Maximum Likelihood and the method of Least Squares are fundamental procedures in statistics. The study of asymptotic consistency of Maximum Likelihood has been central to the field for almost a century (Wald, 1949). Along with consistency, failures of Maximum Likelihood have been thoroughly investigated for nearly as long (Neyman and Scott, 1948; Bahadur, 1958; Ferguson, 1982). In the context of estimation of nonparametric models, the seminal work of (Birgé and Massart, 1993) provided sufficient conditions for minimax optimality (in a non-asymptotic sense) of Least Squares while also presenting an example of a model class where this basic procedure is sub-optimal. Three decades later, we still do not have necessary and sufficient conditions for minimax optimality of Least Squares when the model class is large. While the present paper does not resolve this question, it makes several steps towards understanding the behavior of Least Squares -- equivalently, Empirical Risk Minimization (ERM) with square loss -- in large models. Beyond intellectual curiosity, the question of minimax optimality of Least Squares is driven by the desire to understand the current practice of fitting large or overparametrized models, such as neural networks, to data (cf.

Digital technologies have dramatically accelerated the digital transformation in process industries, boosted new industrial applications, upgraded the production system, and enhanced operational efficiency. In contrast, the challenges and gaps between human and artificial intelligence (AI) have become more and more prominent, whereas the digital divide in process safety is aggregating. The study attempts to address the following questions: (i)What is AI in the process safety context? (ii)What is the difference between AI and humans in process safety? (iii)How do AI and humans collaborate in process safety? (iv)What are the challenges and gaps in human-AI collaboration? (v)How to quantify the risk of human-AI collaboration in process safety? Qualitative risk analysis based on brainstorming and literature review, and quantitative risk analysis based on layer of protection analysis (LOPA) and Bayesian network (BN), were applied to explore and model. The importance of human reliability should be stressed in the digital age, not usually to increase the reliability of AI, and human-centered AI design in process safety needs to be propagated.

The accurate prediction of the two-phase heat transfer coefficient (HTC) as a function of working fluids, channel geometries and process conditions is key to the optimal design and operation of compact heat exchangers. Advances in artificial intelligence research have recently boosted the application of machine learning (ML) algorithms to obtain data-driven surrogate models for the HTC. For most supervised learning algorithms, the task is that of a nonlinear regression problem. Despite the fact that these models have been proven capable of outperforming traditional empirical correlations, they have key limitations such as overfitting the data, the lack of uncertainty estimation, and interpretability of the results. To address these limitations, in this paper, we use a multi-output Gaussian process regression (GPR) to estimate the HTC in microchannels as a function of the mass flow rate, heat flux, system pressure and channel diameter and length. The model is trained using the Brunel Two-Phase Flow database of high-fidelity experimental data. The advantages of GPR are data efficiency, the small number of hyperparameters to be trained (typically of the same order of the number of input dimensions), and the automatic trade-off between data fit and model complexity guaranteed by the maximization of the marginal likelihood (Bayesian approach). Our paper proposes research directions to improve the performance of the GPR-based model in extrapolation.

Reinforcement learning can effectively learn amortised design policies for designing sequences of experiments. However, current methods rely on contrastive estimators of expected information gain, which require an exponential number of contrastive samples to achieve an unbiased estimation. We propose an alternative lower bound estimator, based on the cross-entropy of the joint model distribution and a flexible proposal distribution. This proposal distribution approximates the true posterior of the model parameters given the experimental history and the design policy. Our estimator requires no contrastive samples, can achieve more accurate estimates of high information gains, allows learning of superior design policies, and is compatible with implicit probabilistic models. We assess our algorithm's performance in various tasks, including continuous and discrete designs and explicit and implicit likelihoods.

Offline inverse reinforcement learning (Offline IRL) aims to recover the structure of rewards and environment dynamics that underlie observed actions in a fixed, finite set of demonstrations from an expert agent. Accurate models of expertise in executing a task has applications in safety-sensitive applications such as clinical decision making and autonomous driving. However, the structure of an expert's preferences implicit in observed actions is closely linked to the expert's model of the environment dynamics (i.e. the ``world''). Thus, inaccurate models of the world obtained from finite data with limited coverage could compound inaccuracy in estimated rewards. To address this issue, we propose a bi-level optimization formulation of the estimation task wherein the upper level is likelihood maximization based upon a conservative model of the expert's policy (lower level). The policy model is conservative in that it maximizes reward subject to a penalty that is increasing in the uncertainty of the estimated model of the world. We propose a new algorithmic framework to solve the bi-level optimization problem formulation and provide statistical and computational guarantees of performance for the associated reward estimator. Finally, we demonstrate that the proposed algorithm outperforms the state-of-the-art offline IRL and imitation learning benchmarks by a large margin, over the continuous control tasks in MuJoCo and different datasets in the D4RL benchmark.

Conventional Gaussian process regression exclusively assumes the existence of noise in the output data of model observations. In many scientific and engineering applications, however, the input locations of observational data may also be compromised with uncertainties owing to modeling assumptions, measurement errors, etc. In this work, we propose a Bayesian method that integrates the variability of input data into Gaussian process regression. Considering two types of observables -- noise-corrupted outputs with fixed inputs and those with prior-distribution-defined uncertain inputs, a posterior distribution is estimated via a Bayesian framework to infer the uncertain data locations. Thereafter, such quantified uncertainties of inputs are incorporated into Gaussian process predictions by means of marginalization. The effectiveness of this new regression technique is demonstrated through several numerical examples, in which a consistently good performance of generalization is observed, while a substantial reduction in the predictive uncertainties is achieved by the Bayesian inference of uncertain inputs.

Recent work studies the cognitive capabilities of language models through psychological tests designed for humans. While these studies are helpful for understanding the general capabilities of these models, there is no guarantee that a model possessing sufficient capabilities to pass those tests would actually use those capabilities in performing real-life tasks. In this work, we formulate task-oriented cognitive capabilities, which are human-like cognitive capabilities that language models leverage to perform tasks. These capabilities are (i) the ability to quickly generate good candidate utterances (the search capability) (ii) the ability to predict how a listener interprets those utterances and choose the most appropriate one (the pragmatic capability). We design an evaluation scheme for comparing these capabilities of a language model with those of a human. Applying this scheme to examine various models in a navigation instruction generation problem, we find that their pragmatic capability is severely lacking. This insight leads us to augment them with better models of the listener and obtain a significant boost of 11% in success rate in guiding real humans. Our work advocates for having a principled procedure for aligning language models with humans that involves (i) formulating task-oriented capabilities, (ii) devising a method to quantify their deficiency, and (iii) iteratively improving them.

In this work, we present a novel robustness measure for continuous-time stochastic trajectories with respect to Signal Temporal Logic (STL) specifications. We show the soundness of the measure and develop a monitor for reasoning about partial trajectories. Using this monitor, we introduce an STL sampling-based motion planning algorithm for robots under uncertainty. Given a minimum robustness requirement, this algorithm finds satisfying motion plans; alternatively, the algorithm also optimizes for the measure. We prove probabilistic completeness and asymptotic optimality, and demonstrate the effectiveness of our approach on several case studies.

We consider the ubiquitous linear inverse problems with additive Gaussian noise and propose an unsupervised sampling approach called diffusion model based posterior sampling (DMPS) to reconstruct the unknown signal from noisy linear measurements. Specifically, using one diffusion model (DM) as an implicit prior, the fundamental difficulty in performing posterior sampling is that the noise-perturbed likelihood score, i.e., gradient of an annealed likelihood function, is intractable. To circumvent this problem, we introduce a simple yet effective closed-form approximation of it using an uninformative prior assumption. Extensive experiments are conducted on a variety of noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all tasks, the proposed DMPS demonstrates highly competitive or even better performances on various tasks while being 3 times faster than the state-of-the-art competitor diffusion posterior sampling (DPS). The code to reproduce the results is available at https://github.com/mengxiangming/dmps.

It turns out there are a number of reasons why imperfect recall is relevant for AI agents; moreover, in cases where it is We study single-player extensive-form games with relevant, it is clear what the agent will and will not remember imperfect recall, such as the Sleeping Beauty problem - unlike in the case of human memory, which is harder to predict or the Absentminded Driver game. For such and consequently to model in standard representations of games, two natural equilibrium concepts have been imperfect recall. Imperfect-recall games already appear in the proposed as alternative solution concepts to ex-ante AI literature in the context of solving very large games such optimality. One equilibrium concept uses generalized as poker: one technique for solving such games is abstraction double halving (GDH) as a belief system and - i.e., reducing the game to a smaller, simplified one to solve evidential decision theory (EDT), and another one instead - and this process can give rise to imperfect recall in uses generalized thirding (GT) as a belief system the abstracted game [Waugh et al., 2009; Lanctot et al., 2012; and causal decision theory (CDT).