In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes stochastic, and more precisely discretely indexed. Due to the discrete nature of the underlying additional latent variable, DIF inherit the good computational behavior of NF: they benefit from both a tractable density as well as a straightforward sampling scheme, and can thus be used for the dual problems of Variational Inference (VI) and of Variational density estimation (VDE). On the other hand, DIF can also be understood as an extension of mixture density models, in which the constant mixture weights are replaced by flexible functions. As a consequence, DIF are better suited for capturing distributions with discontinuities, sharp edges and fine details, which is a main advantage of this construction. Finally we propose a methodology for constructiong DIF in practice, and see that DIF can be sequentially cascaded, and cascaded with NF.

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The Cut posterior and related Semi-Modular Inference are Generalised Bayes methods for Modular Bayesian evidence combination. Analysis is broken up over modular sub-models of the joint posterior distribution. Model-misspecification in multi-modular models can be hard to fix by model elaboration alone and the Cut posterior and SMI offer a way round this. Information entering the analysis from misspecified modules is controlled by an influence parameter $\eta$ related to the learning rate. This paper contains two substantial new methods. First, we give variational methods for approximating the Cut and SMI posteriors which are adapted to the inferential goals of evidence combination. We parameterise a family of variational posteriors using a Normalising Flow for accurate approximation and end-to-end training. Secondly, we show that analysis of models with multiple cuts is feasible using a new Variational Meta-Posterior. This approximates a family of SMI posteriors indexed by $\eta$ using a single set of variational parameters.

The improvements in the edge computing technology pave the road for diversified applications that demand real-time interaction. However, due to the mobility of the end-users and the dynamic edge environment, it becomes challenging to handle the task offloading with high performance. Moreover, since each application in mobile devices has different characteristics, a task orchestrator must be adaptive and have the ability to learn the dynamics of the environment. For this purpose, we develop a deep reinforcement learning based task orchestrator, DeepEdge, which learns to meet different task requirements without needing human interaction even under the heavily-loaded stochastic network conditions in terms of mobile users and applications. Given the dynamic offloading requests and time-varying communication conditions, we successfully model the problem as a Markov process and then apply the Double Deep Q-Network (DDQN) algorithm to implement DeepEdge. To evaluate the robustness of DeepEdge, we experiment with four different applications including image rendering, infotainment, pervasive health, and augmented reality in the network under various loads. Furthermore, we compare the performance of our agent with the four different task offloading approaches in the literature. Our results show that DeepEdge outperforms its competitors in terms of the percentage of satisfactorily completed tasks.

We study the problem of identifying the best arm in a multi-armed bandit environment when each arm is a time-homogeneous and ergodic discrete-time Markov process on a common, finite state space. The state evolution on each arm is governed by the arm's transition probability matrix (TPM). A decision entity that knows the set of arm TPMs but not the exact mapping of the TPMs to the arms, wishes to find the index of the best arm as quickly as possible, subject to an upper bound on the error probability. The decision entity selects one arm at a time sequentially, and all the unselected arms continue to undergo state evolution ({\em restless} arms). For this problem, we derive the first-known problem instance-dependent asymptotic lower bound on the growth rate of the expected time required to find the index of the best arm, where the asymptotics is as the error probability vanishes. Further, we propose a sequential policy that, for an input parameter $R$, forcibly selects an arm that has not been selected for $R$ consecutive time instants. We show that this policy achieves an upper bound that depends on $R$ and is monotonically non-increasing as $R\to\infty$. The question of whether, in general, the limiting value of the upper bound as $R\to\infty$ matches with the lower bound, remains open. We identify a special case in which the upper and the lower bounds match. Prior works on best arm identification have dealt with (a) independent and identically distributed observations from the arms, and (b) rested Markov arms, whereas our work deals with the more difficult setting of restless Markov arms.

Black-box variational inference (BBVI) now sees widespread use in machine learning and statistics as a fast yet flexible alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, stochastic optimization methods for BBVI remain unreliable and require substantial expertise and hand-tuning to apply effectively. In this paper, we propose Robust, Automated, and Accurate BBVI (RAABBVI), a framework for reliable BBVI optimization. RAABBVI is based on rigorously justified automation techniques, includes just a small number of intuitive tuning parameters, and detects inaccurate estimates of the optimal variational approximation. RAABBVI adaptively decreases the learning rate by detecting convergence of the fixed--learning-rate iterates, then estimates the symmetrized Kullback--Leiber (KL) divergence between the current variational approximation and the optimal one. It also employs a novel optimization termination criterion that enables the user to balance desired accuracy against computational cost by comparing (i) the predicted relative decrease in the symmetrized KL divergence if a smaller learning were used and (ii) the predicted computation required to converge with the smaller learning rate. We validate the robustness and accuracy of RAABBVI through carefully designed simulation studies and on a diverse set of real-world model and data examples.

Ising machines are unconventional computer architectures based on physics principles, named after the German physicist Ernst Ising. In recent years, they have been found to be particularly promising tools for solving combinatorial optimization (CO) problems and create artificial models of the brain. A team of researchers in the group of Sayeef Salahuddin, a TSMC distinguished Professor of EECS at the University of California, Berkeley, has recently been exploring the potential of Ising machines for finding solutions to complex optimization problems in great depth. Their most recent paper, published in Nature Electronics, introduced a new Ising machine comprised of many restricted Boltzmann machines (RBMs), which was found to achieve remarkable results on complex combinatorial optimization tasks. "In the recent years, a lot of work has gone into Ising machines to accelerate optimization problems, which our work builds on," Saavan Patel, the lead author who carried out the study, told TechXplore.

A general control policy framework based on deep reinforcement learning (DRL) is introduced for closed-loop decision making in subsurface flow settings. Traditional closed-loop modeling workflows in this context involve the repeated application of data assimilation/history matching and robust optimization steps. Data assimilation can be particularly challenging in cases where both the geological style (scenario) and individual model realizations are uncertain. The closed-loop reservoir management (CLRM) problem is formulated here as a partially observable Markov decision process, with the associated optimization problem solved using a proximal policy optimization algorithm. This provides a control policy that instantaneously maps flow data observed at wells (as are available in practice) to optimal well pressure settings. The policy is represented by a temporal convolution and gated transformer blocks. Training is performed in a preprocessing step with an ensemble of prior geological models, which can be drawn from multiple geological scenarios. Example cases involving the production of oil via water injection, with both 2D and 3D geological models, are presented. The DRL-based methodology is shown to result in an NPV increase of 15% (for the 2D cases) and 33% (3D cases) relative to robust optimization over prior models, and to an average improvement of 4% in NPV relative to traditional CLRM. The solutions from the control policy are found to be comparable to those from deterministic optimization, in which the geological model is assumed to be known, even when multiple geological scenarios are considered. The control policy approach results in a 76% decrease in computational cost relative to traditional CLRM with the algorithms and parameter settings considered in this work.

The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields are mathematical structures that models the interaction between these variables by means of an inverse temperature parameter, responsible for controlling the spatial dependence structure along the field. In this paper, we derive closed-form expressions for the Kullback-Leibler divergence between two pairwise isotropic Gaussian-Markov random fields in both univariate and multivariate cases. The proposed equation allows the development of novel similarity measures in image processing and machine learning applications, such as image denoising and unsupervised metric learning.

Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from complicated distributions that are hard to sample from classically, but which seldom arise in applications. Here we introduce a quantum algorithm to sample from distributions that pose a bottleneck in several applications, which we implement on a superconducting quantum processor. The algorithm performs Markov chain Monte Carlo (MCMC), a popular iterative sampling technique, to sample from the Boltzmann distribution of classical Ising models. In each step, the quantum processor explores the model in superposition to propose a random move, which is then accepted or rejected by a classical computer and returned to the quantum processor, ensuring convergence to the desired Boltzmann distribution. We find that this quantum algorithm converges in fewer iterations than common classical MCMC alternatives on relevant problem instances, both in simulations and experiments. It therefore opens a new path for quantum computers to solve useful--not merely difficult--problems in the near term.