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As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable…
We develop, clarify and test various aspects of cluster methods dynamical mean field methods using a soluble toy model as a benchmark. We find that the Cellular Dynamical Mean Field Theory (C-DMFT) converges very rapidly and compare its…
Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifying the statistical…
While limited coupled cluster theory is \textit{formally} nonvariational, it is not broadly appreciated whether this is a major issue \textit{in practice}. We carried out a detailed comparison with \textit{de facto} full CI energies for a…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view…
This paper proposes a novel data-driven approach for identifying and modelling areas with similar temperature variations throufigureh clustering and Space-Time AutoRegressive (STAR) models. Using annual temperature data from 168 countries…
In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…
Clustering methods seek to partition data such that elements are more similar to elements in the same cluster than to elements in different clusters. The main challenge in this task is the lack of a unified definition of a cluster,…
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…
Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal.…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
The conditional extremes (CE) framework has proven useful for analysing the joint tail behaviour of random vectors. However, when applied across many locations or variables, it can be difficult to interpret or compare the resulting extremal…
We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field (cMF) states, and apply it to describe the ground state of strongly-correlated spin systems. In cluster mean-field theory, the ground…
We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel those observables are used to construct…
Multiview clustering (MVC) segregates data samples into meaningful clusters by synthesizing information across multiple views. Moreover, deep learning-based methods have demonstrated their strong feature learning capabilities in MVC…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
We explore the possibility of modifying the multiplicity of the basic cluster in the entropy functional used in the cluster variation method so that truncation errors owing to finite size of the basic cluster may be corrected. The numerical…