Related papers: Statistical Problems with Planted Structures: Info…
Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
Random graph models with community structure have been studied extensively in the literature. For both the problems of detecting and recovering community structure, an interesting landscape of statistical and computational phase transitions…
Misinformation is still a major societal problem and the arrival of Large Language Models (LLMs) only added to it. This paper analyzes synthetic, false, and genuine information in the form of text from spectral analysis, visualization, and…
This paper investigates the problem of inferring knowledge from data so that the inferred knowledge is interpretable and informative to humans who have prior knowledge. Given a dataset as a collection of system trajectories, we infer…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
Information-theoretic (IT) measures are ubiquitous in artificial intelligence: entropy drives decision-tree splits and uncertainty quantification, cross-entropy is the default classification loss, mutual information underpins representation…
In a variety of physically relevant settings for learning from quantum data, designing protocols that can computationally efficiently extract information remains largely an art, and there are important cases where we believe this to be…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
Many statistical inference problems correspond to recovering the values of a set of hidden variables from sparse observations on them. For instance, in a planted constraint satisfaction problem such as planted 3-SAT, the clauses are sparse…
In social networks, information and influence diffuse among users as cascades. While the importance of studying cascades has been recognized in various applications, it is difficult to observe the complete structure of cascades in practice.…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
Numerical analysts might be expected to pay close attention to a branch of complexity theory called information-based complexity theory (IBCT), which produces an abundance of impressive results about the quest for approximate solutions to…
While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…