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Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
Large Language Models (LLMs) tend to be unreliable in the factuality of their answers. To address this problem, NLP researchers have proposed a range of techniques to estimate LLM's confidence over facts. However, due to the lack of a…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
Inspired by the linear programming method developed by Cohn and Elkies (Ann. Math. 157(2): 689-714, 2003), we introduce a new linear programming method to solve the sphere packing problem. More concretely, we consider sequences of auxiliary…
In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
In machine learning (ML) verification, the majority of procedures are non-quantitative and therefore cannot be used for verifying probabilistic models, or be applied in domains where hard guarantees are practically unachievable. The…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual…
A new approach to the tracking of sinusoidal chirps using linear programming is proposed. It is demonstrated that the classical algorithm of McAulay and Quatieri is greedy and exhibits exponential complexity for long searches, while…
We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…
Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is…
Pretrained language models (LMs) are susceptible to generate text with nonfactual information. In this work, we measure and improve the factual accuracy of large-scale LMs for open-ended text generation. We design the FactualityPrompts test…
Many of today's problems require techniques that involve the solution of arbitrarily large systems $A\mathbf{x}=\mathbf{b}$. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor…