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Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
This article presents a "Hybrid Self-Attention NEAT" method to improve the original NeuroEvolution of Augmenting Topologies (NEAT) algorithm in high-dimensional inputs. Although the NEAT algorithm has shown a significant result in different…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
FAST problem is finding minimum feedback arc set problem in tournaments. In this paper we present some algorithms that are similar to sorting algorithms for FAST problem and we analyze them. We present Pseudo_InsertionSort algorithm for…
The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…
We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O…
The rise of deep learning has marked significant progress in fields such as computer vision, natural language processing, and medical imaging, primarily through the adaptation of pre-trained models for specific tasks. Traditional…
Spectral inference provides fast algorithms and provable optimality for latent topic analysis. But for real data these algorithms require additional ad-hoc heuristics, and even then often produce unusable results. We explain this poor…
This paper describes the implementation of a new interior point solver for linear programming for the open-source optimization library HiGHS. The solver uses a direct factorisation to solve the Newton systems, choosing the best approach…
Collaborative filtering (CF) is a popular technique in today's recommender systems, and matrix approximation-based CF methods have achieved great success in both rating prediction and top-N recommendation tasks. However, real-world…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
Feature fusion is a commonly used strategy in image retrieval tasks, which aggregates the matching responses of multiple visual features. Feasible sets of features can be either descriptors (SIFT, HSV) for an entire image or the same…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
We design and analyze an adaptive $hp$-finite element method (hp-AFEM) in dimensions $n=1,2$. The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best $hp$-approximation of the current discrete solution and data to a…
Finding the largest cardinality feasible subset of an infeasible set of linear constraints is the Maximum Feasible Subsystem problem (MAX FS). Solving this problem is crucial in a wide range of applications such as machine learning and…
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…
One of the classical problems in machine learning and data mining is feature selection. A feature selection algorithm is expected to be quick, and at the same time it should show high performance. MeLiF algorithm effectively solves this…
Federated fine-tuning (FFT) attempts to fine-tune a pre-trained model with private data from distributed clients by exchanging models rather than data under the orchestration of a parameter server (PS). To overcome the bottleneck forged by…