Marios Papamichalis

Fernando Galaz-Garcia, Marios Papamichalis, Kathryn Turnbull et al.

We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions that are straightforward to sample from, suitable for use within Monte Carlo algorithms and latent variable models, such as autoencoders. As an illustration, we empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model. Finally, we take advantage of the generalized description of this framework to posit questions for future work.

Marios Papamichalis, Regina Ruane

Contact-rich robot dynamics are hybrid: a single observation can match several latent states and contact regimes (free, impact, stick--slip). A standard amortized filter that places no probability on a feasible contact transition will permanently lose the branch the robot actually follows. We introduce VHYDRO, a variational hybrid dynamics learner that prevents this branch loss. At each step, VHYDRO mixes the learned proposal with a feasible transition law before sampling and importance weighting, ensuring that every transition retained by the model-feasible carrier remains covered. VHYDRO jointly infers a continuous latent state and a discrete contact mode, and fits a sparse port-Hamiltonian law to each recovered regime. On top of this, three guarantees connect: support coverage stabilizes filtering, the stabilized filter concentrates the discrete contact posterior on coherent regimes, and mode-pure segments admit sparse port-Hamiltonian recovery. The recovery error separates cleanly into filtering, derivative, mode-impurity, and physics-residual parts. Three empirical findings track the same mechanism. Under heavy occlusion the support-safe filter stays usable while a non-defensive proposal collapses. On ManiSkill demonstrations and on four Sawyer/BridgeData task families the discrete state forms temporally coherent contact-regime segments that the discrete state yields a stronger joint profile across ARI, change-point F1, and segment purity than post-hoc and mode-free baselines. On hybrid systems with known equations the mode-conditioned sparse fit recovers the active physical terms; purely predictive baselines do not.

Marios Papamichalis, Abhishek Ray, Ilias Bilionis et al.

Probabilistic machine learning models are often insufficient to help with decisions on interventions because those models find correlations - not causal relationships. If observational data is only available and experimentation are infeasible, the correct approach to study the impact of an intervention is to invoke Pearl's causality framework. Even that framework assumes that the underlying causal graph is known, which is seldom the case in practice. When the causal structure is not known, one may use out-of-the-box algorithms to find causal dependencies from observational data. However, there exists no method that also accounts for the decision-maker's prior knowledge when developing the causal structure either. The objective of this paper is to develop rational approaches for making decisions from observational data in the presence of causal graph uncertainty and prior knowledge from the decision-maker. We use ensemble methods like Bayesian Model Averaging (BMA) to infer set of causal graphs that can represent the data generation process. We provide decisions by computing the expected value and risk of potential interventions explicitly. We demonstrate our approach by applying them in different example contexts.

Kolawole Ogunsina, Marios Papamichalis, Daniel DeLaurentis

Disruption management during the airline scheduling process can be compartmentalized into proactive and reactive processes depending upon the time of schedule execution. The state of the art for decision-making in airline disruption management involves a heuristic human-centric approach that does not categorically study uncertainty in proactive and reactive processes for managing airline schedule disruptions. Hence, this paper introduces an uncertainty transfer function model (UTFM) framework that characterizes uncertainty for proactive airline disruption management before schedule execution, reactive airline disruption management during schedule execution, and proactive airline disruption management after schedule execution to enable the construction of quantitative tools that can allow an intelligent agent to rationalize complex interactions and procedures for robust airline disruption management. Specifically, we use historical scheduling and operations data from a major U.S. airline to facilitate the development and assessment of the UTFM, defined by hidden Markov models (a special class of probabilistic graphical models) that can efficiently perform pattern learning and inference on portions of large data sets. We employ the UTFM to assess two independent and separately disrupted flight legs from the airline route network. Assessment of a flight leg from Dallas to Houston, disrupted by air traffic control hold for bad weather at Dallas, revealed that proactive disruption management for turnaround in Dallas before schedule execution is impractical because of zero transition probability between turnaround and taxi-out.