63 citations · 149 across the 13 of their papers we have counts for
17 papers
Inverse of a Sum of Random Matrices: A Dynamical Mean-Field Approach
Burak Çakmak, Manfred Opper
We study , where are symmetric positive definite, with limiting eige…
Joint Message Detection, Channel, and User Position Estimation for Unsourced Random Access in Cell-Free Networks
Eleni Gkiouzepi, Burak Çakmak, Manfred Opper +1
We consider unsourced random access (uRA) in user-centric cell-free (CF) wireless networks, where random access users send codewords from a common codebook during specifically dedi…
A Convergence Analysis of Approximate Message Passing with Non-Separable Functions and Applications to Multi-Class Classification
Burak Çakmak, Yue M. Lu, Manfred Opper
Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we presen…
Analysis of Random Sequential Message Passing Algorithms for Approximate Inference
Burak Çakmak, Yue M. Lu, Manfred Opper
We analyze the dynamics of a random sequential message passing algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To mode…
Exact solution to the random sequential dynamics of a message passing algorithm
Burak Çakmak, Manfred Opper
We analyze the random sequential dynamics of a message passing algorithm for Ising models with random interactions in the large system limit. We derive exact results for the two-ti…
A Dynamical Mean-Field Theory for Learning in Restricted Boltzmann Machines
Burak Çakmak, Manfred Opper
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models…
Understanding the dynamics of message passing algorithms: a free probability heuristics
Manfred Opper, Burak Çakmak
We use freeness assumptions of random matrix theory to analyze the dynamical behavior of inference algorithms for probabilistic models with dense coupling matrices in the limit of…
Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach
Burak Çakmak, Manfred Opper
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between…
Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices
Burak Çakmak, Manfred Opper
We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the ther…
Expectation Propagation for Approximate Inference: Free Probability Framework
Burak Çakmak, Manfred Opper
We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning. Applied to generalized l…
Dynamical Functional Theory for Compressed Sensing
Burak Çakmak, Manfred Opper, Ole Winther +1
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation ma…
Self-Averaging Expectation Propagation
Burak Çakmak, Manfred Opper, Bernard H. Fleury +1
We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems unde…
Cooperative Localization for Mobile Networks: A Distributed Belief Propagation - Mean Field Message Passing Algorithm
Burak Çakmak, Daniel N. Urup, Florian Meyer +3
We propose a hybrid message passing method for distributed cooperative localization and tracking of mobile agents. Belief propagation and mean field message passing are employed fo…
A Theory of Solving TAP Equations for Ising Models with General Invariant Random Matrices
Manfred Opper, Burak Çakmak, Ole Winther
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develo…
S-AMP for Non-linear Observation Models
Burak Çakmak, Ole Winther, Bernard H. Fleury
Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-l…
S-AMP: Approximate Message Passing for General Matrix Ensembles
Burak Çakmak, Ole Winther, Bernard H. Fleury
In this work we propose a novel iterative estimation algorithm for linear observation systems called S-AMP whose fixed points are the stationary points of the exact Gibbs free ener…
Capacity Scaling in MIMO Systems with General Unitarily Invariant Random Matrices
Burak Çakmak, Ralf R. Müller, Bernard H. Fleury
We investigate the capacity scaling of MIMO systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either th…