The inference of causal structures from observed data plays a key role in unveiling the underlying dynamics of the system. This paper exposes a novel method, named Multiscale-Causal Structure Learning (MS-CASTLE), to estimate the structure of linear causal relationships occurring at different time scales. Differently from existing approaches, MS-CASTLE takes explicitly into account instantaneous and lagged inter-relations between multiple time series, represented at different scales, hinging on stationary wavelet transform and non-convex optimization. MS-CASTLE incorporates, as a special case, a single-scale version named SS-CASTLE, which compares favorably in terms of computational efficiency, performance and robustness with respect to the state of the art onto synthetic data. We used MS-CASTLE to study the multiscale causal structure of the risk of 15 global equity markets, during covid-19 pandemic, illustrating how MS-CASTLE can extract meaningful information thanks to its multiscale analysis, outperforming SS-CASTLE. We found that the most persistent and strongest interactions occur at mid-term time resolutions. Moreover, we identified the stock markets that drive the risk during the considered period: Brazil, Canada and Italy. The proposed approach can be exploited by financial investors who, depending to their investment horizon, can manage the risk within equity portfolios from a causal perspective.

Real-Time Bidding (RTB) is an important mechanism in modern online advertising systems. Advertisers employ bidding strategies in RTB to optimize their advertising effects subject to various financial requirements, especially the return-on-investment (ROI) constraint. ROIs change non-monotonically during the sequential bidding process, and often induce a see-saw effect between constraint satisfaction and objective optimization. While some existing approaches show promising results in static or mildly changing ad markets, they fail to generalize to highly dynamic ad markets with ROI constraints, due to their inability to adaptively balance constraints and objectives amidst non-stationarity and partial observability. In this work, we specialize in ROI-Constrained Bidding in non-stationary markets. Based on a Partially Observable Constrained Markov Decision Process, our method exploits an indicator-augmented reward function free of extra trade-off parameters and develops a Curriculum-Guided Bayesian Reinforcement Learning (CBRL) framework to adaptively control the constraint-objective trade-off in non-stationary ad markets. Extensive experiments on a large-scale industrial dataset with two problem settings reveal that CBRL generalizes well in both in-distribution and out-of-distribution data regimes, and enjoys superior learning efficiency and stability.

We consider an expected-value ranking and selection problem where all k solutions' simulation outputs depend on a common uncertain input model. Given that the uncertainty of the input model is captured by a probability simplex on a finite support, we define the most probable best (MPB) to be the solution whose probability of being optimal is the largest. To devise an efficient sampling algorithm to find the MPB, we first derive a lower bound to the large deviation rate of the probability of falsely selecting the MPB, then formulate an optimal computing budget allocation (OCBA) problem to find the optimal static sampling ratios for all solution-input model pairs that maximize the lower bound. We devise a series of sequential algorithms that apply interpretable and computationally efficient sampling rules and prove their sampling ratios achieve the optimality conditions for the OCBA problem as the simulation budget increases. The algorithms are benchmarked against a state-of-the-art sequential sampling algorithm designed for contextual ranking and selection problems and demonstrated to have superior empirical performances at finding the MPB.

Bayesian modeling helps applied researchers articulate assumptions about their data and develop models tailored for specific applications. Thanks to good methods for approximate posterior inference, researchers can now easily build, use, and revise complicated Bayesian models for large and rich data. These capabilities, however, bring into focus the problem of model criticism. Researchers need tools to diagnose the fitness of their models, to understand where they fall short, and to guide their revision. In this paper we develop a new method for Bayesian model criticism, the population predictive check (Pop-PC). Pop-PCs are built on posterior predictive checks (PPCs), a seminal method that checks a model by assessing the posterior predictive distribution on the observed data. However, PPCs use the data twice -- both to calculate the posterior predictive and to evaluate it -- which can lead to overconfident assessments of the quality of a model. Pop-PCs, in contrast, compare the posterior predictive distribution to a draw from the population distribution, a heldout dataset. This method blends Bayesian modeling with frequenting assessment. Unlike the PPC, we prove that the Pop-PC is properly calibrated. Empirically, we study Pop-PC on classical regression and a hierarchical model of text data.

One of the main challenges in autonomous racing is to design algorithms for motion planning at high speed, and across complex racing courses. End-to-end trajectory synthesis has been previously proposed where the trajectory for the ego vehicle is computed based on camera images from the racecar. This is done in a supervised learning setting using behavioral cloning techniques. In this paper, we address the limitations of behavioral cloning methods for trajectory synthesis by introducing Differential Bayesian Filtering (DBF), which uses probabilistic B\'ezier curves as a basis for inferring optimal autonomous racing trajectories based on Bayesian inference. We introduce a trajectory sampling mechanism and combine it with a filtering process which is able to push the car to its physical driving limits. The performance of DBF is evaluated on the DeepRacing Formula One simulation environment and compared with several other trajectory synthesis approaches as well as human driving performance. DBF achieves the fastest lap time, and the fastest speed, by pushing the racecar closer to its limits of control while always remaining inside track bounds.

Maintaining an up-to-date map to reflect recent changes in the scene is very important, particularly in situations involving repeated traversals by a robot operating in an environment over an extended period. Undetected changes may cause a deterioration in map quality, leading to poor localization, inefficient operations, and lost robots. Volumetric methods, such as truncated signed distance functions (TSDFs), have quickly gained traction due to their real-time production of a dense and detailed map, though map updating in scenes that change over time remains a challenge. We propose a framework that introduces a novel probabilistic object state representation to track object pose changes in semi-static scenes. The representation jointly models a stationarity score and a TSDF change measure for each object. A Bayesian update rule that incorporates both geometric and semantic information is derived to achieve consistent online map maintenance. To extensively evaluate our approach alongside the state-of-the-art, we release a novel real-world dataset in a warehouse environment. We also evaluate on the public ToyCar dataset. Our method outperforms state-of-the-art methods on the reconstruction quality of semi-static environments.

We use Gaussian stochastic weight averaging (SWAG) to assess the model-form uncertainty associated with neural-network-based function approximation relevant to fluid flows. SWAG approximates a posterior Gaussian distribution of each weight, given training data, and a constant learning rate. Having access to this distribution, it is able to create multiple models with various combinations of sampled weights, which can be used to obtain ensemble predictions. The average of such an ensemble can be regarded as the `mean estimation', whereas its standard deviation can be used to construct `confidence intervals', which enable us to perform uncertainty quantification (UQ) with regard to the training process of neural networks. We utilize representative neural-network-based function approximation tasks for the following cases: (i) a two-dimensional circular-cylinder wake; (ii) the DayMET dataset (maximum daily temperature in North America); (iii) a three-dimensional square-cylinder wake; and (iv) urban flow, to assess the generalizability of the present idea for a wide range of complex datasets. SWAG-based UQ can be applied regardless of the network architecture, and therefore, we demonstrate the applicability of the method for two types of neural networks: (i) global field reconstruction from sparse sensors by combining convolutional neural network (CNN) and multi-layer perceptron (MLP); and (ii) far-field state estimation from sectional data with two-dimensional CNN. We find that SWAG can obtain physically-interpretable confidence-interval estimates from the perspective of model-form uncertainty. This capability supports its use for a wide range of problems in science and engineering.

High-quality calibrated uncertainty estimates are crucial for numerous real-world applications, especially for deep learning-based deployed ML systems. While Bayesian deep learning techniques allow uncertainty estimation, training them with large-scale datasets is an expensive process that does not always yield models competitive with non-Bayesian counterparts. Moreover, many of the high-performing deep learning models that are already trained and deployed are non-Bayesian in nature and do not provide uncertainty estimates. To address these issues, we propose BayesCap that learns a Bayesian identity mapping for the frozen model, allowing uncertainty estimation. BayesCap is a memory-efficient method that can be trained on a small fraction of the original dataset, enhancing pretrained non-Bayesian computer vision models by providing calibrated uncertainty estimates for the predictions without (i) hampering the performance of the model and (ii) the need for expensive retraining the model from scratch. The proposed method is agnostic to various architectures and tasks. We show the efficacy of our method on a wide variety of tasks with a diverse set of architectures, including image super-resolution, deblurring, inpainting, and crucial application such as medical image translation. Moreover, we apply the derived uncertainty estimates to detect out-of-distribution samples in critical scenarios like depth estimation in autonomous driving.

Model hubs with many pre-trained models (PTMs) have become a cornerstone of deep learning. Although built at a high cost, they remain \emph{under-exploited} -- practitioners usually pick one PTM from the provided model hub by popularity and then fine-tune the PTM to solve the target task. This na\"ive but common practice poses two obstacles to full exploitation of pre-trained model hubs: first, the PTM selection by popularity has no optimality guarantee, and second, only one PTM is used while the remaining PTMs are ignored. An alternative might be to consider all possible combinations of PTMs and extensively fine-tune each combination, but this would not only be prohibitive computationally but may also lead to statistical over-fitting. In this paper, we propose a new paradigm for exploiting model hubs that is intermediate between these extremes. The paradigm is characterized by two aspects: (1) We use an evidence maximization procedure to estimate the maximum value of label evidence given features extracted by pre-trained models. This procedure can rank all the PTMs in a model hub for various types of PTMs and tasks \emph{before fine-tuning}. (2) The best ranked PTM can either be fine-tuned and deployed if we have no preference for the model's architecture or the target PTM can be tuned by the top $K$ ranked PTMs via a Bayesian procedure that we propose. This procedure, which we refer to as \emph{B-Tuning}, not only improves upon specialized methods designed for tuning homogeneous PTMs, but also applies to the challenging problem of tuning heterogeneous PTMs where it yields a new level of benchmark performance.

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to a large number of model parameters. A promising approach to high-dimensional likelihood-free inference involves estimating low-dimensional marginal posteriors by conditioning only on summary statistics believed to be informative for the low-dimensional component, and then combining the low-dimensional approximations in some way. In this paper, we demonstrate that such low-dimensional approximations can be surprisingly poor in practice for seemingly intuitive summary statistic choices. We describe an idealized low-dimensional summary statistic that is, in principle, suitable for marginal estimation. However, a direct approximation of the idealized choice is difficult in practice. We thus suggest an alternative approach to marginal estimation which is easier to implement and automate. Given an initial choice of low-dimensional summary statistic that might only be informative about a marginal posterior location, the new method improves performance by first crudely localising the posterior approximation using all the summary statistics to ensure global identifiability, followed by a second step that hones in on an accurate low-dimensional approximation using the low-dimensional summary statistic. We show that the posterior this approach targets can be represented as a logarithmic pool of posterior distributions based on the low-dimensional and full summary statistics, respectively. The good performance of our method is illustrated in several examples.