ProbHMI: Probabilistic HMI & Health Inference

• ProbHMI is a family of approaches that model uncertainty explicitly in human-machine interfaces and latent health states.
• It employs probabilistic frameworks ranging from error-timing and workload posteriors to hidden semi-Markov models for health state inference.
• Applications span risk-informed nuclear interface analysis, automated driving HMI, human motion forecasting, and remaining useful life prediction.

Searching arXiv for papers on “ProbHMI” and closely related formulations to ground the article. ProbHMI is a label used in recent technical literature for several distinct but methodologically related research programs centered on explicit uncertainty treatment. In one lineage, it denotes probabilistic human–machine interface analysis for risk-informed human reliability, workload inference, supervisory support, and uncertainty-aware motion prediction; in another, it denotes “Probabilistic Health Monitoring and Inference,” a higher-order hidden semi-Markov framework for latent health-state estimation and remaining useful life prediction. Across these usages, the recurring principle is that interaction, reliability, workload, motion, or health are modeled as distributions, posterior states, or quantified tail risks rather than as purely deterministic phenomena (Xiao et al., 28 Jun 2025, Ma et al., 19 Jul 2025, Liu et al., 2024, Liao et al., 2020).

1. Scope, terminology, and recurring probabilistic commitments

In current arXiv usage, ProbHMI is not a single canonical architecture. It names several probabilistic formalisms whose targets differ, but whose common structure is explicit inference under uncertainty. The main documented usages surveyed here are summarized below.

Usage of ProbHMI	Core probabilistic object	Representative paper
Risk-informed HMI reliability	Path-level error incidence, timing tails, PIF classes	(Xiao et al., 28 Jun 2025)
Objective HMI workload assessment	Posterior workload state from psychophysiology	(Liu et al., 2024)
Supervisory driving HMI with probabilistic extensions	Probabilistic spacing and coupling-risk cues	(Hager et al., 18 May 2026)
Human-centered stochastic control	Joint human–machine state and variability distributions	(Kille et al., 2024)
3D human motion forecasting	Latent predictive densities and quantiles	(Ma et al., 19 Jul 2025)
Health Monitoring and Inference	Hidden health states, state durations, RUL distribution	(Liao et al., 2020)

The mathematical commitments differ by application. InSight-R models required time as $T_{reqd} \sim \text{Lognormal}(\mu,\sigma=0.28)$ and identifies human failure events from “error-prone” and “time-deviated” paths (Xiao et al., 28 Jun 2025). The workload-assessment formulation defines a posterior $p(w \mid x, H)$ over workload state given psychophysiological features and HMI design (Liu et al., 2024). The motion-forecasting formulation models future latent states with factorized Gaussians and exposes density and quantile information through an invertible mapping (Ma et al., 19 Jul 2025). The health-monitoring formulation uses higher-order hidden semi-Markov dynamics and simulation-based remaining useful life prediction (Liao et al., 2020).

This suggests that ProbHMI is best understood as a family resemblance term. A plausible implication is that the core unifier is not domain, but the locus at which probability enters the system: interface paths, operator workload, supervisory state, motor variability, future pose trajectories, or latent degradation state.

2. ProbHMI as risk-informed interface-induced human reliability

A technically explicit ProbHMI formulation appears in “InSight-R: A Framework for Risk-informed Human Failure Event Identification and Interface-Induced Risk Assessment Driven by AutoGraph” (Xiao et al., 28 Jun 2025). The framework targets digital nuclear control environments, where conventional HRA methods are described as relying heavily on expert judgment for identifying human failure events (HFEs) and assigning performance influencing factors (PIFs). InSight-R addresses this by linking empirical behavioral data to an interface-embedded knowledge graph (IE-KG) constructed by AutoGraph, so that procedures, GUI elements, and observed user actions become machine-readable and analyzable.

The IE-KG formalizes the structure and semantics of human–system interaction. Nodes represent interface elements such as panels, buttons, indicators, and parameters, with spatial, semantic, and procedural attributes. Edges encode hierarchical and logical relations such as system$\rightarrow$panel$\rightarrow$parameter, “navigates to,” “contains,” “is sibling of,” and “is required before.” Paths $P_{ijk}$ denote specific navigation or operation sequences. AutoGraph captures input events, cursor coordinates, timestamps, and screenshots; constructs the IE-KG; maps procedural steps to graph paths; aligns observed actions to node visits and path traversals; and flags multi-action steps.

The HFE-identification pipeline has three phases. Phase I builds the IE-KG and maps tasks to paths. Phase II identifies “error-prone” paths and “time-deviated” paths. In the case study, the error-prone EOC paths were $P_{122}$, $P_{125}$, $P_{211}$, $P_{212}$, $P_{214}$, $p(w \mid x, H)$0, $p(w \mid x, H)$1, $p(w \mid x, H)$2, $p(w \mid x, H)$3, $p(w \mid x, H)$4, $p(w \mid x, H)$5, and $p(w \mid x, H)$6; rare outcome errors occurred on $p(w \mid x, H)$7, $p(w \mid x, H)$8, and $p(w \mid x, H)$9. Tail-risk candidates were reported for $\rightarrow$0, $\rightarrow$1, $\rightarrow$2, $\rightarrow$3, $\rightarrow$4, $\rightarrow$5, $\rightarrow$6, $\rightarrow$7, and $\rightarrow$8. The final identified HFEs included the union of these sets, with a combined exemplar list of $\rightarrow$9, $\rightarrow$0, and $\rightarrow$1. Empirically, errors were random, but $\rightarrow$2 of $\rightarrow$3 occurred on relatively long-duration paths, and errors concentrated on flowchart-based interfaces rather than table-based ones.

The timing model follows IDHEAS-ECA guidance. If the median task time is known, $\rightarrow$4 and $\rightarrow$5; if only $\rightarrow$6 is available, $\rightarrow$7; then $\rightarrow$8. This gives path-level tail-risk flags and enables scenario-level probability-of-delay reasoning under time constraints. The framework is therefore “probabilistic” not only because it counts errors, but because it models the temporal distribution of path execution.

Phase III quantifies designer–user conflict from IE-KG-derived metrics and maps them to IDHEAS-ECA HSI PIF classes. The three reported metrics are

$\rightarrow$9

Here, semantic interference uses cosine similarity from text embeddings, with $P_{ijk}$0 indicating interference. These metrics were mapped to HSI0, HSI1, and HSI5 with an MLP classifier having four fully connected layers $P_{ijk}$1, batch normalization, ReLU, and dropout $P_{ijk}$2. Reported 5-fold cross-validation accuracies were $P_{ijk}$3, $P_{ijk}$4, $P_{ijk}$5, $P_{ijk}$6, and $P_{ijk}$7, with mean $P_{ijk}$8.

The case study used six trained graduate students in nuclear science or technology, each session lasting about $P_{ijk}$9–$P_{122}$0 minutes, for about $P_{122}$1 hours total data. Quantitative observations included that $P_{122}$2 of outcome errors occurred on high-conflict interfaces (HSI5), specifically $P_{122}$3 and $P_{122}$4. The same paper also emphasizes that conflict is not determinative: not all conflicts cause errors, and not all errors come from conflicts. This is a central corrective to a common oversimplification. InSight-R does not equate poor interface metrics with inevitable failure; rather, it places conflict features, timing tails, and observed errors into a single risk-informed inference pipeline.

3. ProbHMI in automated driving: workload inference and supervisory HMI

A second ProbHMI strand treats the HMI itself as an object of probabilistic evaluation or extension in automated driving. In “Workload Assessment of Human-Machine Interface: A Simulator Study with Psychophysiological Measures,” objective workload is assessed using ECG and EDA during SAE L2 HMI interaction (Liu et al., 2024). Three HMI designs were tested: Fog, with small icons, low contrast, and no feedback on failed activation; Trans-fog, with large high-contrast icons but no feedback; and Trans, with large high-contrast icons and explicit feedback. The study used $P_{122}$5 licensed drivers in a within-subject design. RMSSD was computed in a $P_{122}$6 window around L2 activation, and SCR magnitude in a $P_{122}$7 window.

The reported repeated-measures ANOVA results showed that RMSSD differed by HMI, $P_{122}$8, $P_{122}$9, $P_{125}$0, with Holm-corrected post hoc comparisons showing Trans $P_{125}$1 Fog and Trans $P_{125}$2 Trans-fog. SCR also differed by HMI, $P_{125}$3, $P_{125}$4, $P_{125}$5, with Trans $P_{125}$6 Fog. The ordering by objective workload was Trans $P_{125}$7 Trans-fog $P_{125}$8 Fog. The same framework proposes a probabilistic workload model with workload states $P_{125}$9, feature vector $P_{211}$0, and posterior

$P_{211}$1

This shifts HMI assessment from post hoc subjective rating toward event-centered probabilistic inference.

A related supervisory-HMI formulation appears in “In-Vehicle Human-Machine Interface to Support Drivers in Conditionally Automated Platooning” (Hager et al., 18 May 2026). The implemented HMI continuously presented platoon connection state (“connected” or “disconnected”), coupling iconography, and numerical inter-vehicle distance in meters, with an auditory alarm when distance fell below a predefined threshold. In a within-subject $P_{211}$2 factorial simulator study with $P_{211}$3, the HMI reduced manual interventions during intact platooning: intervention rates were about $P_{211}$4 higher without the HMI, with rate ratio $P_{211}$5, $P_{211}$6 CI $P_{211}$7, $P_{211}$8. By contrast, no significant effects were found for collisions or response latency: collision odds had $P_{211}$9, $P_{212}$0 CI $P_{212}$1, $P_{212}$2, and response latency had $P_{212}$3, $P_{212}$4 CI $P_{212}$5, $P_{212}$6.

This result addresses another common misconception. Additional information did not automatically improve emergency reaction or collision outcomes. The documented benefit was supervisory stability during nominal platooning, not stronger braking performance after disconnection. The paper then proposes an explicit ProbHMI extension rather than reporting it as deployed: confidence intervals around the distance readout, TTC bands with uncertainty, $P_{212}$7 for thresholds such as $P_{212}$8, automation confidence levels such as $P_{212}$9, and system-state reliability metrics such as V2V integrity. The underlying safety quantities are standard:

$P_{214}$0

In this driving lineage, ProbHMI therefore means that transparency is augmented by probabilistic state reliability and predictive risk, not merely by more interface elements.

4. ProbHMI as stochastic control and uncertainty-aware motion forecasting

A third usage emphasizes explicit modeling of human variability and future human motion. “Study on Human-Variability-Respecting Optimal Control Affecting Human Interaction Experience” models human motor behavior in a discrete-time linear stochastic system with additive and signal-dependent noise, following Todorov’s linear-quadratic sensorimotor framework (Kille et al., 2024). The automation policy is deterministic, $P_{214}$1, while the human policy is linear feedback, $P_{214}$2. Human cost and noise parameters are identified from observed trajectories via inverse stochastic optimal control. The Human-Variability-Respecting Optimal Controller (HVROC) is then parameterized in a “high variability” mode that mimics the human-only covariance profile of position and a “low variability” mode that reduces it.

The reported study used one identified subject in a 1D reaching task, with $P_{214}$3 repetitions of $P_{214}$4 used for identification. Simulation results showed that both HVROC variants reduced variance relative to human-only behavior, the “low variability” controller reduced peak variance by about $P_{214}$5 relative to the “high variability” controller, and both controllers reached the reference $P_{214}$6 faster than the human-only simulation. No statistical tests or stability guarantees were reported. The paper’s main contribution is therefore conceptual and architectural: variability is treated as a design target, not merely as disturbance.

An uncertainty-aware forecasting formulation appears in “Uncertainty-aware Probabilistic 3D Human Motion Forecasting via Invertible Networks” (Ma et al., 19 Jul 2025). Here, ProbHMI is the explicit model name. The method consists of a Pose Transformation Module (PTM), an invertible mapping $P_{214}$7, and a Pose Forecasting Module (PFM), a single-layer GRU that predicts future latent distributions. The change-of-variables relation is

$P_{214}$8

Because the flow uses NICE-style additive coupling, the log-determinant is $P_{214}$9. Future latent states are modeled as factorized Gaussians,

$p(w \mid x, H)$00

and sampling can be stochastic or quantile-based:

$p(w \mid x, H)$01

This architecture makes uncertainty a direct output rather than an implicit by-product of sampling. On Human3.6M in the diverse setup with $p(w \mid x, H)$02 samples, ProbHMI reported $p(w \mid x, H)$03, $p(w \mid x, H)$04 (best), $p(w \mid x, H)$05, $p(w \mid x, H)$06, $p(w \mid x, H)$07, and $p(w \mid x, H)$08 (best), with about $p(w \mid x, H)$09M parameters. On HumanEva-I, it reported $p(w \mid x, H)$10, $p(w \mid x, H)$11 (best), $p(w \mid x, H)$12, $p(w \mid x, H)$13, and $p(w \mid x, H)$14. In deterministic Human3.6M forecasting, average MAE across actions was $p(w \mid x, H)$15 at $p(w \mid x, H)$16, $p(w \mid x, H)$17 at $p(w \mid x, H)$18, $p(w \mid x, H)$19 at $p(w \mid x, H)$20, $p(w \mid x, H)$21 at $p(w \mid x, H)$22, $p(w \mid x, H)$23 at $p(w \mid x, H)$24, and $p(w \mid x, H)$25 at $p(w \mid x, H)$26. Runtime on an NVIDIA 2080Ti was reported as $p(w \mid x, H)$27 per sequence. Ablations showed degradation without part-aware prediction or with standard NICE in place of the part-aware graph-conditioned flow.

The control and motion-forecasting strands share a specific probabilistic ethos: distributions over human behavior are not merely estimated after the fact, but used to shape assistance or downstream risk-aware decision making. A plausible implication is that this is the most direct sense in which ProbHMI becomes operational for shared autonomy and human–robot collaboration.

5. ProbHMI as Probabilistic Health Monitoring and Inference

A distinct and terminologically important usage defines ProbHMI as “Probabilistic Health Monitoring and Inference” rather than human–machine interface (Liao et al., 2020). The framework is built on a Higher Order Hidden Semi-Markov Model (HOHSMM) for systems or components with unobservable health states and complex transition dynamics. Its purpose is to ingest condition-monitoring time series, track latent health states probabilistically, and predict remaining useful life (RUL) with uncertainty.

The model generalizes both HMMs and HSMMs. Hidden segment states $p(w \mid x, H)$28 evolve with higher-order dependence,

$p(w \mid x, H)$29

while segment durations are explicitly modeled through a state-specific distribution $p(w \mid x, H)$30. Observations within each segment are i.i.d. under a state-indexed emission family, commonly Gaussian. The framework uses Bayesian learning with Gibbs sampling, hierarchical Dirichlet priors over transitions, latent allocation variables to reduce parameter growth, explicit duration estimation, and a practical segmentation update driven by a jump-size threshold $p(w \mid x, H)$31. Decoding estimates hidden health states, and RUL is predicted by Monte Carlo simulation from the decoded current state history until an absorbing or failure state is reached.

The case study used the NASA C-MAPSS FD001 turbofan dataset. The first principal component of the $p(w \mid x, H)$32 sensor channels plus $p(w \mid x, H)$33 settings served as the univariate health indicator. The study assumed $p(w \mid x, H)$34 health states, used $p(w \mid x, H)$35 trajectories for training and $p(w \mid x, H)$36 for testing, and found that lag inclusion probabilities indicated second-order transitions. For RUL prediction, $p(w \mid x, H)$37 simulated paths per unit were generated. The paper reported qualitatively accurate decoding and RUL trajectories that closely tracked piecewise ground truth, but it did not report explicit RMSE, MAE, or PHM scores.

This usage is conceptually adjacent to other ProbHMI lineages because it also emphasizes interpretable latent state trajectories and calibrated predictive distributions. Yet its domain target is different. The ambiguity is terminological rather than methodological: in this strand, “HMI” names health monitoring and inference, not interface design.

6. Probabilistic-model interfaces, elicitation, and synthesis

ProbHMI systems that expose uncertainty to human experts also depend on the design of the interface through which probabilities are inspected and edited. “User Interface Tools for Navigation in Conditional Probability Tables and Elicitation of Probabilities in Bayesian Networks” describes two navigation views for large CPTs—CPTree and SCPT—and interactive elicitation widgets based on probability wheels and bar graphs (Wang et al., 2013). The underlying UI problem is combinatorial: for a discrete child $p(w \mid x, H)$38 with parents $p(w \mid x, H)$39, the number of free CPT parameters is

$p(w \mid x, H)$40

and each row must satisfy

$p(w \mid x, H)$41

CPTree renders the CPT as a hierarchy of parent names and outcomes, so that a root-to-leaf path corresponds to one parent instantiation. SCPT provides a shrinkable hierarchical table. Both support expand/collapse, parent reordering, multiple selection, and context-specific independence editing. The pie-style and bar-style elicitation widgets enforce sum-to-one constraints and permit locking outcomes during adjustment.

The usability study reported statistically significant differences in speed and accuracy between graphical elicitation and direct numerical input. Relative to direct numeric input, the bar graph was reported as $p(w \mid x, H)$42 more accurate and $p(w \mid x, H)$43 faster; relative to the pie chart, it was $p(w \mid x, H)$44 more accurate and $p(w \mid x, H)$45 faster. The design lesson is narrow but durable: when a ProbHMI system exposes explicit distributions, interface mechanisms for navigating, constraining, and eliciting those distributions materially affect error rate and efficiency.

Taken together, the surveyed literature suggests that ProbHMI is best treated as an umbrella for uncertainty-explicit human-centered systems rather than a single protocol. Some formulations center on path-level human reliability; some on psychophysiological workload posteriors; some on supervisory driving support with probabilistic risk displays; some on stochastic control or motion-forecast quantiles; and some on latent health-state monitoring. A plausible implication is that future consolidation, if it occurs, will be less about standardizing one model class than about standardizing how uncertainty is represented, calibrated, updated, and communicated to human decision makers.