We study the problem of learning directed acyclic graphs from continuous observational data, generated according to a linear Gaussian structural equation model. State-of-the-art structure learning methods for this setting have at least one of the following shortcomings: i) they cannot provide optimality guarantees and can suffer from learning sub-optimal models; ii) they rely on the stringent assumption that the noise is homoscedastic, and hence the underlying model is fully identifiable. We overcome these shortcomings and develop a computationally efficient mixed-integer programming framework for learning medium-sized problems that accounts for arbitrary heteroscedastic noise. We present an early stopping criterion under which we can terminate the branch-and-bound procedure to achieve an asymptotically optimal solution and establish the consistency of this approximate solution. In addition, we show via numerical experiments that our method outperforms three state-of-the-art algorithms and is robust to noise heteroscedasticity, whereas the performance of the competing methods deteriorates under strong violations of the identifiability assumption. The software implementation of our method is available as the Python package \emph{micodag}.

We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a generalization of the standard KL divergence and a criterion for conducting risk minimization. Under a compact support assumption, we prove an $\mc{O}(1/{\sqrt{n}})$ bound on the expected estimation error when using the $h$-lifted KL divergence, which extends the results of Rakhlin et al. (2005, ESAIM: Probability and Statistics, Vol. 9) and Li and Barron (1999, Advances in Neural Information ProcessingSystems, Vol. 12) to permit the risk bounding of density functions that are not strictly positive. We develop a procedure for the computation of the corresponding maximum $h$-lifted likelihood estimators ($h$-MLLEs) using the Majorization-Maximization framework and provide experimental results in support of our theoretical bounds.

Accurate spatio-temporal information about the current situation is crucial for smart city applications such as modern routing algorithms. Often, this information describes the state of stationary resources, e.g. the availability of parking bays, charging stations or the amount of people waiting for a vehicle to pick them up near a given location. To exploit this kind of information, predicting future states of the monitored resources is often mandatory because a resource might change its state within the time until it is needed. To train an accurate predictive model, it is often not possible to obtain a continuous time series on the state of the resource. For example, the information might be collected from traveling agents visiting the resource with an irregular frequency. Thus, it is necessary to develop methods which work on sparse observations for training and prediction. In this paper, we propose time-inhomogeneous discrete Markov models to allow accurate prediction even when the frequency of observation is very rare. Our new model is able to blend recent observations with historic data and also provide useful probabilistic estimates for future states. Since resources availability in a city is typically time-dependent, our Markov model is time-inhomogeneous and cyclic within a predefined time interval. To train our model, we propose a modified Baum-Welch algorithm. Evaluations on real-world datasets of parking bay availability show that our new method indeed yields good results compared to methods being trained on complete data and non-cyclic variants.

The widespread adoption of electric vehicles (EVs) poses several challenges to power distribution networks and smart grid infrastructure due to the possibility of significantly increasing electricity demands, especially during peak hours. Furthermore, when EVs participate in demand-side management programs, charging expenses can be reduced by using optimal charging control policies that fully utilize real-time pricing schemes. However, devising optimal charging methods and control strategies for EVs is challenging due to various stochastic and uncertain environmental factors. Currently, most EV charging controllers operate based on a centralized model. In this paper, we introduce a novel approach for distributed and cooperative charging strategy using a Multi-Agent Reinforcement Learning (MARL) framework. Our method is built upon the Deep Deterministic Policy Gradient (DDPG) algorithm for a group of EVs in a residential community, where all EVs are connected to a shared transformer. This method, referred to as CTDE-DDPG, adopts a Centralized Training Decentralized Execution (CTDE) approach to establish cooperation between agents during the training phase, while ensuring a distributed and privacy-preserving operation during execution. We theoretically examine the performance of centralized and decentralized critics for the DDPG-based MARL implementation and demonstrate their trade-offs. Furthermore, we numerically explore the efficiency, scalability, and performance of centralized and decentralized critics. Our theoretical and numerical results indicate that, despite higher policy gradient variances and training complexity, the CTDE-DDPG framework significantly improves charging efficiency by reducing total variation by approximately %36 and charging cost by around %9.1 on average...

Large-scale geolocation telematics data acquired from connected vehicles has the potential to significantly enhance mobility infrastructures and operational systems within smart cities. To effectively utilize this data, it is essential to accurately match the geolocation data to the road segments. However, this matching is often not trivial due to the low sampling rate and errors exacerbated by multipath effects in urban environments. Traditionally, statistical modeling techniques such as Hidden-Markov models incorporating domain knowledge into the matching process have been extensively used for map-matching tasks. However, rule-based map-matching tasks are noise-sensitive and inefficient in processing large-scale trajectory data. Deep learning techniques directly learn the relationship between observed data and road networks from the data, often without the need for hand-crafted rules or domain knowledge. This renders them an efficient approach for map-matching large-scale datasets and makes them more robust to the noise. This paper introduces a sequence-to-sequence deep-learning model, specifically the transformer-based encoder-decoder model, to perform as a surrogate for map-matching algorithms. The encoder-decoder architecture initially encodes the series of noisy GPS points into a representation that automatically captures autoregressive behavior and spatial correlations between GPS points. Subsequently, the decoder associates data points with the road network features and thus transforms these representations into a sequence of road segments. The model is trained and evaluated using GPS traces collected in Manhattan, New York. Achieving an accuracy of 76%, transformer-based encoder-decoder models extensively employed in natural language processing presented a promising performance for translating noisy GPS data to the navigated routes in urban road networks.

Large language models primarily rely on inductive reasoning for decision making. This results in unreliable decisions when applied to real-world tasks that often present incomplete contexts and conditions. Thus, accurate probability estimation and appropriate interpretations are required to enhance decision-making reliability. In this paper, we propose a Bayesian inference framework called BIRD for large language models. BIRD provides controllable and interpretable probability estimation for model decisions, based on abductive factors, LLM entailment, as well as learnable deductive Bayesian modeling. Experiments show that BIRD produces probability estimations that align with human judgments over 65% of the time using open-sourced Llama models, outperforming the state-of-the-art GPT-4 by 35%. We also show that BIRD can be directly used for trustworthy decision making on many real-world applications.

Recent advancements in deep learning (DL) have posed a significant challenge for automatic speech recognition (ASR). ASR relies on extensive training datasets, including confidential ones, and demands substantial computational and storage resources. Enabling adaptive systems improves ASR performance in dynamic environments. DL techniques assume training and testing data originate from the same domain, which is not always true. Advanced DL techniques like deep transfer learning (DTL), federated learning (FL), and reinforcement learning (RL) address these issues. DTL allows high-performance models using small yet related datasets, FL enables training on confidential data without dataset possession, and RL optimizes decision-making in dynamic environments, reducing computation costs. This survey offers a comprehensive review of DTL, FL, and RL-based ASR frameworks, aiming to provide insights into the latest developments and aid researchers and professionals in understanding the current challenges. Additionally, transformers, which are advanced DL techniques heavily used in proposed ASR frameworks, are considered in this survey for their ability to capture extensive dependencies in the input ASR sequence. The paper starts by presenting the background of DTL, FL, RL, and Transformers and then adopts a well-designed taxonomy to outline the state-of-the-art approaches. Subsequently, a critical analysis is conducted to identify the strengths and weaknesses of each framework. Additionally, a comparative study is presented to highlight the existing challenges, paving the way for future research opportunities.

The purpose of this paper is twofold. First, we propose a novel algorithm for estimating parameters in one-dimensional Gaussian mixture models (GMMs). The algorithm takes advantage of the Hankel structure inherent in the Fourier data obtained from independent and identically distributed (i.i.d) samples of the mixture. For GMMs with a unified variance, a singular value ratio functional using the Fourier data is introduced and used to resolve the variance and component number simultaneously. The consistency of the estimator is derived. Compared to classic algorithms such as the method of moments and the maximum likelihood method, the proposed algorithm does not require prior knowledge of the number of Gaussian components or good initial guesses. Numerical experiments demonstrate its superior performance in estimation accuracy and computational cost. Second, we reveal that there exists a fundamental limit to the problem of estimating the number of Gaussian components or model order in the mixture model if the number of i.i.d samples is finite. For the case of a single variance, we show that the model order can be successfully estimated only if the minimum separation distance between the component means exceeds a certain threshold value and can fail if below. We derive a lower bound for this threshold value, referred to as the computational resolution limit, in terms of the number of i.i.d samples, the variance, and the number of Gaussian components. Numerical experiments confirm this phase transition phenomenon in estimating the model order. Moreover, we demonstrate that our algorithm achieves better scores in likelihood, AIC, and BIC when compared to the EM algorithm.

We propose a novel method (floZ), based on normalizing flows, for estimating the Bayesian evidence (and its numerical uncertainty) from a set of samples drawn from the unnormalized posterior distribution. We validate it on distributions whose evidence is known analytically, up to 15 parameter space dimensions, and compare with two state-of-the-art techniques for estimating the evidence: nested sampling (which computes the evidence as its main target) and a k-nearest-neighbors technique that produces evidence estimates from posterior samples. Provided representative samples from the target posterior are available, our method is more robust to posterior distributions with sharp features, especially in higher dimensions. It has wide applicability, e.g., to estimate the evidence from variational inference, Markov-chain Monte Carlo samples, or any other method that delivers samples from the unnormalized posterior density.

Parallelisation in Bayesian optimisation is a common strategy but faces several challenges: the need for flexibility in acquisition functions and kernel choices, flexibility dealing with discrete and continuous variables simultaneously, model misspecification, and lastly fast massive parallelisation. To address these challenges, we introduce a versatile and modular framework for batch Bayesian optimisation via probabilistic lifting with kernel quadrature, called SOBER, which we present as a Python library based on GPyTorch/BoTorch. Our framework offers the following unique benefits: (1) Versatility in downstream tasks under a unified approach.