Residential electricity demand at granular scales is driven by what people do and for how long. Accurately forecasting this demand for applications like microgrid management and demand response therefore requires generative models that can produce realistic daily activity sequences, capturing both the timing and duration of human behavior. This paper develops a generative model of human activity sequences using nationally representative time-use diaries at a 10-minute resolution. We use this model to quantify which demographic factors are most critical for improving predictive performance. We propose a hierarchical semi-Markov framework that addresses two key modeling challenges. First, a time-inhomogeneous Markov \emph{router} learns the patterns of ``which activity comes next." Second, a semi-Markov \emph{hazard} component explicitly models activity durations, capturing ``how long" activities realistically last. To ensure statistical stability when data are sparse, the model pools information across related demographic groups and time blocks. The entire framework is trained and evaluated using survey design weights to ensure our findings are representative of the U.S. population. On a held-out test set, we demonstrate that explicitly modeling durations with the hazard component provides a substantial and statistically significant improvement over purely Markovian models. Furthermore, our analysis reveals a clear hierarchy of demographic factors: Sex, Day-Type, and Household Size provide the largest predictive gains, while Region and Season, though important for energy calculations, contribute little to predicting the activity sequence itself. The result is an interpretable and robust generator of synthetic activity traces, providing a high-fidelity foundation for downstream energy systems modeling.

Recommender systems are widely used for suggesting books, education materials, and products to users by exploring their behaviors. In reality, users' preferences often change over time, leading to studies on time-dependent recommender systems. However, most existing approaches that deal with time information remain primitive. In this paper, we extend existing methods and propose a hidden semi-Markov model to track the change of users' interests. Particularly, this model allows for capturing the different durations of user stays in a (latent) interest state, which can better model the heterogeneity of user interests and focuses. We derive an expectation maximization algorithm to estimate the parameters of the framework and predict users' actions. Experiments on three real-world datasets show that our model significantly outperforms the state-of-the-art time-dependent and static benchmark methods. Further analyses of the experiment results indicate that the performance improvement is related to the heterogeneity of state durations and the drift of user interests in the dataset.

This paper presents a method of unsupervised learning of harmonic analysis based on a hidden semi-Markov model (HSMM). We introduce the chord quality templates, which specify the probability of pitch class emissions given a root note and a chord quality. Other probability distributions that comprise the HSMM are automatically learned via unsupervised learning, which has been a challenge in existing research. The results of the harmonic analysis of the proposed model were evaluated using existing labeled data. While our proposed method has yet to perform as well as existing models that used supervised learning and complex rule design, it has the advantage of not requiring expensive labeled data or rule elaboration. Furthermore, we also show how to recognize the tonic without prior knowledge, based on the transition probabilities of the Markov model.

Deep reinforcement learning (DRL) algorithms have proven effective in robot navigation, especially in unknown environments, through directly mapping perception inputs into robot control commands. Most existing methods adopt uniform execution duration with robots taking commands at fixed intervals. As such, the length of execution duration becomes a crucial parameter to the navigation algorithm. In particular, if the duration is too short, then the navigation policy would be executed at a high frequency, with increased training difficulty and high computational cost. Meanwhile, if the duration is too long, then the policy becomes unable to handle complex situations, like those with crowded obstacles. It is thus tricky to find the "sweet" duration range; some duration values may render a DRL model to fail to find a navigation path. In this paper, we propose to employ adaptive execution duration to overcome this problem. Specifically, we formulate the navigation task as a Semi-Markov Decision Process (SMDP) problem to handle adaptive execution duration. We also improve the distributed proximal policy optimization (DPPO) algorithm and provide its theoretical guarantee for the specified SMDP problem. We evaluate our approach both in the simulator and on an actual robot. The results show that our approach outperforms the other DRL-based method (with fixed execution duration) by 10.3% in terms of the navigation success rate.

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network's universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.

Sequential data modeling and analysis have become indispensable tools for analyzing sequential data, such as time-series data, because larger amounts of sensed event data have become available. These methods capture the sequential structure of data of interest, such as input-output relations and correlation among datasets. However, because most studies in this area are specialized or limited to their respective applications, rigorous requirement analysis of such models has not been undertaken from a general perspective. Therefore, we particularly examine the structure of sequential data, and extract the necessity of `state duration' and `state interval' of events for efficient and rich representation of sequential data. Specifically addressing the hidden semi-Markov model (HSMM) that represents such state duration inside a model, we attempt to add representational capability of a state interval of events onto HSMM. To this end, we propose two extended models: an interval state hidden semi-Markov model (IS-HSMM) to express the length of a state interval with a special state node designated as "interval state node"; and an interval length probability hidden semi-Markov model (ILP-HSMM) which represents the length of the state interval with a new probabilistic parameter "interval length probability." Exhaustive simulations have revealed superior performance of the proposed models in comparison with HSMM. These proposed models are the first reported extensions of HMM to support state interval representation as well as state duration representation.

Animal behavior is not driven simply by its current observations, but is strongly influenced by internal states. Estimating the structure of these internal states is crucial for understanding the neural basis of behavior. In principle, internal states can be estimated by inverting behavior models, as in inverse model-based Reinforcement Learning. However, this requires careful parameterization and risks model-mismatch to the animal. Here we take a data-driven approach to infer latent states directly from observations of behavior, using a partially observable switching semi-Markov process. This process has two elements critical for capturing animal behavior: it captures non-exponential distribution of times between observations, and transitions between latent states depend on the animal's actions, features that require more complex non-markovian models to represent. To demonstrate the utility of our approach, we apply it to the observations of a simulated optimal agent performing a foraging task, and find that latent dynamics extracted by the model has correspondences with the belief dynamics of the agent. Finally, we apply our model to identify latent states in the behaviors of monkey performing a foraging task, and find clusters of latent states that identify periods of time consistent with expectant waiting. This data-driven behavioral model will be valuable for inferring latent cognitive states, and thereby for measuring neural representations of those states.

After birth, extremely preterm infants often require specialized respiratory management in the form of invasive mechanical ventilation (IMV). Protracted IMV is associated with detrimental outcomes and morbidities. Premature extubation, on the other hand, would necessitate reintubation which is risky, technically challenging and could further lead to lung injury or disease. We present an approach to modeling respiratory patterns of infants who succeeded extubation and those who required reintubation which relies on Markov models. We compare the use of traditional Markov chains to semi-Markov models which emphasize cross-pattern transitions and timing information, and to multi-chain Markov models which can concisely represent non-stationarity in respiratory behavior over time. The models we developed expose specific, unique similarities as well as vital differences between the two populations.

Deep architecture such as hierarchical semi-Markov models is an important class of models for nested sequential data. Current exact inference schemes either cost cubic time in sequence length, or exponential time in model depth. These costs are prohibitive for large-scale problems with arbitrary length and depth. In this contribution, we propose a new approximation technique that may have the potential to achieve sub-cubic time complexity in length and linear time depth, at the cost of some loss of quality. The idea is based on two well-known methods: Gibbs sampling and Rao-Blackwellisation. We provide some simulation-based evaluation of the quality of the RGBS with respect to run time and sequence length.

This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a posteriori state-persistence in particular. This paper also introduces a new Bayesian nonparametric framework for generating left-to- right and other structured, explicit-duration infinite hidden Markov models that we call the infinite structured hidden semi-Markov model .