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We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a $2\times 2$ symmetric matrix. Previous results on this problem were restricted either to the case where the…
Learned representations in deep reinforcement learning (DRL) have to extract task-relevant information from complex observations, balancing between robustness to distraction and informativeness to the policy. Such stable and rich…
Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems. However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and…
Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM)…
New generations of ultracold-atom experiments are continually raising the demand for efficient solutions to optimal control problems. Here, we apply Bayesian optimization to improve a state-preparation protocol recently implemented in an…
Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…
In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees of freedom of such a model can be partitioned in free and prescribed sets to define the boundary…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
Phasor measurement units (PMUs) provide accurate and high-fidelity measurements in order to monitor the state of the power grid and support various control and planning tasks. However, PMUs have a high installation cost prohibiting their…
State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Performativity, the phenomenon where outcomes are influenced by predictions, is particularly prevalent in social contexts where individuals strategically respond to a deployed model. In order to preserve the high accuracy of machine…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the ``small data'' limit where the number N of points in the training set is small. Many extensions have since been proposed,…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
Model checking probabilistic CTL properties of Markov decision processes with convex uncertainties has been recently investigated by Puggelli et al. Such model checking algorithms typically suffer from the state space explosion. In this…
When the dynamics of a system are difficult to model and/or time-consuming to evaluate, such as in deformable object manipulation tasks, motion planning algorithms struggle to find feasible plans efficiently. Such problems are often reduced…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…