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Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…
We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…
The classical work of (Arora et al., 1999) provides a scheme that gives, for any $\epsilon>0$, a polynomial time $1-\epsilon$ approximation algorithm for dense instances of a family of $\mathcal{NP}$-hard problems, such as Max-CUT and…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
Thompson sampling for multi-armed bandit problems is known to enjoy favorable performance in both theory and practice. However, it suffers from a significant limitation computationally, arising from the need for samples from posterior…
Probabilistic generative neural networks are useful for many applications, such as image classification, speech recognition and occlusion removal. However, the power budget for hardware implementations of neural networks can be extremely…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
The current data explosion poses great challenges to the approximate aggregation with an efficiency and accuracy. To address this problem, we propose a novel approach to calculate the aggregation answers with a high accuracy using only a…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression algorithms fall short at characterizing patterns other than statistical ones not different…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
The Langevin algorithms are frequently used to sample the posterior distributions in Bayesian inference. In many practical problems, however, the posterior distributions often consist of non-differentiable components, posing challenges for…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…