Analyzing State Sequences with Probabilistic Suffix Trees: ThePSTRPackage

Abstract

This article presents the PST R package for categorical sequence analysis with probabilistic suffix trees (PSTs), i.e., structures that store variable-length Markov chains (VLMCs). VLMCs allow to model high-order dependencies in categorical sequences with parsimonious models based on simple estimation procedures. The package is specifically adapted to the field of social sciences, as it allows for VLMC models to be learned from sets of individual sequences possibly containing missing values; in addition, the package is extended to account for case weights. This article describes how a VLMC model is learned from one or more categorical sequences and stored in a PST. The PST can then be used for sequence prediction, i.e., to assign a probability to whole observed or artificial sequences. This feature supports data mining applications such as the extraction of typical patterns and outliers. This article also introduces original visualization tools for both the model and the outcomes of sequence prediction. Other features such as functions for pattern mining and artificial sequence generation are described as well. The PST package also allows for the computation of probabilistic divergence between two models and the fitting of segmented VLMCs, where sub-models fitted to distinct strata of the learning sample are stored in a single PST.

Sequence Analysis: Where Are We, Where Are We Going?

“…These issues have no definitive solution thus far and deserve further research. While different schemes for imputing missing values have been proposed (e.g., Halpin 2015; Gabadinho and Ritschard 2016), there remains the question of the maximal proportion of missing values that are appropriate to impute in a sequence. Moreover, the real impact of such imputations on the SA outcome remains to be investigated.…”

“…However, the difficulty to synthesize the outcome of Markov-based transition models-especially when more realistic models with order greater than one are considered-negatively affected the extension of their usage. The graphical rendering of hidden Markov models (HMM) by Helske and Helske (2017) (see also Helske et al 2018, in this bundle) as well as the use and rendering of probabilistic suffix trees (Gabadinho and Ritschard 2016) for sequence analysis should facilitate the access to such probabilistic approaches and shed light on how the current situation is linked to the history of previous situations.…”

Do Different Approaches in Population Science Lead to Divergent or Convergent Models?

“…Its goal is to explore and describe the course of events as a whole, without worrying about the risk of knowing the events or their determinants. There have also been recent attempts at a Bayesian extension of the sequence approach with the aid of Hidden Markov Models (Bolano 2014;Helske et al 2018) or variable length Markov models (Gabadinho and Ritschard 2016).…”

Deep Tree Models for ‘Big’ Biological Data

“…But higher-order Markov models are typically impossible to estimate and use in practice, as the number of parameters involved grows exponentially with memory length. In order to overcome this obstacle, numerous approaches have been developed, using more effective, lowerdimensional model classes; see, e.g., the broad discussions in [4,2,10,7].…”

“…The class of variable-memory Markov chain models we consider here were first introduced in Rissanen's celebrated work [22,19], and have also been employed (in some cases with minor variations) in the Probabilistic Suffix Tree (PST) [23,1,7] and Variable-Length Markov Chain (VLMC) [4,3,17] literature. A different class of parsimonious models for higher-order memory modelling, the Markov Transition Distribution (MTD) model, was introduced by Raftery in 1985 [18] and explored further in [2].…”