Related papers: From Clustering Supersequences to Entropy Minimizi…
From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
The channel output entropy of a transmitted word is the entropy of the possible channel outputs and similarly, the input entropy of a received word is the entropy of all possible transmitted words. The goal of this work is to study these…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
Sentence embedding methods offer a powerful approach for working with short textual constructs or sequences of words. By representing sentences as dense numerical vectors, many natural language processing (NLP) applications have improved…
Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually defined through the use of some classical losses from…
Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…
We study the entropy $S$ of longest increasing subsequences (LIS), i.e., the logarithm of the number of distinct LIS. We consider two ensembles of sequences, namely random permutations of integers and sequences drawn i.i.d.\ from a limited…
In the deletion channel, an important problem is to determine the number of subsequences derived from a string $U$ of length $n$ when subjected to $t$ deletions. It is well-known that the number of subsequences in the setting exhibits a…
This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…
We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary…
We introduce the Random Subsequence Model, a spin glass model on pairs of random strings $(X,Y) \in \{0,1\}^N \times \{0,1\}^M$ whose partition function counts subsequence embeddings of $Y$ into $X$. We study two variants: the null model,…
Semi-supervised clustering techniques have emerged as valuable tools for leveraging prior information in the form of constraints to improve the quality of clustering outcomes. Despite the proliferation of such methods, the ability to…
We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems,…
A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…
Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is…