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Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis…

By revisiting the mathematical foundation of the uncertainty relation, skew information-based uncertainty sequences are developed for any two quantum channels. A reinforced version of the Cauchy-Schwarz inequality is adopted to improve the…

We explore fairness from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We…

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference…

Estimating the Kullback-Leibler (KL) divergence between two distributions given samples from them is well-studied in machine learning and information theory. Motivated by considerations of multi-group fairness, we seek KL divergence…

Selective classification enables models to make predictions only when they are sufficiently confident, aiming to enhance safety and reliability, which is important in high-stakes scenarios. Previous methods mainly use deep neural networks…

In this paper, using the concept of natural density, we have introduced the ideas of statistical and rough statistical convergence in an $S$-metric space. We have investigated some of their basic properties. We have defined statistical…

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation $\mathbf{t}$ by striking a trade-off…

Conformal prediction is a popular technique for constructing prediction intervals with distribution-free coverage guarantees. The coverage is marginal, meaning it only holds on average over the entire population but not necessarily for any…

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…

Change point detection in time series aims to identify moments when the probability distribution of time series changes. It is widely applied in many areas, such as human activity sensing and medical science. In the context of multivariate…

Neural processes are meta-learning models that map context sets to predictive distributions. While inspired by stochastic processes, NPs do not generally satisfy the Kolmogorov consistency conditions required to define a valid stochastic…

Consider two forecasters, each making a single prediction for a sequence of events over time. We ask a relatively basic question: how might we compare these forecasters, either online or post-hoc, while avoiding unverifiable assumptions on…

Similarity-based clustering methods separate data into clusters according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose {\em Clustering by Discriminative…

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…

During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan…

Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…

The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing…

Time series generation (TSG) synthesizes realistic sequences and has achieved remarkable success. Among TSG, conditional models generate sequences given observed covariates, however, such models learn observational correlations without…