In this paper, we critically evaluate Bayesian methods for uncertainty estimation in deep learning, focusing on the widely applied Laplace approximation and its variants. Our findings reveal that the conventional method of fitting the Hessian matrix negatively impacts out-of-distribution (OOD) detection efficiency. We propose a different point of view, asserting that focusing solely on optimizing prior precision can yield more accurate uncertainty estimates in OOD detection while preserving adequate calibration metrics. Moreover, we demonstrate that this property is not connected to the training stage of a model but rather to its intrinsic properties. Through extensive experimental evaluation, we establish the superiority of our simplified approach over traditional methods in the out-of-distribution domain.

Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.

State estimation poses substantial challenges in robotics, often involving encounters with multimodality in real-world scenarios. To address these challenges, it is essential to calculate Maximum a posteriori (MAP) sequences from joint probability distributions of latent states and observations over time. However, it generally involves a trade-off between approximation errors and computational complexity. In this article, we propose a new method for MAP sequence estimation called Stein-MAP, which effectively manages multimodality with fewer approximation errors while significantly reducing computational and memory burdens. Our key contribution lies in the introduction of a sequential variational inference framework designed to handle temporal dependencies among transition states within dynamical system models. The framework integrates Stein's identity from probability theory and reproducing kernel Hilbert space (RKHS) theory, enabling computationally efficient MAP sequence estimation. As a MAP sequence estimator, Stein-MAP boasts a computational complexity of O(N), where N is the number of particles, in contrast to the O(N^2) complexity of the Viterbi algorithm. The proposed method is empirically validated through real-world experiments focused on range-only (wireless) localization. The results demonstrate a substantial enhancement in state estimation compared to existing methods. A remarkable feature of Stein-MAP is that it can attain improved state estimation with only 40 to 50 particles, as opposed to the 1000 particles that the particle filter or its variants require.

Recent advances in theoretical biology suggest that basal cognition and sentient behaviour are emergent properties of in vitro cell cultures and neuronal networks, respectively. Such neuronal networks spontaneously learn structured behaviours in the absence of reward or reinforcement. In this paper, we characterise this kind of self-organisation through the lens of the free energy principle, i.e., as self-evidencing. We do this by first discussing the definitions of reactive and sentient behaviour in the setting of active inference, which describes the behaviour of agents that model the consequences of their actions. We then introduce a formal account of intentional behaviour, that describes agents as driven by a preferred endpoint or goal in latent state-spaces. We then investigate these forms of (reactive, sentient, and intentional) behaviour using simulations. First, we simulate the aforementioned in vitro experiments, in which neuronal cultures spontaneously learn to play Pong, by implementing nested, free energy minimising processes. The simulations are then used to deconstruct the ensuing predictive behaviour, leading to the distinction between merely reactive, sentient, and intentional behaviour, with the latter formalised in terms of inductive planning. This distinction is further studied using simple machine learning benchmarks (navigation in a grid world and the Tower of Hanoi problem), that show how quickly and efficiently adaptive behaviour emerges under an inductive form of active inference.

Channel estimation in reconfigurable intelligent surfaces (RIS)-aided systems is crucial for optimal configuration of the RIS and various downstream tasks such as user localization. In RIS-aided systems, channel estimation involves estimating two channels for the user-RIS (UE-RIS) and RIS-base station (RIS-BS) links. In the literature, two approaches are proposed: (i) cascaded channel estimation where the two channels are collapsed into a single one and estimated using training signals at the BS, and (ii) separate channel estimation that estimates each channel separately either in a passive or semi-passive RIS setting. In this work, we study the separate channel estimation problem in a fully passive RIS-aided millimeter-wave (mmWave) single-user single-input multiple-output (SIMO) communication system. First, we adopt a variational-inference (VI) approach to jointly estimate the UE-RIS and RIS-BS instantaneous channel state information (I-CSI). In particular, auxiliary posterior distributions of the I-CSI are learned through the maximization of the evidence lower bound. However, estimating the I-CSI for both links in every coherence block results in a high signaling overhead to control the RIS in scenarios with highly mobile users. Thus, we extend our first approach to estimate the slow-varying statistical CSI of the UE-RIS link overcoming the highly variant I-CSI. Precisely, our second method estimates the I-CSI of RIS-BS channel and the UE-RIS channel covariance matrix (CCM) directly from the uplink training signals in a fully passive RIS-aided system. The simulation results demonstrate that using maximum a posteriori channel estimation using the auxiliary posteriors can provide a capacity that approaches the capacity with perfect CSI.

We derive a concentration bound of the type `for all $n \geq n_0$ for some $n_0$' for TD(0) with linear function approximation. We work with online TD learning with samples from a single sample path of the underlying Markov chain. This makes our analysis significantly different from offline TD learning or TD learning with access to independent samples from the stationary distribution of the Markov chain. We treat TD(0) as a contractive stochastic approximation algorithm, with both martingale and Markov noises. Markov noise is handled using the Poisson equation and the lack of almost sure guarantees on boundedness of iterates is handled using the concept of relaxed concentration inequalities.

Regular blood pressure (BP) monitoring in clinical and ambulatory settings plays a crucial role in the prevention, diagnosis, treatment, and management of cardiovascular diseases. Recently, the widespread adoption of ambulatory BP measurement devices has been driven predominantly by the increased prevalence of hypertension and its associated risks and clinical conditions. Recent guidelines advocate for regular BP monitoring as part of regular clinical visits or even at home. This increased utilization of BP measurement technologies has brought up significant concerns, regarding the accuracy of reported BP values across settings. In this survey, focusing mainly on cuff-based BP monitoring technologies, we highlight how BP measurements can demonstrate substantial biases and variances due to factors such as measurement and device errors, demographics, and body habitus. With these inherent biases, the development of a new generation of cuff-based BP devices which use artificial-intelligence (AI) has significant potential. We present future avenues where AI-assisted technologies can leverage the extensive clinical literature on BP-related studies together with the large collections of BP records available in electronic health records. These resources can be combined with machine learning approaches, including deep learning and Bayesian inference, to remove BP measurement biases and to provide individualized BP-related cardiovascular risk indexes.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

A site's recommendation system relies on knowledge of its users' preferences to offer relevant recommendations to them. These preferences are for attributes that comprise items and content shown on the site, and are estimated from the data of users' interactions with the site. Another form of users' preferences is material too, namely, users' preferences for the site over other sites, since that shows users' base level propensities to engage with the site. Estimating users' preferences for the site, however, faces major obstacles because (a) the focal site usually has no data of its users' interactions with other sites; these interactions are users' unobserved behaviors for the focal site; and (b) the Machine Learning literature in recommendation does not offer a model of this situation. Even if (b) is resolved, the problem in (a) persists since without access to data of its users' interactions with other sites, there is no ground truth for evaluation. Moreover, it is most useful when (c) users' preferences for the site can be estimated at the individual level, since the site can then personalize recommendations to individual users. We offer a method to estimate individual user's preference for a focal site, under this premise. In particular, we compute the focal site's share of a user's online engagements without any data from other sites. We show an evaluation framework for the model using only the focal site's data, allowing the site to test the model. We rely upon a Hierarchical Bayes Method and perform estimation in two different ways - Markov Chain Monte Carlo and Stochastic Gradient with Langevin Dynamics. Our results find good support for the approach to computing personalized share of engagement and for its evaluation.

Diffusion models possess powerful generative capabilities enabling the mapping of noise to data using reverse stochastic differential equations. However, in image restoration tasks, the focus is on the mapping relationship from low-quality images to high-quality images. To address this, we introduced the Generalized Ornstein-Uhlenbeck Bridge (GOUB) model. By leveraging the natural mean-reverting property of the generalized OU process and further adjusting the variance of its steady-state distribution through the Doob's h-transform, we achieve diffusion mappings from point to point with minimal cost. This allows for end-to-end training, enabling the recovery of high-quality images from low-quality ones. Additionally, we uncovered the mathematical essence of some bridge models, all of which are special cases of the GOUB and empirically demonstrated the optimality of our proposed models. Furthermore, benefiting from our distinctive parameterization mechanism, we proposed the Mean-ODE model that is better at capturing pixel-level information and structural perceptions. Experimental results show that both models achieved state-of-the-art results in various tasks, including inpainting, deraining, and super-resolution. Code is available at https://github.com/Hammour-steak/GOUB.