Related papers: Relations between multi-resolution analysis and qu…
Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori on the coefficient matrix. In this paper, we study quantized…
We consider a robust version of multiple-set linear canonical analysis obtained by using a S-estimator of covariance operator. The related influence functions are derived. Asymptotic properties of this robust method are obtained and a…
Quantum computing leverages quantum mechanics to address computational problems in ways that differ fundamentally from classical approaches. While current quantum hardware remains error-prone and limited in scale, Variational Quantum…
Quantum machine learning (QML) has recently made significant advancements in various topics. Despite the successes, the safety and interpretability of QML applications have not been thoroughly investigated. This work proposes using…
Calculating molecular properties using quantum devices can be done through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available,…
Relations between categorical variables can be analyzed conveniently by multiple correspondence analysis (MCA). %It is well suited to discover relations that may exist between categories of different variables. The graphical representation…
Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
Fact-checking techniques can mitigate hallucinations in Large Language Models (LLMs), a prominent issue in specialized domains. As parameter-efficient techniques such as Low-Rank Adaptation (LoRA) can overcome substantial computational…
This paper, as a continuing work of [1], focus on establishing the fact that if we equip a reciprocal multi-agent (RMA) system with a triangulated Laman graph (TLG), then the associated potential function is generically an equivariant Morse…
Many AI researchers and cognitive scientists have argued that analogy is the core of cognition. The most influential work on computational modeling of analogy-making is Structure Mapping Theory (SMT) and its implementation in the Structure…
Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors…
By deriving influence functions related to multiple-set linear canonical analysis (MSLCA) we show that the classical version of this analysis, based on empirical covariance operators, is not robust. Then, we introduce a robust version of…
The search for empirical schemes to evidence the nonclassicality of large masses is a central quest of current research. However, practical schemes to witness the irreducible quantumness of an arbitrarily large mass are still lacking. To…
We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…
This paper presents a robust matrix elastic net based canonical correlation analysis (RMEN-CCA) for multiple view unsupervised learning problems, which emphasizes the combination of CCA and the robust matrix elastic net (RMEN) used as…
In this paper, we introduce Functional Generalized Canonical Correlation Analysis (FGCCA), a new framework for exploring associations between multiple random processes observed jointly. The framework is based on the multiblock Regularized…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
Many analyses of multivariate data focus on evaluating the dependence between two sets of variables, rather than the dependence among individual variables within each set. Canonical correlation analysis (CCA) is a classical data analysis…
Magnetic resonance imaging (MRI) quality assessment is crucial for clinical decision-making, yet remains challenging due to data scarcity and protocol variability. Traditional approaches face fundamental trade-offs: signal-based methods…