Related papers: Kernel Belief Propagation
We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…
In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified message-passing algorithm architecture. We generalize the…
The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…
Belief propagation with quantum messages (BPQM) provides a low-complexity alternative to collective measurements for communication over classical--quantum channels. Prior BPQM constructions and density-evolution (DE) analyses have focused…
Uncertainty quantification is essential for deploying machine learning models in high-stakes domains such as scientific discovery and healthcare. Conformal Prediction (CP) provides finite-sample coverage guarantees under exchangeability, an…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
A key idea in coding for the broadcast channel (BC) is binning, in which the transmitter encode information by selecting a codeword from an appropriate bin (the messages are thus the bin indexes). This selection is normally done by solving…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data.…
We consider online learning for minimizing regret in unknown, episodic Markov decision processes (MDPs) with continuous states and actions. We develop variants of the UCRL and posterior sampling algorithms that employ nonparametric Gaussian…
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…
Gaussian belief propagation (GaBP) is an iterative algorithm for computing the mean of a multivariate Gaussian distribution, or equivalently, the minimum of a multivariate positive definite quadratic function. Sufficient conditions, such as…
Envelope methods improve the estimation efficiency in multivariate linear regression by identifying and separating the material and immaterial parts of the responses or the predictors and estimating the regression coefficients using only…
Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…
The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the…