The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional to the ambient data dimension, resulting in overly conservative theory that fails to explain its practical efficiency. This has motivated the recent work Li and Yan (2024a) to investigate how the DDPM can achieve sampling speed-ups through automatic exploitation of intrinsic low dimensionality of data. We strengthen this line of work by demonstrating, in some sense, optimal adaptivity to unknown low dimensionality. For a broad class of data distributions with intrinsic dimension $k$, we prove that the iteration complexity of the DDPM scales nearly linearly with $k$, which is optimal when using KL divergence to measure distributional discrepancy. Notably, our work is closely aligned with the independent concurrent work Potaptchik et al. (2024) -- posted two weeks prior to ours -- in establishing nearly linear-$k$ convergence guarantees for the DDPM.

We present the results of the "Fast Calorimeter Simulation Challenge 2022" -- the CaloChallenge. We study state-of-the-art generative models on four calorimeter shower datasets of increasing dimensionality, ranging from a few hundred voxels to a few tens of thousand voxels. The 31 individual submissions span a wide range of current popular generative architectures, including Variational AutoEncoders (VAEs), Generative Adversarial Networks (GANs), Normalizing Flows, Diffusion models, and models based on Conditional Flow Matching. We compare all submissions in terms of quality of generated calorimeter showers, as well as shower generation time and model size. To assess the quality we use a broad range of different metrics including differences in 1-dimensional histograms of observables, KPD/FPD scores, AUCs of binary classifiers, and the log-posterior of a multiclass classifier. The results of the CaloChallenge provide the most complete and comprehensive survey of cutting-edge approaches to calorimeter fast simulation to date. In addition, our work provides a uniquely detailed perspective on the important problem of how to evaluate generative models. As such, the results presented here should be applicable for other domains that use generative AI and require fast and faithful generation of samples in a large phase space.

Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). A standard approach to FM, called conditional flow matching (CFM), exploits the fact that the marginal vector field of a CNF can be learned by fitting least-square regression to the so-called conditional vector field specified given one or both ends of the flow path. We show that viewing CFM training from a Bayesian decision theoretic perspective on parameter estimation opens the door to generalizations of CFM algorithms. We propose one such extension by introducing a CFM algorithm based on defining conditional probability paths given what we refer to as ``streams'', instances of latent stochastic paths that connect pairs of noise and observed data. Further, we advocate the modeling of these latent streams using Gaussian processes (GPs). The unique distributional properties of GPs, and in particular the fact that the velocity of a GP is still a GP, allows drawing samples from the resulting stream-augmented conditional probability path without simulating the actual streams, and hence the ``simulation-free" nature of CFM training is preserved. We show that this generalization of the CFM can substantially reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the quality of the generated samples under common metrics. Additionally, we show that adopting the GP on the streams allows for flexibly linking multiple related training data points (e.g., time series) and incorporating additional prior information. We empirically validate our claim through both simulations and applications to two hand-written image datasets.

Artificial General Intelligence (AGI) Agents and Robots must be able to cope with everchanging environments and tasks. They must be able to actively construct new internal causal models of their interactions with the environment when new structural changes take place in the environment. Thus, we claim that active causal structure learning with latent variables (ACSLWL) is a necessary component to build AGI agents and robots. This paper describes how a complex planning and expectation-based detour behavior can be learned by ACSLWL when, unexpectedly, and for the first time, the simulated robot encounters a sort of "transparent" barrier in its pathway towards its target. ACSWL consists of acting in the environment, discovering new causal relations, constructing new causal models, exploiting the causal models to maximize its expected utility, detecting possible latent variables when unexpected observations occur, and constructing new structures - internal causal models and optimal estimation of the associated parameters, to be able to cope efficiently with the new encountered situations. That is, the agent must be able to construct new causal internal models that transform a previously unexpected and inefficient (sub-optimal) situation, into a predictable situation with an optimal operating plan.

Inferring atmospheric properties of exoplanets from observed spectra is key to understanding their formation, evolution, and habitability. Since traditional Bayesian approaches to atmospheric retrieval (e.g., nested sampling) are computationally expensive, a growing number of machine learning (ML) methods such as neural posterior estimation (NPE) have been proposed. We seek to make ML-based atmospheric retrieval (1) more reliable and accurate with verified results, and (2) more flexible with respect to the underlying neural networks and the choice of the assumed noise models. First, we adopt flow matching posterior estimation (FMPE) as a new ML approach to atmospheric retrieval. FMPE maintains many advantages of NPE, but provides greater architectural flexibility and scalability. Second, we use importance sampling (IS) to verify and correct ML results, and to compute an estimate of the Bayesian evidence. Third, we condition our ML models on the assumed noise level of a spectrum (i.e., error bars), thus making them adaptable to different noise models. Both our noise level-conditional FMPE and NPE models perform on par with nested sampling across a range of noise levels when tested on simulated data. FMPE trains about 3 times faster than NPE and yields higher IS efficiencies. IS successfully corrects inaccurate ML results, identifies model failures via low efficiencies, and provides accurate estimates of the Bayesian evidence. FMPE is a powerful alternative to NPE for fast, amortized, and parallelizable atmospheric retrieval. IS can verify results, thus helping to build confidence in ML-based approaches, while also facilitating model comparison via the evidence ratio. Noise level conditioning allows design studies for future instruments to be scaled up, for example, in terms of the range of signal-to-noise ratios.

A variational Bayesian inference for measured wave intensity, such as X-ray intensity, is proposed in this paper. The data is popular to obtain information about unobservable features of an object, such as a material sample and the components of it. The proposed method assumes particles represent the wave, and their behaviors are stochastically modeled. The inference is accurate even if the data is noisy because of a smooth prior setting. Moreover, in this paper, two experimental results show feasibility of the proposed method.

Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically intractable posteriors, necessitating approximation methods. To this end, we propose efficient schemes to approximate the effects of non-Gaussian likelihoods by Gaussian densities based on variational inference and moment matching in transformed bases. These enable efficient inference strategies originally designed for models with a Gaussian likelihood to be deployed. Our empirical results demonstrate that the proposed matching strategies attain good approximation quality for binary and multiclass classification in large-scale point-estimate and distributional inferential settings. In challenging streaming problems, the proposed methods outperform all existing likelihood approximations and approximate inference methods in the exact models. As a by-product, we show that the proposed approximate log-likelihoods are a superior alternative to least-squares on raw labels for neural network classification.

The analysis of neural power spectra plays a crucial role in understanding brain function and dysfunction. While recent efforts have led to the development of methods for decomposing spectral data, challenges remain in performing statistical analysis and group-level comparisons. Here, we introduce Bayesian Spectral Decomposition (BSD), a Bayesian framework for analysing neural spectral power. BSD allows for the specification, inversion, comparison, and analysis of parametric models of neural spectra, addressing limitations of existing methods. We first establish the face validity of BSD on simulated data and show how it outperforms an established method (\fooof{}) for peak detection on artificial spectral data. We then demonstrate the efficacy of BSD on a group-level study of EEG spectra in 204 healthy subjects from the LEMON dataset. Our results not only highlight the effectiveness of BSD in model selection and parameter estimation, but also illustrate how BSD enables straightforward group-level regression of the effect of continuous covariates such as age. By using Bayesian inference techniques, BSD provides a robust framework for studying neural spectral data and their relationship to brain function and dysfunction.

We propose an importance sampling method for tractable and efficient estimation of counterfactual expressions in general settings, named Exogenous Matching. By minimizing a common upper bound of counterfactual estimators, we transform the variance minimization problem into a conditional distribution learning problem, enabling its integration with existing conditional distribution modeling approaches. We validate the theoretical results through experiments under various types and settings of Structural Causal Models (SCMs) and demonstrate the outperformance on counterfactual estimation tasks compared to other existing importance sampling methods. We also explore the impact of injecting structural prior knowledge (counterfactual Markov boundaries) on the results. Finally, we apply this method to identifiable proxy SCMs and demonstrate the unbiasedness of the estimates, empirically illustrating the applicability of the method to practical scenarios.

In the highly competitive environment of the banking industry, it is essential to precisely forecast the behavior of customers in order to maximize the effectiveness of marketing initiatives and improve financial consequences. The purpose of this research is to examine the efficacy of logit and probit models in predicting term deposit subscriptions using a Portuguese bank's direct marketing data. There are several demographic, economic, and behavioral characteristics in the dataset that affect the probability of subscribing. To increase model performance and provide an unbiased evaluation, the target variable was balanced, considering the inherent imbalance in the dataset. The two model's prediction abilities were evaluated using Bayesian techniques and Leave-One-Out Cross-Validation (LOO-CV). The logit model performed better than the probit model in handling this classification problem. The results highlight the relevance of model selection when dealing with complicated decision-making processes in the financial services industry and imbalanced datasets. Findings from this study shed light on how banks can optimize their decision-making processes, improve their client segmentation, and boost their marketing campaigns by utilizing machine learning models.