Approximate State-Transition Modeling of Language Disorder Portrayals in Media

Quantitative analysis of how cognitive-linguistic impairments are depicted in broadcast and digital outlets requires dynamic models that capture both disfluency patterns and sampling noise. This paper presents a first-order Markov-chain framework enhanced by a controlled smoothing operator to mitigate spurious low-frequency transitions. We define an empirical transition matrix from annotated utterance segments (fluent, hesitation, error) and apply a Gaussian-kernel–based approximation to produce a smoothed stochastic matrix with provable perturbation bounds. Theoretical results guarantee that the t-step transition error grows at most linearly with the smoothing magnitude and that stationary-distribution shifts remain bounded by the ratio of approximation error to the spectral gap. On a large, multi-source corpus (≈20,000 segments), cross-validated smoothing achieves a 12% perplexity reduction over the unsmoothed chain and reduces cumulative error-state estimation deviation by 19% compared to a threshold-based baseline. A compact case study further illustrates the bias–variance trade-off inherent in smoothing: aggressive approximation on small sequences can dramatically inflate unlikely transitions, underscoring the need for corpus-sensitive parameter tuning. These findings demonstrate that kernel-smoothed stochastic models offer interpretable, computationally efficient tools for analyzing disfluency dynamics over time. Future work will explore higher-order dependencies, nonstationary transition matrices, and hybrid deep‐learning integrations to capture richer contextual patterns in discourse sequences.

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