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).

Many event sequence data exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependency is crucial for scientific investigation. The de facto model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use direct or nonlinear transform of standard MHP intensity with constant baseline, inconsistent with real-world data. Under irregular and unknown heterogeneous intensity, capturing temporal dependency is hard as one struggles to distinguish the effect of mutual interaction from that of intensity fluctuation. In this paper, we address the short-term temporal dependency detection issue. We show the maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated but may be reduced by order of magnitude, using heterogeneous intensity not of the target HP but of the interacting HP. Then we proposed a robust and computationally-efficient method modified from MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, no repeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.

Particle filtering is a common technique for six degree of freedom (6D) pose estimation due to its ability to tractably represent belief over object pose. However, the particle filter is prone to particle deprivation due to the high-dimensional nature of 6D pose. When particle deprivation occurs, it can cause mode collapse of the underlying belief distribution during importance sampling. If the region surrounding the true state suffers from mode collapse, recovering its belief is challenging since the area is no longer represented in the probability mass formed by the particles. Previous methods mitigate this problem by randomizing and resetting particles in the belief distribution, but determining the frequency of reinvigoration has relied on hand-tuning abstract heuristics. In this paper, we estimate the necessary reinvigoration rate at each time step by introducing a Counter-Hypothetical likelihood function, which is used alongside the standard likelihood. Inspired by the notions of plausibility and implausibility from Evidential Reasoning, the addition of our Counter-Hypothetical likelihood function assigns a level of doubt to each particle. The competing cumulative values of confidence and doubt across the particle set are used to estimate the level of failure within the filter, in order to determine the portion of particles to be reinvigorated. We demonstrate the effectiveness of our method on the rigid body object 6D pose tracking task.

In this work, we introduce a novel framework which combines physics and machine learning methods to analyse acoustic signals. Three methods are developed for this task: a Bayesian inference approach for inferring the spectral acoustics characteristics, a neural-physical model which equips a neural network with forward and backward physical losses, and the non-linear least squares approach which serves as benchmark. The inferred propagation coefficient leads to the room impulse response (RIR) quantity which can be used for relocalisation with uncertainty. The simplicity and efficiency of this framework is empirically validated on simulated data.

In domains with high stakes such as law, recruitment, and healthcare, learning models frequently rely on sensitive user data for inference, necessitating the complete set of features. This not only poses significant privacy risks for individuals but also demands substantial human effort from organizations to verify information accuracy. This paper asks whether it is necessary to use \emph{all} input features for accurate predictions at inference time. The paper demonstrates that, in a personalized setting, individuals may only need to disclose a small subset of their features without compromising decision-making accuracy. The paper also provides an efficient sequential algorithm to determine the appropriate attributes for each individual to provide. Evaluations across various learning tasks show that individuals can potentially report as little as 10\% of their information while maintaining the same accuracy level as a model that employs the full set of user information.

This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative probability functions. We then provide a library of examples of these functions and a system for composing them. Additionally, we discuss a relative version of Bayesian inference and its digital implementation. Finally, we prove the topological closure of the relative probability space, highlighting its ability to preserve information under limits.