Related papers: Simulations, Computations, and Statistics for Long…
This paper shows that a simple algorithm produces the {\em all-prefixes-LCSs-graph} in $O(mn)$ time for two input sequences of size $m$ and $n$. Given any prefix $p$ of the first input sequence and any prefix $q$ of the second input…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
Many constructs that characterize language, like its complexity or emotionality, have a naturally continuous semantic structure; a public speech is not just "simple" or "complex," but exists on a continuum between extremes. Although large…
The distributions of the $m$-th longest runs of multivariate random sequences are considered. For random sequences made up of $k$ kinds of letters, the lengths of the runs are sorted in two ways to give two definitions of run length…
Live sequence charts (LSCs) have been proposed as an inter-object scenario-based specification and visual programming language for reactive systems. In this paper, we introduce a logic-based framework to check the consistency of an LSC…
Measuring the similarity of short written contexts is a fundamental problem in Natural Language Processing. This article provides a unifying framework by which short context problems can be categorized both by their intended application and…
Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the…
In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of…
Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…
Let $(X_k)_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be two independent sequences of i.i.d. random variables, with values in a finite and totally ordered alphabet $\mathcal{A}_m:=\{1,\dots,m\}$, and having respective probability mass function…
Can large language models (LLMs) simulate social surveys? To answer this question, we conducted millions of simulations in which LLMs were asked to answer subjective questions. A comparison of different LLM responses with the European…
The longest square subsequence (LSS) problem consists of computing a longest subsequence of a given string $S$ that is a square, i.e., a longest subsequence of form $XX$ appearing in $S$. It is known that an LSS of a string $S$ of length…
Cosine similarity is a widely used measure of the relatedness of pre-trained word embeddings, trained on a language modeling goal. Datasets such as WordSim-353 and SimLex-999 rate how similar words are according to human annotators, and as…
Large language models (LLMs) often struggle to accurately read and comprehend extremely long texts. Current methods for improvement typically rely on splitting long contexts into fixed-length chunks. However, fixed truncation risks…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis…
This paper presents a new approach for measuring semantic similarity/distance between words and concepts. It combines a lexical taxonomy structure with corpus statistical information so that the semantic distance between nodes in the…
Let $W^{(n)}$ be the $n$-letter word obtained by repeating a fixed word $W$, and let $R_n$ be a random $n$-letter word over the same alphabet. We show several results about the length of the longest common subsequence (LCS) between…
Large language models (LLMs) have exhibited impressive performance and surprising emergent properties. However, their effectiveness remains limited by the fixed context window of the transformer architecture, posing challenges for…
Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC…