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Self-consistency methods are the core technique for improving the reasoning reliability of multimodal large language models (MLLMs). By generating multiple reasoning results through repeated sampling and selecting the best answer via…
Conditional Value-at-Risk (CVaR) is a central tail-risk measure in stochastic structural mechanics, yet its accurate evaluation under high-dimensional, spatially correlated material uncertainty remains computationally prohibitive for…
This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding…
Variational dimensionality reduction methods are widely used for their accuracy, generative capabilities, and robustness. We introduce a unifying framework that generalizes both such as traditional and state-of-the-art methods. The…
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to…
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node,…
Markov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to…
Variational Inference (VI) is a popular alternative to asymptotically exact sampling in Bayesian inference. Its main workhorse is optimization over a reverse Kullback-Leibler divergence (RKL), which typically underestimates the tail of the…
In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the {\it integrated covariation} (the…
Due to the mechanism of recording, the presence of multiple transactions at each recording time becomes a common feature for high-frequency data in financial market. Using random matrix theory, this paper considers the estimation of…
We study the problem of distributed multi-view representation learning. In this problem, $K$ agents observe each one distinct, possibly statistically correlated, view and independently extracts from it a suitable representation in a manner…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
Multiplicative-Additive System Virtual (MAV) is a logic that extends Multiplicative-Additive Linear Logic with a self-dual non-commutative operator expressing the concept of "before" or "sequencing". MAV is also an extenson of the the logic…
We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and…
Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from unnormalized densities by leveraging the momentum of a particle moving in a potential well. We provide a novel analysis of ULMC, motivated by two central questions:…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high…
The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid…
A new algorithm for dynamic independent vector extraction is proposed. It is based on the mixing model where mixing parameters related to the source-of-interest (SOI) are time-variant while the separating parameters are time-invariant. A…
In recent several years, the information bottleneck (IB) principle provides an information-theoretic framework for deep multi-view clustering (MVC) by compressing multi-view observations while preserving the relevant information of multiple…