Related papers: Expansion Lemma -- Variations and Applications to …
Most blind deconvolution methods usually pre-define a large kernel size to guarantee the support domain. Blur kernel estimation error is likely to be introduced, yielding severe artifacts in deblurring results. In this paper, we first…
This paper introduces the problem of coresets for regression problems to panel data settings. We first define coresets for several variants of regression problems with panel data and then present efficient algorithms to construct coresets…
In a (parameterized) graph edge modification problem, we are given a graph $G$, an integer $k$ and a (usually well-structured) class of graphs $\mathcal{G}$, and ask whether it is possible to transform $G$ into a graph $G' \in \mathcal{G}$…
Let F be a finite family of graphs. In the F-Deletion problem, one is given a graph G and an integer k, and the goal is to find k vertices whose deletion results in a graph with no minor from the family F. This may be regarded as a…
Language Models are the underpin of all modern Natural Language Processing (NLP) tasks. The introduction of the Transformers architecture has contributed significantly into making Language Modeling very effective across many NLP task,…
In this paper, we propose an algorithm that, given an undirected graph $G$ of $m$ edges and an integer $k$, computes a graph $G'$ and an integer $k'$ in $O(k^4 m)$ time such that (1) the size of the graph $G'$ is $O(k^2)$, (2) $k'\leq k$,…
The Minimum Vertex Cover problem, a classical NP-complete problem, presents significant challenges for exact solution on large graphs. Fixed-Parameter Tractability (FPT) offers a powerful paradigm to address such problems by exploiting a…
The problem of modifying a given graph to satisfy certain properties has been one of the central topics in parameterized tractability study. In this paper, we study the cycle contraction problem, which makes a graph into a cycle by edge…
For the sake of reliability, the kernels of Interactive Theorem Provers (ITPs) are generally kept relatively small. On top of the kernel, additional symbols and inference rules are defined. This paper presents an analysis of how kernel…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…
We propose simple polynomial-time algorithms for two linear conic feasibility problems. For a matrix $A\in \mathbb{R}^{m\times n}$, the kernel problem requires a positive vector in the kernel of $A$, and the image problem requires a…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
Tool learning has emerged as a promising direction by extending Large Language Models' (LLMs) capabilities with external tools. Existing tool learning studies primarily focus on the general-purpose tool-use capability, which addresses…
In the Maximize Phylogenetic Diversity problem, we are given a phylogenetic tree that represents the genetic proximity of species, and we are asked to select a subset of species of maximum phylogenetic diversity to be preserved through…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
We study ordinal embedding relaxations in the realm of parameterized complexity. We prove the existence of a quadratic kernel for the {\sc Betweenness} problem parameterized above its tight lower bound, which is stated as follows. For a set…
Exploring the power of linear programming for combinatorial optimization problems has been recently receiving renewed attention after a series of breakthrough impossibility results. From an algorithmic perspective, the related questions…
Parameterized algorithms have been subject to extensive research of recent years and allow to solve hard problems by exploiting a parameter of the corresponding problem instances. There, one goal is to devise algorithms, where the runtime…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…