Likelihood-based deep generative models (DGMs) have gained significant attention for their ability to approximate the distributions of high-dimensional data. However, these models lack a performance guarantee in assigning higher likelihood values to in-distribution (ID) inputs, data the models are trained on, compared to out-of-distribution (OOD) inputs. This counter-intuitive behaviour is particularly pronounced when ID inputs are more complex than OOD data points. One potential approach to address this challenge involves leveraging the gradient of a data point with respect to the parameters of the DGMs. A recent OOD detection framework proposed estimating the joint density of layer-wise gradient norms for a given data point as a model-agnostic method, demonstrating superior performance compared to the Typicality Test across likelihood-based DGMs and image dataset pairs. In particular, most existing methods presuppose access to fully converged models, the training of which is both time-intensive and computationally demanding. In this work, we demonstrate that using immature models,stopped at early stages of training, can mostly achieve equivalent or even superior results on this downstream task compared to mature models capable of generating high-quality samples that closely resemble ID data. This novel finding enhances our understanding of how DGMs learn the distribution of ID data and highlights the potential of leveraging partially trained models for downstream tasks. Furthermore, we offer a possible explanation for this unexpected behaviour through the concept of support overlap.

This paper addresses the critical challenge of latent heterogeneity in online decision-making, where individual responses to business actions vary due to unobserved characteristics. While existing approaches in data-driven decision-making have focused on observable heterogeneity through contextual features, they fall short when heterogeneity stems from unobservable factors such as lifestyle preferences and personal experiences. We propose a novel latent heterogeneous bandit framework that explicitly models this unobserved heterogeneity in customer responses, with promotion targeting as our primary example. Our methodology introduces an innovative algorithm that simultaneously learns latent group memberships and group-specific reward functions. Through theoretical analysis and empirical validation using data from a mobile commerce platform, we establish high-probability bounds for parameter estimation, convergence rates for group classification, and comprehensive regret bounds. Notably, our theoretical analysis reveals two distinct types of regret measures: a ``strong regret'' against an oracle with perfect knowledge of customer memberships, which remains non-sub-linear due to inherent classification uncertainty, and a ``regular regret'' against an oracle aware only of deterministic components, for which our algorithm achieves a sub-linear rate that is minimax optimal in horizon length and dimension. We further demonstrate that existing bandit algorithms ignoring latent heterogeneity incur constant average regret that accumulates linearly over time. Our framework provides practitioners with new tools for decision-making under latent heterogeneity and extends to various business applications, including personalized pricing, resource allocation, and inventory management.

We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified target distribution in finite time. Our approach relies on the stochastic interpolants framework to define a time-indexed collection of probability densities that bridge a Gaussian distribution to the target distribution. Subsequently, we derive a diffusion process that obeys the aforementioned probability density at each time instant. Obtaining such a diffusion process involves solving certain Hamilton-Jacobi-Bellman PDEs. We solve these PDEs using the theory of forward-backward stochastic differential equations (FBSDE) together with machine learning-based methods. Through numerical experiments, we demonstrate that our algorithm can effectively draw samples from distributions that conventional methods struggle to handle.

The increasing availability of computer-mediated knowledge and the advancement of information and communication technologies have altered the methods through which health care information is sought [3] [25] [30]. The Internet has had a significant impact on healthcare service and is a virtual medical library for an estimated 75-80% of users in developed countries [4] [5] [11]. On an average day, more than six million patients and their caregivers in the United States use the Internet to obtain health and medical information. This number exceeds the average daily number of 2.27 million Americans who make visits to physician offices [11] [18] [26]. Furthermore, not only patients but their caregivers want to get actively involved in the health-care management of their loved ones. In a research nearly 60% of people who identified themselves as caregivers use the Internet to find answers to their health-related questions [16]. This computer mediated environment has become, as Vargo and Lusch [32] argue, a fundamental hub where "people exchange to acquire the benefits of specialized competencies (knowledge and skills), or services."

We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions between distinct dynamical regimes. We extend this analysis and compute the transitions for an analytically tractable manifold model where the statistical model for the data is a mixture of lower dimensional Gaussians embedded in higher dimensional space. We compute the so-called speciation and collapse transition times, as a function of the ratio of manifold-to-ambient space dimensions, and other characteristics of the data model. An important tool used in our analysis is the exact formula for the mutual information (or free energy) of Generalized Linear Models.

This paper addresses the challenges in learning-based monocular positioning by proposing VKFPos, a novel approach that integrates Absolute Pose Regression (APR) and Relative Pose Regression (RPR) via an Extended Kalman Filter (EKF) within a variational Bayesian inference framework. Our method shows that the essential posterior probability of the monocular positioning problem can be decomposed into APR and RPR components. This decomposition is embedded in the deep learning model by predicting covariances in both APR and RPR branches, allowing them to account for associated uncertainties. These covariances enhance the loss functions and facilitate EKF integration. Experimental evaluations on both indoor and outdoor datasets show that the single-shot APR branch achieves accuracy on par with state-of-the-art methods. Furthermore, for temporal positioning, where consecutive images allow for RPR and EKF integration, VKFPos outperforms temporal APR and model-based integration methods, achieving superior accuracy.

The notion of generalization has moved away from the classical one defined in statistical learning theory towards an emphasis on out-of-domain generalization (OODG). Recently, there is a growing focus on inductive generalization, where a progression of difficulty implicitly governs the direction of domain shifts. In inductive generalization, it is often assumed that the training data lie in the easier side, while the testing data lie in the harder side. The challenge is that training data are always finite, but a learner is expected to infer an inductive principle that could be applied in an unbounded manner. This emerging regime has appeared in the literature under different names, such as length/logical/algorithmic extrapolation, but a formal definition is lacking. This work provides such a formalization that centers on the concept of model successors. Then we outline directions to adapt well-established techniques towards the learning of model successors. This work calls for restructuring of the research discussion around inductive generalization from fragmented task-centric communities to a more unified effort, focused on universal properties of learning and computation.

Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits and proof-of-principle error-correction on a single logical qubit. Nevertheless, despite significant progress and excitement, the path toward a full-stack scalable technology is largely unknown. There are significant outstanding quantum hardware, fabrication, software architecture, and algorithmic challenges that are either unresolved or overlooked. These issues could seriously undermine the arrival of utility-scale quantum computers for the foreseeable future. Here, we provide a comprehensive review of these scaling challenges. We show how the road to scaling could be paved by adopting existing semiconductor technology to build much higher-quality qubits, employing system engineering approaches, and performing distributed quantum computation within heterogeneous high-performance computing infrastructures. These opportunities for research and development could unlock certain promising applications, in particular, efficient quantum simulation/learning of quantum data generated by natural or engineered quantum systems. To estimate the true cost of such promises, we provide a detailed resource and sensitivity analysis for classically hard quantum chemistry calculations on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. Furthermore, we argue that, to tackle industry-scale classical optimization and machine learning problems in a cost-effective manner, heterogeneous quantum-probabilistic computing with custom-designed accelerators should be considered as a complementary path toward scalability.

Recent advances have shown that statistical tests for the rank of cross-covariance matrices play an important role in causal discovery. These rank tests include partial correlation tests as special cases and provide further graphical information about latent variables. Existing rank tests typically assume that all the continuous variables can be perfectly measured, and yet, in practice many variables can only be measured after discretization. For example, in psychometric studies, the continuous level of certain personality dimensions of a person can only be measured after being discretized into order-preserving options such as disagree, neutral, and agree. Motivated by this, we propose Mixed data Permutation-based Rank Test (MPRT), which properly controls the statistical errors even when some or all variables are discretized. Theoretically, we establish the exchangeability and estimate the asymptotic null distribution by permutations; as a consequence, MPRT can effectively control the Type I error in the presence of discretization while previous methods cannot. Empirically, our method is validated by extensive experiments on synthetic data and real-world data to demonstrate its effectiveness as well as applicability in causal discovery.