models in which the number of individuals with reproductive capacity in each generation is controlled by a random control function. The purpose of this work is to examine the…
Approximate nearest neighbor (ANN) search is a key component in many modern machine learning pipelines; recent use cases include retrieval-augmented generation (RAG) and vector databases. Clustering-based ANN algorithms, that use score…
Simulation can evaluate a statistical method for properties such as Type I Error, FDR, or bias on a grid of hypothesized parameter values. But what about the gaps between the grid-points? Continuous Simulation Extension (CSE) is a…
Composed Image Retrieval (CIR) uses a reference image and a modification text as a query to retrieve a target image satisfying the requirement of ``modifying the reference image according to the text instructions''. However, existing CIR…
The development of rigorous quality assessment model relies on the collection of reliable subjective data, where the perceived quality of visual multimedia is rated by the human observers. Different subjective assessment protocols can be…
Statistical model checking delivers quantitative verification results with statistical guarantees by applying Monte Carlo simulation to formal models. It scales to model sizes and model types that are out of reach for exhaustive, analytical…
Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood;…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
The posterior Cram\'er-Rao lower bound (PCRLB) derived in Tichavsk\'y et al., 1998, provides a bound on the mean square error (MSE) obtained with any non-linear state filter. Computing the PCRLB involves solving complex, multi-dimensional…
Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…
To use machine learning in high stakes applications (e.g. medicine), we need tools for building confidence in the system and evaluating whether it is reliable. Methods to improve model reliability often require new learning algorithms (e.g.…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology…