Sparse Markov Chains for Sequence Data

Partially Observable Markov Models Inferred Using Statistical Tests Reveal Context-Dependent Syllable Transitions in Bengalese Finch Songs

Generative models have diverse applications, including language processing and birdsong analysis. In this study, we demonstrate how a statistical test, designed to prevent overgeneralization in sequence generation, can be used to infer minimal models for the syllable sequences in Bengalese finch songs. We focus on the partially observable Markov model (POMM), which consists of states and the probabilistic transitions between them. Each state is associated with a specific syllable, with the possibility that multiple states may correspond to the same syllable. This characteristic differentiates the POMM from a standard Markov model, where each syllable is linked to a single state. The presence of multiple states for a syllable suggests that transitions between syllables are influenced by the specific contexts in which these transitions occur. We apply this method to analyze the songs of six adult male Bengalese finches, both before and after they were deafened. Our results indicate that auditory feedback plays a crucial role in shaping the context-dependent syllable transitions characteristic of Bengalese finch songs.

Dynamic order Markov model for categorical sequence clustering

Markov models are extensively used for categorical sequence clustering and classification due to their inherent ability to capture complex chronological dependencies hidden in sequential data. Existing Markov models are based on an implicit assumption that the probability of the next state depends on the preceding context/pattern which is consist of consecutive states. This restriction hampers the models since some patterns, disrupted by noise, may be not frequent enough in a consecutive form, but frequent in a sparse form, which can not make use of the information hidden in the sequential data. A sparse pattern corresponds to a pattern in which one or some of the state(s) between the first and last one in the pattern is/are replaced by wildcard(s) that can be matched by a subset of values in the state set. In this paper, we propose a new model that generalizes the conventional Markov approach making it capable of dealing with the sparse pattern and handling the length of the sparse patterns adaptively, i.e. allowing variable length pattern with variable wildcards. The model, named Dynamic order Markov model (DOMM), allows deriving a new similarity measure between a sequence and a set of sequences/cluster. DOMM builds a sparse pattern from sub-frequent patterns that contain significant statistical information veiled by the noise. To implement DOMM, we propose a sparse pattern detector (SPD) based on the probability suffix tree (PST) capable of discovering both sparse and consecutive patterns, and then we develop a divisive clustering algorithm, named DMSC, for Dynamic order Markov model for categorical sequence clustering. Experimental results on real-world datasets demonstrate the promising performance of the proposed model.

Modelling sequences and temporal networks with dynamic community structures

In evolving complex systems such as air traffic and social organisations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and links that change over time, they remain highly complex. It is therefore often necessary to use methods that extract the temporal networks' large-scale dynamic community structure. However, such methods are subject to overfitting or suffer from effects of arbitrary, a priori-imposed timescales, which should instead be extracted from data. Here we simultaneously address both problems and develop a principled data-driven method that determines relevant timescales and identifies patterns of dynamics that take place on networks, as well as shape the networks themselves. We base our method on an arbitrary-order Markov chain model with community structure, and develop a nonparametric Bayesian inference framework that identifies the simplest such model that can explain temporal interaction data.The description of temporal networks is usually simplified in terms of their dynamic community structures, whose identification however relies on a priori assumptions. Here the authors present a data-driven method that determines relevant timescales for the dynamics and uses it to identify communities.