Artificial neural networks (ANNs) are highly flexible predictive models. However, reliably quantifying uncertainty for their predictions is a continuing challenge. There has been much recent work on "recalibration" of predictive distributions for ANNs, so that forecast probabilities for events of interest are consistent with certain frequency evaluations of them. Uncalibrated probabilistic forecasts are of limited use for many important decision-making tasks. To address this issue, we propose a localized recalibration of ANN predictive distributions using the dimension-reduced representation of the input provided by the ANN hidden layers. Our novel method draws inspiration from recalibration techniques used in the literature on approximate Bayesian computation and likelihood-free inference methods. Most existing calibration methods for ANNs can be thought of as calibrating either on the input layer, which is difficult when the input is high-dimensional, or the output layer, which may not be sufficiently flexible. Through a simulation study, we demonstrate that our method has good performance compared to alternative approaches, and explore the benefits that can be achieved by localizing the calibration based on different layers of the network. Finally, we apply our proposed method to a diamond price prediction problem, demonstrating the potential of our approach to improve prediction and uncertainty quantification in real-world applications.

We present a first study of Bayesian forecasting of electricity prices traded on the German continuous intraday market which fully incorporates parameter uncertainty. Our target variable is the IDFull price index, forecasts are given in terms of posterior predictive distributions. For validation we use the exceedingly volatile electricity prices of 2022, which have hardly been the subject of forecasting studies before. As a benchmark model, we use all available intraday transactions at the time of forecast creation to compute a current value for the IDFull. According to the weak-form efficiency hypothesis, it would not be possible to significantly improve this benchmark built from last price information. We do, however, observe statistically significant improvement in terms of both point measures and probability scores. Finally, we challenge the declared gold standard of using LASSO for feature selection in electricity price forecasting by presenting strong statistical evidence that Orthogonal Matching Pursuit (OMP) leads to better forecasting performance.

Despite the frequent use of agent-based models (ABMs) for studying social phenomena, parameter estimation remains a challenge, often relying on costly simulation-based heuristics. This work uses variational inference to estimate the parameters of an opinion dynamics ABM, by transforming the estimation problem into an optimization task that can be solved directly. Our proposal relies on probabilistic generative ABMs (PGABMs): we start by synthesizing a probabilistic generative model from the ABM rules. Then, we transform the inference process into an optimization problem suitable for automatic differentiation. In particular, we use the Gumbel-Softmax reparameterization for categorical agent attributes and stochastic variational inference for parameter estimation. Furthermore, we explore the trade-offs of using variational distributions with different complexity: normal distributions and normalizing flows. We validate our method on a bounded confidence model with agent roles (leaders and followers). Our approach estimates both macroscopic (bounded confidence intervals and backfire thresholds) and microscopic ($200$ categorical, agent-level roles) more accurately than simulation-based and MCMC methods. Consequently, our technique enables experts to tune and validate their ABMs against real-world observations, thus providing insights into human behavior in social systems via data-driven analysis.

The lack of an efficient preamble detection algorithm remains a challenge for solving preamble collision problems in intelligent massive random access (RA) in practical communication scenarios. To solve this problem, we present a novel early preamble detection scheme based on a maximum likelihood estimation (MLE) model at the first step of the grant-based RA procedure. A novel blind normalized Stein variational gradient descent (SVGD)-based detector is proposed to obtain an approximate solution to the MLE model. First, by exploring the relationship between the Hadamard transform and wavelet transform, a new modified Hadamard transform (MHT) is developed to separate high-frequencies from important components using the second-order derivative filter. Next, to eliminate noise and mitigate the vanishing gradients problem in the SVGD-based detectors, the block MHT layer is designed based on the MHT, scaling layer, soft-thresholding layer, inverse MHT and sparsity penalty. Then, the blind normalized SVGD algorithm is derived to perform preamble detection without prior knowledge of noise power and the number of active devices. The experimental results show the proposed block MHT layer outperforms other transform-based methods in terms of computation costs and denoising performance. Furthermore, with the assistance of the block MHT layer, the proposed blind normalized SVGD algorithm achieves a higher preamble detection accuracy and throughput than other state-of-the-art detection methods.

We introduce a cooperative Bayesian optimization problem for optimizing black-box functions of two variables where two agents choose together at which points to query the function but have only control over one variable each. This setting is inspired by human-AI teamwork, where an AI-assistant helps its human user solve a problem, in this simplest case, collaborative optimization. We formulate the solution as sequential decision-making, where the agent we control models the user as a computationally rational agent with prior knowledge about the function. We show that strategic planning of the queries enables better identification of the global maximum of the function as long as the user avoids excessive exploration. This planning is made possible by using Bayes Adaptive Monte Carlo planning and by endowing the agent with a user model that accounts for conservative belief updates and exploratory sampling of the points to query.

Morden deep ensembles technique achieves strong uncertainty estimation performance by going through multiple forward passes with different models. This is at the price of a high storage space and a slow speed in the inference (test) time. To address this issue, we propose Density-Regression, a method that leverages the density function in uncertainty estimation and achieves fast inference by a single forward pass. We prove it is distance aware on the feature space, which is a necessary condition for a neural network to produce high-quality uncertainty estimation under distribution shifts. Empirically, we conduct experiments on regression tasks with the cubic toy dataset, benchmark UCI, weather forecast with time series, and depth estimation under real-world shifted applications. We show that Density-Regression has competitive uncertainty estimation performance under distribution shifts with modern deep regressors while using a lower model size and a faster inference speed.

Abrupt maneuvers by surrounding vehicles (SVs) can typically lead to safety concerns and affect the task efficiency of the ego vehicle (EV), especially with model uncertainties stemming from environmental disturbances. This paper presents a real-time fail-operational controller that ensures the asymptotic convergence of an uncertain EV to a safe state, while preserving task efficiency in dynamic environments. An incremental Bayesian learning approach is developed to facilitate online learning and inference of changing environmental disturbances. Leveraging disturbance quantification and constraint transformation, we develop a stochastic fail-operational barrier based on the control barrier function (CBF). With this development, the uncertain EV is able to converge asymptotically from an unsafe state to a defined safe state with probabilistic stability. Subsequently, the stochastic fail-operational barrier is integrated into an efficient fail-operational controller based on quadratic programming (QP). This controller is tailored for the EV operating under control constraints in the presence of environmental disturbances, with both safety and efficiency objectives taken into consideration. We validate the proposed framework in connected cruise control (CCC) tasks, where SVs perform aggressive driving maneuvers. The simulation results demonstrate that our method empowers the EV to swiftly return to a safe state while upholding task efficiency in real time, even under time-varying environmental disturbances.

Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these contexts, with autoregressive models being especially prominent. This dissertation focuses on using autoregressive models to answer complex probabilistic queries that go beyond single-step prediction, such as the timing of future events or the likelihood of a specific event occurring before another. In particular, we develop a broad class of novel and efficient approximation techniques for marginalization in sequential models that are model-agnostic. These techniques rely solely on access to and sampling from next-step conditional distributions of a pre-trained autoregressive model, including both traditional parametric models as well as more recent neural autoregressive models. Specific approaches are presented for discrete sequential models, for marked temporal point processes, and for stochastic jump processes, each tailored to a well-defined class of informative, long-range probabilistic queries.

Existing causal discovery methods based on combinatorial optimization or search are slow, prohibiting their application on large-scale datasets. In response, more recent methods attempt to address this limitation by formulating causal discovery as structure learning with continuous optimization but such approaches thus far provide no statistical guarantees. In this paper, we show that by efficiently parallelizing existing causal discovery methods, we can in fact scale them to thousands of dimensions, making them practical for substantially larger-scale problems. In particular, we parallelize the LiNGAM method, which is quadratic in the number of variables, obtaining up to a 32-fold speed-up on benchmark datasets when compared with existing sequential implementations. Specifically, we focus on the causal ordering subprocedure in DirectLiNGAM and implement GPU kernels to accelerate it. This allows us to apply DirectLiNGAM to causal inference on large-scale gene expression data with genetic interventions yielding competitive results compared with specialized continuous optimization methods, and Var-LiNGAM for causal discovery on U.S. stock data.

The generalized linear mixed model (GLMM) is a popular statistical approach for handling correlated data, and is used extensively in applications areas where big data is common, including biomedical data settings. The focus of this paper is scalable statistical inference for the GLMM, where we define statistical inference as: (i) estimation of population parameters, and (ii) evaluation of scientific hypotheses in the presence of uncertainty. Artificial intelligence (AI) learning algorithms excel at scalable statistical estimation, but rarely include uncertainty quantification. In contrast, Bayesian inference provides full statistical inference, since uncertainty quantification results automatically from the posterior distribution. Unfortunately, Bayesian inference algorithms, including Markov Chain Monte Carlo (MCMC), become computationally intractable in big data settings. In this paper, we introduce a statistical inference algorithm at the intersection of AI and Bayesian inference, that leverages the scalability of modern AI algorithms with guaranteed uncertainty quantification that accompanies Bayesian inference. Our algorithm is an extension of stochastic gradient MCMC with novel contributions that address the treatment of correlated data (i.e., intractable marginal likelihood) and proper posterior variance estimation. Through theoretical and empirical results we establish our algorithm's statistical inference properties, and apply the method in a large electronic health records database.