Related papers: A Monte Carlo Approach to the Fluctuation Problem …
Solving systems of Boolean equations is a fundamental task in symbolic computation and algebraic cryptanalysis, with wide-ranging applications in cryptography, coding theory, and formal verification. Among existing approaches, the Boolean…
The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
DNA sequence alignment is important today as it is usually the first step in finding gene mutation, evolutionary similarities, protein structure, drug development and cancer treatment. Covid-19 is one recent example. There are many…
While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…
The Closest String Problem is an NP-hard problem that aims to find a string that has the minimum distance from all sequences that belong to the given set of strings. Its applications can be found in coding theory, computational biology, and…
The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…
Strings in the real world are often encoded with some level of uncertainty. In the character-level uncertainty model, an uncertain string $X$ of length $n$ on an alphabet $\Sigma$ is a sequence of $n$ probability distributions over…
The performance (accuracy and robustness) of several clustering algorithms is studied for linearly dependent random variables in the presence of noise. It turns out that the error percentage quickly increases when the number of observations…
Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that…
The problem called "String reconstruction from substrings" is a mathematical model of sequencing by hybridization that plays an important role in DNA sequencing. In this problem, we are given a blackbox oracle holding an unknown string…
Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…
The minimizers sampling mechanism is a popular mechanism for string sampling introduced independently by Schleimer et al. [SIGMOD 2003] and by Roberts et al. [Bioinf. 2004]. Given two positive integers $w$ and $k$, it selects the…
We consider a novel approach of measuring the homology of DNA sequences based of the variety of optimal alignments in the longest common subsequence sense. The proposed approach is compared with BLAST in measuring the homology of four…
Real-world instructions with multiple constraints pose a significant challenge to existing large language models (LLMs). An observation is that the LLMs exhibit dramatic performance fluctuation when disturbing the order of the incorporated…
We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…
We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces…
This paper investigates to what extent one can improve reinforcement learning algorithms. Our study is split in three parts. First, our analysis shows that the classical asymptotic convergence rate $O(1/\sqrt{N})$ is pessimistic and can be…
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…