Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for defining custom prior distributions that are automatically tuned using ML for use with Bayesian quantum state estimation methods. Previously, researchers have looked to Bayesian quantum state tomography due to its unique advantages like natural uncertainty quantification, the return of reliable estimates under any measurement condition, and minimal mean-squared error. However, practical challenges related to long computation times and conceptual issues concerning how to incorporate prior knowledge most suitably can overshadow these benefits. Using both simulated and experimental measurement results, we demonstrate that ML-defined prior distributions reduce net convergence times and provide a natural way to incorporate both implicit and explicit information directly into the prior distribution. These results constitute a promising path toward practical implementations of Bayesian quantum state tomography.

Flooding is one of the most disastrous natural hazards, responsible for substantial economic losses. A predictive model for flood-induced financial damages is useful for many applications such as climate change adaptation planning and insurance underwriting. This research assesses the predictive capability of regressors constructed on the National Flood Insurance Program (NFIP) dataset using neural networks (Conditional Generative Adversarial Networks), decision trees (Extreme Gradient Boosting), and kernel-based regressors (Gaussian Process). The assessment highlights the most informative predictors for regression. The distribution for claims amount inference is modeled with a Burr distribution permitting the introduction of a bias correction scheme and increasing the regressor's predictive capability. Aiming to study the interaction with physical variables, we incorporate Daymet rainfall estimation to NFIP as an additional predictor. A study on the coastal counties in the eight US South-West states resulted in an $R^2=0.807$. Further analysis of 11 counties with a significant number of claims in the NFIP dataset reveals that Extreme Gradient Boosting provides the best results, that bias correction significantly improves the similarity with the reference distribution, and that the rainfall predictor strengthens the regressor performance.

When used in complex engineered systems, such as communication networks, artificial intelligence (AI) models should be not only as accurate as possible, but also well calibrated. A well-calibrated AI model is one that can reliably quantify the uncertainty of its decisions, assigning high confidence levels to decisions that are likely to be correct and low confidence levels to decisions that are likely to be erroneous. This paper investigates the application of conformal prediction as a general framework to obtain AI models that produce decisions with formal calibration guarantees. Conformal prediction transforms probabilistic predictors into set predictors that are guaranteed to contain the correct answer with a probability chosen by the designer. Such formal calibration guarantees hold irrespective of the true, unknown, distribution underlying the generation of the variables of interest, and can be defined in terms of ensemble or time-averaged probabilities. In this paper, conformal prediction is applied for the first time to the design of AI for communication systems in conjunction to both frequentist and Bayesian learning, focusing on demodulation, modulation classification, and channel prediction.

We advance an information-theoretic model of human language processing in the brain, in which incoming linguistic input is processed at two levels, in terms of a heuristic interpretation and in terms of error correction. We propose that these two kinds of information processing have distinct electroencephalographic signatures, corresponding to the well-documented N400 and P600 components of language-related event-related potentials (ERPs). Formally, we show that the information content (surprisal) of a word in context can be decomposed into two quantities: (A) heuristic surprise, which signals processing difficulty of word given its inferred context, and corresponds with the N400 signal; and (B) discrepancy signal, which reflects divergence between the true context and the inferred context, and corresponds to the P600 signal. Both of these quantities can be estimated using modern NLP techniques. We validate our theory by successfully simulating ERP patterns elicited by a variety of linguistic manipulations in previously-reported experimental data from Ryskin et al. (2021). Our theory is in principle compatible with traditional cognitive theories assuming a `good-enough' heuristic interpretation stage, but with precise information-theoretic formulation.

We consider a multi-agent episodic MDP setup where an agent (leader) takes action at each step of the episode followed by another agent (follower). The state evolution and rewards depend on the joint action pair of the leader and the follower. Such type of interactions can find applications in many domains such as smart grids, mechanism design, security, and policymaking. We are interested in how to learn policies for both the players with provable performance guarantee under a bandit feedback setting. We focus on a setup where both the leader and followers are {\em non-myopic}, i.e., they both seek to maximize their rewards over the entire episode and consider a linear MDP which can model continuous state-space which is very common in many RL applications. We propose a {\em model-free} RL algorithm and show that $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret bounds can be achieved for both the leader and the follower, where $d$ is the dimension of the feature mapping, $H$ is the length of the episode, and $T$ is the total number of steps under the bandit feedback information setup. Thus, our result holds even when the number of states becomes infinite. The algorithm relies on {\em novel} adaptation of the LSVI-UCB algorithm. Specifically, we replace the standard greedy policy (as the best response) with the soft-max policy for both the leader and the follower. This turns out to be key in establishing uniform concentration bound for the value functions. To the best of our knowledge, this is the first sub-linear regret bound guarantee for the Markov games with non-myopic followers with function approximation.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https://github.com/larslorch/avici.

This paper proposes a new 3D gas distribution mapping technique based on the local message passing of Gaussian belief propagation that is capable of resolving in real time, concentration estimates in 3D space whilst accounting for the obstacle information within the scenario, the first of its kind in the literature. The gas mapping problem is formulated as a 3D factor graph of Gaussian potentials, the connections of which are conditioned on local occupancy values. The Gaussian belief propagation framework is introduced as the solver and a new hybrid message scheduler is introduced to increase the rate of convergence. The factor graph problem is then redesigned as a dynamically expanding inference task, coupling the information of consecutive gas measurements with local spatial structure obtained by the robot. The proposed algorithm is compared to the state of the art methods in 2D and 3D simulations and is found to resolve distribution maps orders of magnitude quicker than typical direct solvers. The proposed framework is then deployed for the first time onboard a ground robot in a 3D mapping and exploration task. The system is shown to be able to resolve multiple sensor inputs and output high resolution 3D gas distribution maps in a GPS denied cluttered scenario in real time. This online inference of complicated plume structures provides a new layer of contextual information over its 2D counterparts and enables autonomous systems to take advantage of real time estimates to inform potential next best sampling locations.

Markov Random Fields on two-dimensional lattices are popular probabilistic models for describing features of digital images in a wide range of applications. Classical problems like image segmentation rely on these models to describe unobserved variables used for pixel classification, see for example Held et al. (1997); Zhang et al. (2001). More general inference-oriented models, such as the ones used in texture modeling problems, describe pixel values directly as a Markov Random Field being first introduced by Hassner and Sklansky (1981); Cross and Jain (1983). For a review of Markov Random Fields in image processing and segmentation see, for example, Blake et al. (2011) and Kato et al. (2012). A Markov Random Field in a lattice is a collection of random variables whose dependence structure is implicitly defined by a graph. When the edge structure is completely known, one of the main inferential challenges is caused by cycles that prevent expressing the likelihood function as a product of simpler conditional probabilities as in classical Markov Chain models.

Accurate traffic flow prediction, a hotspot for intelligent transportation research, is the prerequisite for mastering traffic and making travel plans. The speed of traffic flow can be affected by roads condition, weather, holidays, etc. Furthermore, the sensors to catch the information about traffic flow will be interfered with by environmental factors such as illumination, collection time, occlusion, etc. Therefore, the traffic flow in the practical transportation system is complicated, uncertain, and challenging to predict accurately. This paper proposes a deep encoder-decoder prediction framework based on variational Bayesian inference. A Bayesian neural network is constructed by combining variational inference with gated recurrent units (GRU) and used as the deep neural network unit of the encoder-decoder framework to mine the intrinsic dynamics of traffic flow. Then, the variational inference is introduced into the multi-head attention mechanism to avoid noise-induced deterioration of prediction accuracy. The proposed model achieves superior prediction performance on the Guangzhou urban traffic flow dataset over the benchmarks, particularly when the long-term prediction.

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to impose the uncertainty quantification capability so that the learned model can achieve desired performance in accuracy and uncertainty prediction simultaneously. However, training the model from scratch is computationally expensive and may not be feasible in many situations. In this work, we consider a more practical post-hoc uncertainty learning setting, where a well-trained base model is given, and we focus on the uncertainty quantification task at the second stage of training. We propose a novel Bayesian meta-model to augment pre-trained models with better uncertainty quantification abilities, which is effective and computationally efficient. Our proposed method requires no additional training data and is flexible enough to quantify different uncertainties and easily adapt to different application settings, including out-of-domain data detection, misclassification detection, and trustworthy transfer learning. We demonstrate our proposed meta-model approach's flexibility and superior empirical performance on these applications over multiple representative image classification benchmarks.