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The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…
We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…
We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also…
Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum…
Quantum annealing (QA) is a promising approach for solving combinatorial optimization problems; however, it is known to exhibit unfair sampling, in which degenerate ground states are not sampled with equal probability even for sufficiently…
We introduce a novel class of variable selection penalties called TWIN, which provides sensible data-adaptive penalization. Under a linear sparsity regime and random Gaussian designs we show that penalties in the TWIN class have a high…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…
To increase efficiency in automotive manufacturing, newly produced vehicles can move autonomously from the production line to the distribution area. This requires an optimal placement of sensors to ensure full coverage while minimizing the…
By analyzing the characteristics of hardware-native Ising Models and their performance on current and next generation quantum annealers, we provide a framework for determining the prospect of advantage utilizing adiabatic evolution compared…
The broad applicability of Quadratic Unconstrained Binary Optimization (QUBO) constitutes a general-purpose modeling framework for combinatorial optimization problems and are a required format for gate array and quantum annealing computers.…
Quadratic unconstrained binary optimization (QUBO) is the standard interface to quantum annealers, yet a single constrained task admits many QUBO encodings whose penalty choices reshape the energy landscape experienced by hardware. We study…
Adiabatic quantum computing has evolved in recent years from a theoretical field into an immensely practical area, a change partially sparked by D-Wave System's quantum annealing hardware. These multimillion-dollar quantum annealers offer…
Cybersecurity in telecommunication networks often leads to hard combinatorial optimization problems that are challenging to solve with classical methods. This work investigates the practical feasibility of using quantum annealing to address…
We propose a new method for solving binary optimization problems under inequality constraints using a quantum annealer. To deal with inequality constraints, we often use slack variables, as in previous approaches. When we use slack…
Recent advancements in quantum annealing hardware and numerous studies in this area suggests that quantum annealers have the potential to be effective in solving unconstrained binary quadratic programming problems. Naturally, one may desire…
While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit…
The recent availability of quantum annealers as cloud-based services has enabled new ways to handle machine learning problems, and several relevant algorithms have been adapted to run on these devices. In a recent work, linear regression…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…
A quantum annealer exploits quantum effects to solve a particular type of optimization problem. The advantage of this specialized hardware is that it effectively considers all possible solutions in parallel, thereby potentially…