Prediction algorithms, such as deep neural networks (DNNs), are used in many domain sciences to directly estimate internal parameters of interest in simulator-based models, especially in settings where the observations include images or complex high-dimensional data. In parallel, modern neural density estimators, such as normalizing flows, are becoming increasingly popular for uncertainty quantification, especially when both parameters and observations are high-dimensional. However, parameter inference is an inverse problem and not a prediction task; thus, an open challenge is to construct conditionally valid and precise confidence regions, with a guaranteed probability of covering the true parameters of the data-generating process, no matter what the (unknown) parameter values are, and without relying on large-sample theory. Many simulator-based inference (SBI) methods are indeed known to produce biased or overly confident parameter regions, yielding misleading uncertainty estimates. This paper presents WALDO, a novel method to construct confidence regions with finite-sample conditional validity by leveraging prediction algorithms or posterior estimators that are currently widely adopted in SBI. WALDO reframes the well-known Wald test statistic, and uses a computationally efficient regression-based machinery for classical Neyman inversion of hypothesis tests. We apply our method to a recent high-energy physics problem, where prediction with DNNs has previously led to estimates with prediction bias. We also illustrate how our approach can correct overly confident posterior regions computed with normalizing flows.

Recent digital advances have popularized predictive maintenance (PMx), offering enhanced efficiency, automation, accuracy, cost savings, and independence in maintenance. Yet, it continues to face numerous limitations such as poor explainability, sample inefficiency of data-driven methods, complexity of physics-based methods, and limited generalizability and scalability of knowledge-based methods. This paper proposes leveraging Digital Twins (DTs) to address these challenges and enable automated PMx adoption at larger scales. While we argue that DTs have this transformative potential, they have not yet reached the level of maturity needed to bridge these gaps in a standardized way. Without a standard definition for such evolution, this transformation lacks a solid foundation upon which to base its development. This paper provides a requirement-based roadmap supporting standardized PMx automation using DT technologies. A systematic approach comprising two primary stages is presented. First, we methodically identify the Informational Requirements (IRs) and Functional Requirements (FRs) for PMx, which serve as a foundation from which any unified framework must emerge. Our approach to defining and using IRs and FRs to form the backbone of any PMx DT is supported by the track record of IRs and FRs being successfully used as blueprints in other areas, such as for product development within the software industry. Second, we conduct a thorough literature review spanning fields to determine the ways in which these IRs and FRs are currently being used within DTs, enabling us to point to the specific areas where further research is warranted to support the progress and maturation of requirement-based PMx DTs.

Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary data distributions i.e. they generalize beyond generative modeling and can be applied to learning stochastic (and deterministic) processes of arbitrary transfer tasks between two given distributions. In this paper, we highlight that while flow and bridge matching processes preserve the information of the marginal distributions, they do \emph{not} necessarily preserve the coupling information unless additional, stronger optimality conditions are met. This can be problematic if one aims at preserving the original empirical pairing. We show that a simple modification of the matching process recovers this coupling by augmenting the velocity field (or drift) with the information of the initial sample point. Doing so, we lose the Markovian property of the process but preserve the coupling information between distributions. We illustrate the efficiency of our augmentation in learning mixture of image translation tasks.

There is a considerable body of work on data cleaning which employs various principles to rectify erroneous data and transform a dirty dataset into a cleaner one. One of prevalent approaches is probabilistic methods, including Bayesian methods. However, existing probabilistic methods often assume a simplistic distribution (e.g., Gaussian distribution), which is frequently underfitted in practice, or they necessitate experts to provide a complex prior distribution (e.g., via a programming language). This requirement is both labor-intensive and costly, rendering these methods less suitable for real-world applications. In this paper, we propose BClean, a Bayesian Cleaning system that features automatic Bayesian network construction and user interaction. We recast the data cleaning problem as a Bayesian inference that fully exploits the relationships between attributes in the observed dataset and any prior information provided by users. To this end, we present an automatic Bayesian network construction method that extends a structure learning-based functional dependency discovery method with similarity functions to capture the relationships between attributes. Furthermore, our system allows users to modify the generated Bayesian network in order to specify prior information or correct inaccuracies identified by the automatic generation process. We also design an effective scoring model (called the compensative scoring model) necessary for the Bayesian inference. To enhance the efficiency of data cleaning, we propose several approximation strategies for the Bayesian inference, including graph partitioning, domain pruning, and pre-detection. By evaluating on both real-world and synthetic datasets, we demonstrate that BClean is capable of achieving an F-measure of up to 0.9 in data cleaning, outperforming existing Bayesian methods by 2% and other data cleaning methods by 15%.

To facilitate reliable deployments of autonomous robots in the real world, Out-of-Distribution (OOD) detection capabilities are often required. A powerful approach for OOD detection is based on density estimation with Normalizing Flows (NFs). However, we find that prior work with NFs attempts to match the complex target distribution topologically with naive base distributions leading to adverse implications. In this work, we circumvent this topological mismatch using an expressive class-conditional base distribution trained with an information-theoretic objective to match the required topology. The proposed method enjoys the merits of wide compatibility with existing learned models without any performance degradation and minimum computation overhead while enhancing OOD detection capabilities. We demonstrate superior results in density estimation and 2D object detection benchmarks in comparison with extensive baselines. Moreover, we showcase the applicability of the method with a real-robot deployment.

As the two basic fuzzy inference models, fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) have the important application in artificial intelligence. In order to solve FMP and FMT problems, Zadeh proposed a compositional rule of inference (CRI) method. This paper aims mainly to investigate the validity of A-compositional rule of inference (ACRI) method, as a generalized CRI method based on aggregation functions, from a logical view and an interpolative view, respectively. Specifically, the modus ponens (MP) and modus tollens (MT) properties of ACRI method are discussed in detail. It is shown that the aggregation functions to implement FMP and FMT problems provide more generality than the t-norms, uninorms and overlap functions as well-known the laws of T-conditionality, U-conditionality and O-conditionality, respectively. Moreover, two examples are also given to illustrate our theoretical results. Especially, Example 6.2 shows that the output B' in FMP(FMT) problem is close to B(DC) with our proposed inference method when the fuzzy input and the antecedent of fuzzy rule are near (the fuzzy input near with the negation of the seccedent in fuzzy rule).

Parameterized convex minorant (PCM) method is proposed for the approximation of the objective function in amortized optimization. In the proposed method, the objective function approximator is expressed by the sum of a PCM and a nonnegative gap function, where the objective function approximator is bounded from below by the PCM convex in the optimization variable. The proposed objective function approximator is a universal approximator for continuous functions, and the global minimizer of the PCM attains the global minimum of the objective function approximator. Therefore, the global minimizer of the objective function approximator can be obtained by a single convex optimization. As a realization of the proposed method, extended parameterized log-sum-exp network is proposed by utilizing a parameterized log-sum-exp network as the PCM. Numerical simulation is performed for parameterized non-convex objective function approximation and for learning-based nonlinear model predictive control to demonstrate the performance and characteristics of the proposed method. The simulation results support that the proposed method can be used to learn objective functions and to find a global minimizer reliably and quickly by using convex optimization algorithms.

Inverse reinforcement learning (IRL) seeks to learn the reward function from expert trajectories, to understand the task for imitation or collaboration thereby removing the need for manual reward engineering. However, IRL in the context of large, highdimensional problems with unknown dynamics has been particularly challenging. In this paper, we present a new Variational Lower Bound for IRL (VLB-IRL), which is derived under the framework of a probabilistic graphical model with an optimality node. Our method simultaneously learns the reward function and policy under the learned reward function by maximizing the lower bound, which is equivalent to minimizing the reverse Kullback-Leibler divergence between an approximated distribution of optimality given the reward function and the true distribution of optimality given trajectories. This leads to a new IRL method that learns a valid reward function such that the policy under the learned reward achieves expert-level performance on several known domains. Importantly, the method outperforms the existing state-of-the-art IRL algorithms on these domains by demonstrating better reward from the learned policy. Reinforcement learning (RL) is a popular method for automating decision making and control. However, to achieve practical effectiveness, significant engineering of reward features and reward functions has traditionally been necessary.

While there is abundant work on methodology, algorithms, and applications, a smaller body of literature has investigated the relationship between the clusters found by a method and the underlying data-generating mechanism. Assuming that the observed data set is generated by independent and identical observations from a probability law P, consistency concerns the relationship between P and the outcome of a method for random samples of a size converging to infinity. In cluster analysis, the clustering itself and/or distributional parameters characterising the clustering may be of interest. Here we will derive consistency results for model-based clustering, i.e., clustering based on probability mixture models. More precisely, the results will concern maximum likelihood (ML) estimators (MLE) of finite mixtures of distributions from elliptically symmetrical distribution (ESD) families such as the Gaussian distribution. Finite mixture models (FMM) are convex combinations of probability distributions suitable to represent inhomogeneous populations.

We consider inverse problems where the conditional distribution of the observation ${\bf y}$ given the latent variable of interest ${\bf x}$ (also known as the forward model) is known, and we have access to a data set in which multiple instances of ${\bf x}$ and ${\bf y}$ are both observed. In this context, algorithm unrolling has become a very popular approach for designing state-of-the-art deep neural network architectures that effectively exploit the forward model. We analyze the statistical complexity of the gradient descent network (GDN), an algorithm unrolling architecture driven by proximal gradient descent. We show that the unrolling depth needed for the optimal statistical performance of GDNs is of order $\log(n)/\log(\varrho_n^{-1})$, where $n$ is the sample size, and $\varrho_n$ is the convergence rate of the corresponding gradient descent algorithm. We also show that when the negative log-density of the latent variable ${\bf x}$ has a simple proximal operator, then a GDN unrolled at depth $D'$ can solve the inverse problem at the parametric rate $O(D'/\sqrt{n})$. Our results thus also suggest that algorithm unrolling models are prone to overfitting as the unrolling depth $D'$ increases. We provide several examples to illustrate these results.