Related papers: Uniform Universal Sets, Splitters, and Bisectors
We study universal decoding over unknown discrete additive channels determined by a finite-state (unifilar) random process. Aiming at low-complexity decoders, we study variants of noise-guessing decoders that use estimators for the…
A universal cycle (u-cycle) is a compact listing of a collection of combinatorial objects. In this paper, we use natural encodings of these objects to show the existence of u-cycles for collections of subsets, matroids, restricted…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of…
Given $n$ colored balls, we want to detect if more than $\lfloor n/2\rfloor$ of them have the same color, and if so find one ball with such majority color. We are only allowed to choose two balls and compare their colors, and the goal is to…
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…
An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise…
Seriation methods order a set of descriptions given some criterion (e.g., unimodality or minimum distance between similarity scores). Seriation is thus inherently a problem of finding the optimal solution among a set of permutations of…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
There are major advantages in a newer version of Grover's quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…
Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
Sum-of-norms clustering is a popular convexification of $K$-means clustering. We show that, if the dataset is made of a large number of independent random variables distributed according to the uniform measure on the union of two disjoint…
Let $\mathfrak{C}$ be a class of probability distributions over the discrete domain $[n] = \{1,...,n\}.$ We show that if $\mathfrak{C}$ satisfies a rather general condition -- essentially, that each distribution in $\mathfrak{C}$ can be…
The use of surrogate models instead of computationally expensive simulation codes is very convenient in engineering. Roughly speaking, there are two kinds of surrogate models: the deterministic and the probabilistic ones. These last are…
The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether…
We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a…