Probabilistic finite-state machines - part I

This work presents a data-driven statistical approach with which to recognize pen-based music compositions. Unlike previous works, no assumption is made as regards the handwriting notation, but the system is able to adapt to any kind of style obtained from training data. The series of strokes received as input is mapped onto a stochastic representation, which is combined with a formal language that describes musical symbols in terms of stroke primitives.A Probabilistic Finite-State Automaton is then obtained, which defines probabilities over the set of musical sequences. This model is eventually crossed with a semantic language to avoid sequences that do not make musical sense. Finally, a decoding strategy is applied in order to output a hypothesis concerning the musical sequence actually written. Comprehensive experimentation with several decoding algorithms, stroke similarity measures and probability density estimators are tested and evaluated following different metrics of interest to both user-dependent and user-independent scenarios. The results demonstrate that it is possible to learn the handwriting music style, obtaining competitive performances in each case considered.

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“…A Pfa is a generative device for which there are a number of possible definitions 305 (Paz, 1971;Vidal et al, 2005).…”

Section: Building a Probabilistic Automatonmentioning

confidence: 99%

Recognition of pen-based music notation with finite-state machines

Calvo-Zaragoza

Oncina

2017

Expert Systems with Applications

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“…For the purposes of analysis we use probabilistic deterministic finite automata (PDFA) [9], which have the bare minimum needed to represent distributions generated by business processes. A PDFA is a five-tuple A = (Q A , Σ, δ A , q 0 , q F ), where Q A is finite set of states including single start and end states q 0 , q F ; Σ is an alphabet of symbols; and δ A : Q A × Σ × Q A → [0, 1] defines the probability function governing transition between states.…”

Section: Processes As Distributions Over Strings Of Symbolsmentioning

confidence: 99%

A Principled Approach to the Analysis of Process Mining Algorithms

Weber

Bordbar

Tiňo

2011

Lecture Notes in Computer Science

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Abstract. Process mining uses event logs to learn and reason about business process models. Existing algorithms for mining the control-flow of processes in general do not take into account the probabilistic nature of the underlying process, which affects the behaviour of algorithms and the amount of data needed for confidence in mining. We contribute a first step towards a novel probabilistic framework within which to talk about approaches to process mining, and apply it to the well-known Alpha Algorithm. We show that knowledge of model structures and algorithm behaviour can be used to predict the number of traces needed for mining.

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“…Basically, a cfset C is not a dpfa [11] over Z * since F (p) + (b|a)∈Z,q∈Q T (p, (b|a), q) = 1 in general. However, by using Constraints (1) and (2), we can show that for every fixed input string x ∈ X * , P (y|C, x) = z∈L(x,y) P (z|C) defines a distribution over Y * : y∈Y * P (y|C, x) = 1, that is the reason why we speak of conditional fsets.…”

Section: Definitionmentioning

confidence: 99%

“…It is now clear that if we want P to generate a distribution over Y * , then P must be a pfa [11], i.e., for every state, the probability of the outgoing transitions plus the probability of this state to be final must be 1. This is exactly the statements of Constraints (1) and (2).…”

Section: Definitionmentioning

confidence: 99%

A Discriminative Model of Stochastic Edit Distance in the Form of a Conditional Transducer

Marc

Janodet

Sebban

2006

Grammatical Inference: Algorithms and Applications

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Abstract. Many real-world applications such as spell-checking or DNA analysis use the Levenshtein edit-distance to compute similarities between strings. In practice, the costs of the primitive edit operations (insertion, deletion and substitution of symbols) are generally hand-tuned. In this paper, we propose an algorithm to learn these costs. The underlying model is a probabilitic transducer, computed by using grammatical inference techniques, that allows us to learn both the structure and the probabilities of the model. Beyond the fact that the learned transducers are neither deterministic nor stochastic in the standard terminology, they are conditional, thus independant from the distributions of the input strings. Finally, we show through experiments that our method allows us to design cost functions that depend on the string context where the edit operations are used. In other words, we get kinds of context-sensitive edit distances.

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Probabilistic finite-state machines - part I

Cited by 213 publications

References 61 publications

Recognition of pen-based music notation with finite-state machines

Recognition of pen-based music notation with finite-state machines

A Principled Approach to the Analysis of Process Mining Algorithms

A Discriminative Model of Stochastic Edit Distance in the Form of a Conditional Transducer

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