Related papers: Depth Distribution in High Dimensions
The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main…
Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…
Deep clustering has recently emerged as a promising technique for complex data clustering. Despite the considerable progress, previous deep clustering works mostly build or learn the final clustering by only utilizing a single layer of…
Bayesian optimization (BO) has been broadly applied to computational expensive problems, but it is still challenging to extend BO to high dimensions. Existing works are usually under strict assumption of an additive or a linear embedding…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…
Given a $k$-CNF formula and an integer $s$, we study algorithms that obtain $s$ solutions to the formula that are maximally dispersed. For $s=2$, the problem of computing the diameter of a $k$-CNF formula was initiated by Creszenzi and…
We consider the problem of computing the largest-area bichromatic separating box among a set of $n$ red points and a set of $m$ blue points in three dimensions. Currently, the best-known algorithm to solve this problem takes $O(m^2 (m +…
We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…
We propose a new approach to the computation of the hypervolume indicator, based on partitioning the dominated region into a set of axis-parallel hyperrectangles or boxes. We present a nonincremental algorithm and an incremental algorithm,…
Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…
We introduce a new framework term coding for extremal problems in discrete mathematics and information flow, where one chooses interpretations of function symbols so as to maximise the number of satisfying assignments of a finite system of…
The discrete distribution clustering algorithm, namely D2-clustering, has demonstrated its usefulness in image classification and annotation where each object is represented by a bag of weighed vectors. The high computational complexity of…
Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we prove a…
Rotary Position Embedding (RoPE) is widely adopted in large language models (LLMs) due to its efficient encoding of relative positions with strong extrapolation capabilities. However, while its application in higher-dimensional input…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…