Related papers: Post-processing optimization and optimal bounds fo…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of…
The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements…
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…
It is well known that, in the description of quantum observables, positive operator valued measures (POVMs) generalize projection valued measures (PVMs) and they also turn out be more optimal in many tasks. We show that a commutative POVM…
This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an…
Solving Stefan problems via neural networks is inherently challenged by the nonlinear coupling between the solutions and the free boundary, which results in a non-convex optimization problem. To address this, this work proposes an Operator…
A machine-learning-based framework for constructing generator-level observables optimized for parameter extraction in particle physics analyses is introduced, referred to as the Optimal Observable Machine (OOM). Unfoldable differential…
Optimal statistical decisions should transcend the language used to describe them. Yet, how do we guarantee that the choice of coordinates - the parameterisation of an optimisation problem - does not subtly dictate the solution? This paper…
We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…
The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…
In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…
Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of…
In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image…
In example-based super-resolution, the function relating low-resolution images to their high-resolution counterparts is learned from a given dataset. This data-driven approach to solving the inverse problem of increasing image resolution…
The objective of this work is to develop a recursive, discrete time quantum filtering equation for a system that interacts with a probe, on which measurements are performed according to the Positive Operator Valued Measures (POVMs)…
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…
Shadow tomography aims to build a classical description of a quantum state from a sequence of simple random measurements. Physical observables are then reconstructed from the resulting classical shadow. Shadow protocols which use…
To describe the pre- and post-selected quantum ensembles, a complex quantity called the weak value of an operator is used. The weak value is highly controversial due to the fact that it is not bounded by the possible eigenvalues of the…