Related papers: Instrumental and Proximal Causal Inference with Ga…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…
A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However,…
We present a Gaussian Process - Latent Class Choice Model (GP-LCCM) to integrate a non-parametric class of probabilistic machine learning within discrete choice models (DCMs). Gaussian Processes (GPs) are kernel-based algorithms that…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…
Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we…
We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions,…
This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation…
Causal inference is difficult in the presence of unobserved confounders. We introduce the instrumented common confounding (ICC) approach to (nonparametrically) identify causal effects with instruments, which are exogenous only conditional…
Reliable uncertainty quantification for causal effects is crucial in various applications, but remains difficult in nonparametric models, particularly for continuous treatments. We introduce IMPspec, a Gaussian process (GP) framework for…
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…
Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. Instruments are variables which only affect the outcome…
Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal…
Proxy variables are commonly used in causal inference when unmeasured confounding exists. While most existing proximal methods assume a unidirectional causal relationship between two primary variables, many social and biological systems…
We introduce a framework for learning robust visual representations that generalize to new viewpoints, backgrounds, and scene contexts. Discriminative models often learn naturally occurring spurious correlations, which cause them to fail on…
Instrumental variable (IV) regression relies on instruments to infer causal effects from observational data with unobserved confounding. We consider IV regression in time series models, such as vector auto-regressive (VAR) processes. Direct…
Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…
The goal of Causal Discovery is to find automated search methods for learning causal structures from observational data. In some cases all variables of the interested causal mechanism are measured, and the task is to predict the effects one…
One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…