Related papers: Computing Marginal and Conditional Divergences bet…

This work establishes the fundamental limits of the classical problem of multi-user distributed computing of linearly separable functions. In particular, we consider a distributed computing setting involving $L$ users, each requesting a…

The deepening penetration of renewable resources into power systems entails great difficulties that have not been surmounted satisfactorily. An issue that merits special attention is the short-term planning of power systems under net load…

Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty,…

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…

While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…

Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…

The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension…

When and why representations learned by different deep neural networks are similar is an active research topic. We choose to address these questions from the perspective of identifiability theory, which suggests that a measure of…

In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such…

Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…

We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…

For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on…

Distribution shifts, where statistical properties differ between training and test datasets, present a significant challenge in real-world machine learning applications where they directly impact model generalization and robustness. In this…

We present new and improved non-asymptotic deviation bounds for Dirichlet processes (DPs), formulated using the Kullback-Leibler (KL) divergence, which is known for its optimal characterization of the asymptotic behavior of DPs. Our method…

In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…

In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…

We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared…