Angluin's L$^*$ Algorithm Robustness Analysis with Noise

Konsep Inti

Angluin’s PAC learning algorithm behaves well with random noise but poorly with structured noise, showing robustness against unstructured noise.

Abstrak

The article analyzes the robustness of Angluin's L$^*$ algorithm in the presence of noise. It explores different types of noise introduced to DFAs and evaluates how the algorithm performs under these conditions. The study includes noisy outputs, noisy inputs, counter DFAs, and DFA with pathological behaviors. Experimental evaluations are conducted to determine the impact of word distribution on algorithm performance and the reduction of DFA size for efficiency. The results suggest that the algorithm is robust against random noise but struggles with structured noise.
Structure:

Introduction to Discrete-event Systems and Languages
Angluin’s L$^*$ Algorithm Overview
Types of Noise Introduced to DFAs:

Noisy Outputs
Noisy Inputs
Counter DFAs
DFA with Pathological Behaviors

Experimental Evaluation:

Impact of Word Distribution
Reduction of DFA Size

Random Languages vs Structured Languages

Statistik

AngluinのL∗アルゴリズムはランダムノイズに対してうまく機能しますが、構造化されたノイズに対してはうまくいかないことを示しています。

Kutipan

Wawasan Utama Disaring Dari

Analyzing Robustness of Angluin's L$^*$ Algorithm in Presence of Noise

by Lina... pada arxiv.org 03-20-2024

https://arxiv.org/pdf/2306.08266.pdf

Pertanyaan yang Lebih Dalam

ランダムノイズと構造化されたノイズの違いは何ですか？

ランダムノイズは、確率的に導入されるノイズであり、その影響が予測困難である特徴を持ちます。一方、構造化されたノイズはパターンや規則性がある種類のノイズであり、それによって影響を受けるシステムやデータに特定の形式が加わります。具体的な例として、DFA（Deterministic Finite Automaton）への入力値のランダムな変更（ランダム出力）と正確な置換パターンに基づく入力値の変更（構造化された入力）が挙げられます。

KVのアルゴリズムがランダムノイズに対して強力である理由は何ですか

KVアルゴリズムがランダムノイズに対して強力である理由は何ですか？
KVアルゴリズムがランダムノイズに対して強力である主な理由は、「非再帰列挙可能言語」という概念と関連しています。実際、実験結果から明らかになったように、KVアルゴリズムは通常、「無秩序」または「非構造化」状態から生成された言語を学習することが得意です。このような非再帰列挙可能言語では規則性やパターン性が少なく不規則さを示す傾向があります。したがって、KVアルゴリズムはこのような状況下でも効果的に動作し原本のDFA 22:1
L. Ye et al
Vol. 20:1
Introduction
Discrete-event systems and their languages. Discrete-event systems [CL10] form a large
class of dynamic systems that, given some internal state, evolve from one state to another
one due to the occurrence of an event. For instance, discrete-event systems can represent a
cyber-physical process whose events are triggered by a controller or the environment, or,
a business process whose events are triggered by human activities or software executions.
Often, the behaviors of such systems are classified as safe (aka correct, representative, etc.)
or unsafe. Since a behavior may be identified by its sequence of occurred events, this leads
to the notion of a language.
Analysis versus synthesis. There are numerous formalisms to specify (languages of)
discrete-event systems. From a designer’s perpective, the simpler it is the better its analysis will be. So finite automata and their languages (regular languages) are good candidates for the specification thanks to their simplicity.
Angluin's L∗ algorithm learns minimal deterministic finite automaton DFA regular language membership equivalence queries probabilistic approximatively correct PAC version substitutes equivalence query numerous random membership queries high level confidence answer applied kind device viewed algorithm synthesizing automaton abstracting behavior device based observations interested Angluin's PAC learning algorithm behaves devices obtained DFA introducing noise precisely study whether Angluin's algorithm reduces noise produces DFA closer original noisy device propose several ways introduce noise noisy device inverts classification words w.r.t DFA small probability noisy device modifies small probability letters word asking classification w.r.t DFA noisy device combines classification word w.r.t DFA classification word counter automaton noisy DFA obtained random process two DFA language first second accepted rejected second remaining cases accepted probability main experimental contributions consist showing Angluin's algorithm behaves whenever noisy device produced random process poorly structured noise able eliminate pathological behaviours specified regular way theoretically randomness surely yields non-recursively enumerable languages key words phrases Angluin's algorithm PAC learning noises randomness
Logical Methods Computer Science DOI:10.46298/LMCS-20(1:22)2024 © Lina Ye et al CC Creative Commons
Analyzing Robustness Angluin’s L∗ Algorithm Presence Noise Logical Methods Computer Science Volume Issue pp https://lmcs.episciences.org/ Submitted Jun Published Mar ANALYZING ROBUSTNESS ANGLUIN’S ALGORITHM PRESENCE NOISE LINA YE IGOR KHMELNITSKY SERGE HADDAD BENOˆIT BARBOT BENEDIKT BOLLIG MARTIN LEUCKER DANIEL NEIDER RAJARSHI ROY Universit´e Paris-Saclay CNRS ENS Paris-Saclay CentraleSup´elec LMF France e-mail address [e-mail] Universit´e Paris-Saclay CNRS ENS Paris-Saclay LMF France e-mail address [e-mail] Universit´e Paris-Est Cr´eteil France Universit´e Paris-Saclay CNRS ENS Paris-Saclay LMF France Institute Software Engineering Programming Languages Universit¨at zu L¨ubeck Germany TU Dortmund University Germany Center Trustworthy Data Science Security University Alliance Ruhr Germany Max Planck Institute Software Systems Kaiserslautern Germany Abstract Angluin’s ∗algorithm learns minimal deterministic finite automaton...
Context Ends---
Please provide insightful responses to the following questions based on the context provided above:
What is meant by "noise" in this context?
How does introducing different types of noise impact the performance and robustness of Angluin’s L∗ Algorithm?
What experimental contributions were made regarding analyzing robustness against noise?