Related papers: On the Formalization of Importance Measures using …

Importance sampling is a well developed method in statistics. Given a random variable $X$, the problem of estimating its expected value $\mu$ is addressed. The standard approach is to use the sample mean as an estimator $\bar x$. In…

Message importance measure (MIM) is an important index to describe the message importance in the scenario of big data. Similar to the Shannon Entropy and Renyi Entropy, MIM is required to characterize the uncertainty of a random process and…

Interpretability studies often involve tracing the flow of information through machine learning models to identify specific model components that perform relevant computations for tasks of interest. Prior work quantifies the importance of a…

In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…

The recent successful paradigm of solving logical reasoning problems with tool-augmented large language models (LLMs) leverages translation of natural language (NL) statements into First-Order Logic~(FOL) and external theorem provers.…

We propose an importance sampling (IS)-based transport map Hamiltonian Monte Carlo procedure for performing full Bayesian analysis in general nonlinear high-dimensional hierarchical models. Using IS techniques to construct a transport map,…

The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the…

Large language models (LLMs) have shown promise in formal theorem proving, but their token-level processing often fails to capture the inherent hierarchical nature of mathematical proofs. We introduce \textbf{Hierarchical Attention}, a…

Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to…

Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations…

We consider Bayesian inference by importance sampling when the likelihood is analytically intractable but can be unbiasedly estimated. We refer to this procedure as importance sampling squared (IS2), as we can often estimate the likelihood…

As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

We introduce a new scheme based on the marked correlation function to probe gravity using the large-scale structure of the Universe. We illustrate our approach by applying it to simulations of the metric-variation $f(R)$ modified gravity…

Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notions of solutions. Typical examples are satisfying…

This paper presents a formal verification guided approach for a principled design and implementation of robust and resilient learning-enabled systems. We focus on learning-enabled state estimation systems (LE-SESs), which have been widely…

As Reinforcement Learning (RL) agents are increasingly deployed in real-world applications, ensuring their behavior is transparent and trustworthy is paramount. A key component of trust is explainability, yet much of the work in Explainable…

Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by…

Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness. The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in…

We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…