We investigate partially identifiable queries in a class of causal models. We focus on acyclic Structural Causal Models that are quasi-Markovian (that is, each endogenous variable is connected with at most one exogenous confounder). We look into scenarios where endogenous variables are observed (and a distribution over them is known), while exogenous variables are not fully specified. This leads to a representation that is in essence a Bayesian network where the distribution of root variables is not uniquely determined. In such circumstances, it may not be possible to precisely compute a probability value of interest. We thus study the computation of tight probability bounds, a problem that has been solved by multilinear programming in general, and by linear programming when a single confounded component is intervened upon. We present a new algorithm to simplify the construction of such programs by exploiting input probabilities over endogenous variables. For scenarios with a single intervention, we apply column generation to compute a probability bound through a sequence of auxiliary linear integer programs, thus showing that a representation with polynomial cardinality for exogenous variables is possible. Experiments show column generation techniques to be superior to existing methods.

While calibration of probabilistic predictions has been widely studied, this paper rather addresses calibration of likelihood functions. This has been discussed, especially in biometrics, in cases with only two exhaustive and mutually exclusive hypotheses (classes) where likelihood functions can be written as log-likelihood-ratios (LLRs). After defining calibration for LLRs and its connection with the concept of weight-of-evidence, we present the idempotence property and its associated constraint on the distribution of the LLRs. Although these results have been known for decades, they have been limited to the binary case. Here, we extend them to cases with more than two hypotheses by using the Aitchison geometry of the simplex, which allows us to recover, in a vector form, the additive form of the Bayes' rule; extending therefore the LLR and the weight-of-evidence to any number of hypotheses. Especially, we extend the definition of calibration, the idempotence, and the constraint on the distribution of likelihood functions to this multiple hypotheses and multiclass counterpart of the LLR: the isometric-log-ratio transformed likelihood function. This work is mainly conceptual, but we still provide one application to machine learning by presenting a non-linear discriminant analysis where the discriminant components form a calibrated likelihood function over the classes, improving therefore the interpretability and the reliability of the method.

This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle Markov chain Monte Carlo (MCMC) sampling or variational approximations that underestimate uncertainty and lack theoretical guarantees. Our proposed methodology employs spectral decompositions to estimate and align latent factors that are active in at least one view. Conditionally on these factors, we choose jointly conjugate prior distributions for factor loadings and residual variances. The resulting posterior is a simple product of normal-inverse gamma distributions for each variable, bypassing MCMC and facilitating posterior computation. We prove favorable increasing-dimension asymptotic properties, including posterior contraction and central limit theorems for point estimators. We show excellent performance in simulations, including accurate uncertainty quantification, and apply the methodology to integrate four high-dimensional views from a multi-omics dataset of cancer cell samples.

Generating synthetic datasets that accurately reflect real-world observational data is critical for evaluating causal estimators, but remains a challenging task. Existing generative methods offer a solution by producing synthetic datasets anchored in the observed data (source data) while allowing variation in key parameters such as the treatment effect and amount of confounding bias. However, existing methods typically require users to provide point estimates of such parameters (rather than distributions) and fixed estimates (rather than estimates that can be improved with reference to the source data). This denies users the ability to express uncertainty over parameter values and removes the potential for posterior inference, potentially leading to unreliable estimator comparisons. We introduce simulation-based inference for causal evaluation (SBICE), a framework that models generative parameters as uncertain and infers their posterior distribution given a source dataset. Leveraging techniques in simulation-based inference, SBICE identifies parameter configurations that produce synthetic datasets closely aligned with the source data distribution. Empirical results demonstrate that SBICE improves the reliability of estimator evaluations by generating more realistic datasets, which supports a robust and data-consistent approach to causal benchmarking under uncertainty.

Human cognition is profoundly shaped by the environments in which it unfolds. Yet, it remains an open question whether learning and decision making can be explained as a principled adaptation to the statistical structure of real-world tasks. We introduce ecologically rational analysis, a computational framework that unifies the normative foundations of rational analysis with ecological grounding. Leveraging large language models to generate ecologically valid cognitive tasks at scale, and using meta-learning to derive rational models optimized for these environments, we develop a new class of learning algorithms: Ecologically Rational Meta-learned Inference (ERMI). ERMI internalizes the statistical regularities of naturalistic problem spaces and adapts flexibly to novel situations, without requiring hand-crafted heuristics or explicit parameter updates. We show that ERMI captures human behavior across 15 experiments spanning function learning, category learning, and decision making, outperforming several established cognitive models in trial-by-trial prediction. Our results suggest that much of human cognition may reflect adaptive alignment to the ecological structure of the problems we encounter in everyday life.

Diffusion models have shown remarkable promise for image restoration by leveraging powerful priors. Prominent methods typically frame the restoration problem within a Bayesian inference framework, which iteratively combines a denoising step with a likelihood guidance step. However, the interactions between these two components in the generation process remain underexplored. In this paper, we analyze the underlying gradient dynamics of these components and identify significant instabilities. Specifically, we demonstrate conflicts between the prior and likelihood gradient directions, alongside temporal fluctuations in the likelihood gradient itself. We show that these instabilities disrupt the generative process and compromise restoration performance. To address these issues, we propose Stabilized Progressive Gradient Diffusion (SPGD), a novel gradient management technique. SPGD integrates two synergistic components: (1) a progressive likelihood warm-up strategy to mitigate gradient conflicts; and (2) adaptive directional momentum (ADM) smoothing to reduce fluctuations in the likelihood gradient. Extensive experiments across diverse restoration tasks demonstrate that SPGD significantly enhances generation stability, leading to state-of-the-art performance in quantitative metrics and visually superior results. Code is available at https://github.com/74587887/SPGD.

The quasi-repetitive nature of construction work and the resulting lack of generalizability in programming construction robots presents persistent challenges to the broad adoption of robots in the construction industry. Robots cannot achieve generalist capabilities as skills learnt from one domain cannot readily transfer to another work domain or be directly used to perform a different set of tasks. Human workers have to arduously reprogram their scene-understanding, path-planning, and manipulation components to enable the robots to perform alternate work tasks. The methods presented in this paper resolve a significant proportion of such reprogramming workload by proposing a generalizable learning architecture that directly teaches robots versatile task-performance skills through crowdsourced online natural language instructions. A Large Language Model (LLM), a standardized and modularized hierarchical modeling approach, and Building Information Modeling-Robot sematic data pipeline are developed to address the multi-task skill transfer problem. The proposed skill standardization scheme and LLM-based hierarchical skill learning framework were tested with a long-horizon drywall installation experiment using a full-scale industrial robotic manipulator. The resulting robot task learning scheme achieves multi-task reprogramming with minimal effort and high quality.

Stochastic processes on graphs are a powerful tool for modelling complex dynamical systems such as epidemics. A recent line of work focused on the inference problem where one aims to estimate the state of every node at every time, starting from partial observation of a subset of nodes at a subset of times. In these works, the initial state of the process was assumed to be random i.i.d. over nodes. Such an assumption may not be realistic in practice, where one may have access to a set of covariate variables for every node that influence the initial state of the system. In this work, we will assume that the initial state of a node is an unknown function of such covariate variables. Given that functions can be represented by neural networks, we will study a model where the initial state is given by a simple neural network -- notably the single-layer perceptron acting on the known node-wise covariate variables. Within a Bayesian framework, we study how such neural-network prior information enhances the recovery of initial states and spreading trajectories. We derive a hybrid belief propagation and approximate message passing (BP-AMP) algorithm that handles both the spreading dynamics and the information included in the node covariates, and we assess its performance against the estimators that either use only the spreading information or use only the information from the covariate variables. We show that in some regimes, the model can exhibit first-order phase transitions when using a Rademacher distribution for the neural-network weights. These transitions create a statistical-to-computational gap where even the BP-AMP algorithm, despite the theoretical possibility of perfect recovery, fails to achieve it.

As large language models (LLMs) gain popularity in conducting prediction tasks in-context, understanding the sources of uncertainty in in-context learning becomes essential to ensuring reliability. The recent hypothesis of in-context learning performing predictive Bayesian inference opens the avenue for Bayesian uncertainty estimation, particularly for decomposing uncertainty into epistemic uncertainty due to lack of in-context data and aleatoric uncertainty inherent in the in-context prediction task. However, the decomposition idea remains under-explored due to the intractability of the latent parameter posterior from the underlying Bayesian model. In this work, we introduce a variational uncertainty decomposition framework for in-context learning without explicitly sampling from the latent parameter posterior, by optimising auxiliary queries as probes to obtain an upper bound to the aleatoric uncertainty of an LLM's in-context learning procedure, which also induces a lower bound to the epistemic uncertainty. Through experiments on synthetic and real-world tasks, we show quantitatively and qualitatively that the decomposed uncertainties obtained from our method exhibit desirable properties of epistemic and aleatoric uncertainty.

At its core, the package implements an efficient Mode Jumping Markov Chain Monte Carlo (MJMCMC) algorithm, designed to improve mixing in multi-modal posterior landscapes within Bayesian generalized linear models. In addition, it provides a genetically modified MJMCMC (GMJMCMC) algorithm that introduces nonlinear feature generation, thereby enabling the estimation of Bayesian generalized nonlinear models (BGNLMs). Within this framework, the algorithm maintains and updates populations of transformed features, computes their posterior probabilities, and evaluates the posteriors of models constructed from them. We demonstrate the effective use of FBMS for both inferential and predictive modeling in Gaussian regression, focusing on different instances of the BGNLM class of models. Furthermore, through a broad set of applications, we illustrate how the methodology can be extended to increasingly complex modeling scenarios, extending to other response distributions and mixed effect models.