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Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
A novel efficient method for computing the Knowledge-Gradient policy for Continuous Parameters (KGCP) for deterministic optimization is derived. The differences with Expected Improvement (EI), a popular choice for Bayesian optimization of…
State estimation remains a fundamental challenge across numerous domains, from autonomous driving, aircraft tracking to quantum system control. Although Bayesian filtering has been the cornerstone solution, its classical model-based…
We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…
Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
The problem of making sequential decisions in unknown probabilistic environments is studied. In cycle $t$ action $y_t$ results in perception $x_t$ and reward $r_t$, where all quantities in general may depend on the complete history. The…
This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…
The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model.…
This paper investigates the application of game-theoretic principles combined with advanced Kalman filtering techniques to enhance maritime target tracking systems. Specifically, the paper presents a two-player, imperfect information,…
A Bayesian player acting in an infinite multi-player game learns to predict the other players' strategies if his prior assigns positive probability to their play (or contains a grain of truth). Kalai and Lehrer's classic grain of truth…
A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…