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Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not…
Gaussian Processes (GPs) provide a convenient framework for specifying function-space priors, making them a natural choice for modeling uncertainty. In contrast, Bayesian Neural Networks (BNNs) offer greater scalability and extendability…
Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and…
In this paper, we consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process…
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
Conditional Neural Processes (CNP; Garnelo et al., 2018) are an attractive family of meta-learning models which produce well-calibrated predictions, enable fast inference at test time, and are trainable via a simple maximum likelihood…
This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…
Sequential decision problems in applications such as manipulation in warehouses, multi-step meal preparation, and routing in autonomous vehicle networks often involve reasoning about uncertainty, planning over discrete modes as well as…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
A new and rather broad class of stationary (i.e. stochastically translation invariant) random tessellations of the $d$-dimensional Euclidean space is introduced, which are called shape-driven nested Markov tessellations. Locally, these…
Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems,…
A key question in sequence modeling with neural networks is how to represent and learn highly nonlinear and probabilistic state dynamics. Operator theory views such dynamics as linear maps on Hilbert spaces containing mean embedding vectors…
Network Markov Decision Processes (MDPs), a popular model for multi-agent control, pose a significant challenge to efficient learning due to the exponential growth of the global state-action space with the number of agents. In this work,…
Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…
We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or…
Neural Marked Temporal Point Processes (MTPP) are flexible models to capture complex temporal inter-dependencies between labeled events. These models inherently learn two predictive distributions: one for the arrival times of events and…
The effectiveness of neural processes (NPs) in modelling posterior prediction maps -- the mapping from data to posterior predictive distributions -- has significantly improved since their inception. This improvement can be attributed to two…
Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…