Related papers: On spurious fixed points in iterative maximum like…
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
We propose a probabilistic quantum algorithm that decides whether a monochrome picture matches a given template (or one out of a set of templates). As a major advantage to classical pattern recognition, the algorithm just requires a few…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
In this paper, we presented an efficient algorithm to implement the regularization reconstruction of SPECT. Image reconstruction with priori assumptions is usually modeled as a constrained optimization problem. However, there is no…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…
A new algorithmic framework is presented for holographic phase retrieval via maximum likelihood optimization, which allows for practical and robust image reconstruction. This framework is especially well-suited for holographic coherent…
This paper concerns a class of composite image reconstruction models for impluse noise removal, which is rather general and covers existing convex and nonconvex models proposed for reconstructing images with impluse noise. For this…
We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the…
We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…
The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective…
We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix $\rho$) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by…
We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector. These are employed to devise adaptive sequential sampling procedures that guarantee recovery…
Theoretical inverse problems are often studied in an ideal infinite-dimensional setting. The well-posedness theory provides a unique reconstruction of the parameter function, when an infinite amount of data is given. Through the lens of…
This paper is concerned with function reconstruction from samples. The sampling points used in several approaches are (1) structured points connected with fast algorithms or (2) unstructured points coming from, e.g., an initial random draw…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…