Related papers: Algorithmic Thresholds in Mean Field Spin Glasses
In 2012, Pflug and Pichler proved, under regularity assumptions, that the value function in Multistage Stochastic Programming (MSP) is Lipschitz continuous w.r.t. the Nested Distance, which is a distance between scenario trees (or discrete…
Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a…
Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…
We discuss a phase transition in spin glass models which have been rarely considered in the past, namely the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e. at a smaller overlap) than…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
We propose a numerical algorithm for computing approximately optimal solutions of the matching for teams problem. Our algorithm is efficient for problems involving large number of agent categories and allows for non-discrete agent type…
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes-optimal estimator seems intractable in general due to its nonconvex…
Mean-field characterizations of first-order iterative algorithms -- including Approximate Message Passing (AMP), stochastic and proximal gradient descent, and Langevin diffusions -- have enabled a precise understanding of learning dynamics…
Approximate Message Passing (AMP) is a general framework for iterative algorithms, originally developed for compressed sensing and later extended to a wide range of high-dimensional inference problems. Although recent work has advanced…
In this work, we present an $\Omega\left(\min\{\log \Delta, \sqrt{\log n}\}\right)$ lower bound for Maximal Matching (MM) in $\Delta$-ary trees against randomized algorithms. By a folklore reduction, the same lower bound applies to Maximal…
Approximate Message Passing (AMP) algorithmshave recently gathered significant attention across disciplines such as statistical physics, machine learning, and communication systems. This study aims to extend AMP algorithms to non-symmetric…
Simulated annealing (SA) attracts more attention among classical heuristic algorithms because the solution of the combinatorial optimization problem can be naturally mapped to the ground state of the Ising Hamiltonian. However, in practical…
The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under…
One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem…
We study statistical properties of 3D classical spin glass layer of certain width and infinite length. The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between…
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of…