Evaluating the average causal effect (ACE) of a treatment on an outcome often involves overcoming the challenges posed by confounding factors in observational studies. A traditional approach uses the back-door criterion, seeking adjustment sets to block confounding paths between treatment and outcome. However, this method struggles with unmeasured confounders. As an alternative, the front-door criterion offers a solution, even in the presence of unmeasured confounders between treatment and outcome. This method relies on identifying mediators that are not directly affected by these confounders and that completely mediate the treatment's effect. Here, we introduce novel estimation strategies for the front-door criterion based on the targeted minimum loss-based estimation theory. Our estimators work across diverse scenarios, handling binary, continuous, and multivariate mediators. They leverage data-adaptive machine learning algorithms, minimizing assumptions and ensuring key statistical properties like asymptotic linearity, double-robustness, efficiency, and valid estimates within the target parameter space. We establish conditions under which the nuisance functional estimations ensure the root n-consistency of ACE estimators. Our numerical experiments show the favorable finite sample performance of the proposed estimators. We demonstrate the applicability of these estimators to analyze the effect of early stage academic performance on future yearly income using data from the Finnish Social Science Data Archive.

The identification of the Purkinje conduction system in the heart is a challenging task, yet essential for a correct definition of cardiac digital twins for precision cardiology. Here, we propose a probabilistic approach for identifying the Purkinje network from non-invasive clinical data such as the standard electrocardiogram (ECG). We use cardiac imaging to build an anatomically accurate model of the ventricles; we algorithmically generate a rule-based Purkinje network tailored to the anatomy; we simulate physiological electrocardiograms with a fast model; we identify the geometrical and electrical parameters of the Purkinje-ECG model with Bayesian optimization and approximate Bayesian computation. The proposed approach is inherently probabilistic and generates a population of plausible Purkinje networks, all fitting the ECG within a given tolerance. In this way, we can estimate the uncertainty of the parameters, thus providing reliable predictions. We test our methodology in physiological and pathological scenarios, showing that we are able to accurately recover the ECG with our model. We propagate the uncertainty in the Purkinje network parameters in a simulation of conduction system pacing therapy. Our methodology is a step forward in creation of digital twins from non-invasive data in precision medicine. An open source implementation can be found at http://github.com/fsahli/purkinje-learning

Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation methods, leading to a local solution in the design space while the global space is neglected. Bayesian Optimisation is a promising path towards sample-efficient, global optimisation based on probabilistic surrogate models. While Bayesian optimisation methods have demonstrated their strength for problems with a low number of design variables, the scalability to high-dimensional problems while incorporating large-scale constraints is still lacking. Especially in aeroelastic tailoring where directional stiffness properties are embodied into the structural design of aircraft, to control aeroelastic deformations and to increase the aerodynamic and structural performance, the safe operation of the system needs to be ensured by involving constraints resulting from different analysis disciplines. Hence, a global design space search becomes even more challenging. The present study attempts to tackle the problem by using high-dimensional Bayesian Optimisation in combination with a dimensionality reduction approach to solve the optimisation problem occurring in aeroelastic tailoring, presenting a novel approach for high-dimensional problems with large-scale constraints. Experiments on well-known benchmark cases with black-box constraints show that the proposed approach can incorporate large-scale constraints.

In this study, we propose an approach for predicting rare events by exploiting time series in coevolution. Our approach involves a weighted autologistic regression model, where we leverage the temporal behavior of the data to enhance predictive capabilities. By addressing the issue of imbalanced datasets, we establish constraints leading to weight estimation and to improved performance. Evaluation on synthetic and real-world datasets confirms that our approach outperform state-of-the-art of predicting home equipment failure methods.

This paper proposes a Bayes Net based Monte Carlo optimization for motion planning (BN-MCO). Primarily, we adjust the potential fields determined by goal and start constraints to progressively guide the sampled clusters toward the goal and start points. Then, we utilize the Gaussian mixed modal (GMM) to perform the Monte Carlo optimization, confronting these two non-convex potential fields. Moreover, KL divergence measures the bias between the true distribution determined by the fields and the proposed GMM, whose parameters are learned incrementally according to the manifold information of the bias. In this way, the Bayesian network consisting of sequential updated GMMs expands until the constraints are satisfied and the shortest path method can find a feasible path. Finally, we tune the key parameters and benchmark BN-MCO against the other 5 planners on LBR-iiwa in a bookshelf. The result shows the highest success rate and moderate solving efficiency of BN-MCO.

Robots cannot yet match humans' ability to rapidly learn the shapes of novel 3D objects and recognize them robustly despite clutter and occlusion. We present Bayes3D, an uncertainty-aware perception system for structured 3D scenes, that reports accurate posterior uncertainty over 3D object shape, pose, and scene composition in the presence of clutter and occlusion. Bayes3D delivers these capabilities via a novel hierarchical Bayesian model for 3D scenes and a GPU-accelerated coarse-to-fine sequential Monte Carlo algorithm. Quantitative experiments show that Bayes3D can learn 3D models of novel objects from just a handful of views, recognizing them more robustly and with orders of magnitude less training data than neural baselines, and tracking 3D objects faster than real time on a single GPU. We also demonstrate that Bayes3D learns complex 3D object models and accurately infers 3D scene composition when used on a Panda robot in a tabletop scenario.

Statisticians and machine learners analyze observed data by synthesizing models of those data. These models take a variety of forms, with several of the most widely used being directed graphical models, probabilistic programs, and structural causal models (SCMs). Applications of these frameworks have included cognitive modeling [7, 20], simulation-based inference [9], and model-based planning [12, 21]. Unfortunately, the richer the model class, the weaker the mathematical tools available to reason rigorously about it: SCMs built on linear equations with Gaussian noise admit easy inference, while graphical models have a clear meaning and a wide array of inference algorithms but encode a limited family of models. Probabilistic programs can encode any computably sampleable distribution, but the definition of their densities commonly relies on operational analogies with directed graphical models.

By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been recognised in various applications, their performance relies on the knowledge of dynamic models and measurement models, as well as the construction of effective proposal distributions. An emerging trend involves constructing components of particle filters using neural networks and optimising them by gradient descent, and such data-adaptive particle filtering approaches are often called differentiable particle filters. Due to the expressiveness of neural networks, differentiable particle filters are a promising computational tool for performing inference on sequential data in complex, high-dimensional tasks, such as vision-based robot localisation. In this paper, we review recent advances in differentiable particle filters and their applications. We place special emphasis on different design choices for key components of differentiable particle filters, including dynamic models, measurement models, proposal distributions, optimisation objectives, and differentiable resampling techniques.

Diffusion models have emerged as powerful tools for high-quality data generation, such as image generation. Despite its success in continuous spaces, discrete diffusion models, which apply to domains such as texts and natural languages, remain under-studied and often suffer from slow generation speed. In this paper, we propose a novel de-randomized diffusion process, which leads to an accelerated algorithm for discrete diffusion models. Our technique significantly reduces the number of function evaluations (i.e., calls to the neural network), making the sampling process much faster. Furthermore, we introduce a continuous-time (i.e., infinite-step) sampling algorithm that can provide even better sample qualities than its discrete-time (finite-step) counterpart. Extensive experiments on natural language generation and machine translation tasks demonstrate the superior performance of our method in terms of both generation speed and sample quality over existing methods for discrete diffusion models.

Accurate estimation of sub-surface properties like moisture content and depth of layers is crucial for applications spanning sub-surface condition monitoring, precision agriculture, and effective wildfire risk assessment. Soil in nature is often covered by overlaying surface material, making its characterization using conventional methods challenging. In addition, the estimation of the properties of the overlaying layer is crucial for applications like wildfire assessment. This study thus proposes a Bayesian model-updating-based approach for ground penetrating radar (GPR) waveform inversion to predict sub-surface properties like the moisture contents and depths of the soil layer and overlaying material accumulated above the soil. The dielectric permittivity of material layers were predicted with the proposed method, along with other parameters, including depth and electrical conductivity of layers. The proposed Bayesian model updating approach yields probabilistic estimates of these parameters that can provide information about the confidence and uncertainty related to the estimates. The methodology was evaluated for a diverse range of experimental data collected through laboratory and field investigations. Laboratory investigations included variations in soil moisture values and depth of the top layer (or overlaying material), and the field investigation included measurement of field soil moisture for sixteen days. The results demonstrated predictions consistent with time-domain reflectometry (TDR) measurements and conventional gravimetric tests. The top layer depth could also be predicted with reasonable accuracy. The proposed method provides a promising approach for uncertainty-aware sub-surface parameter estimation that can enable decision-making for risk assessment across a wide range of applications.