Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.

We address the consistency of a kernel ridge regression estimate of the conditional mean embedding (CME), which is an embedding of the conditional distribution of $Y$ given $X$ into a target reproducing kernel Hilbert space $\mathcal{H}_Y$. The CME allows us to take conditional expectations of target RKHS functions, and has been employed in nonparametric causal and Bayesian inference. We address the misspecified setting, where the target CME is in the space of Hilbert-Schmidt operators acting from an input interpolation space between $\mathcal{H}_X$ and $L_2$, to $\mathcal{H}_Y$. This space of operators is shown to be isomorphic to a newly defined vector-valued interpolation space. Using this isomorphism, we derive a novel and adaptive statistical learning rate for the empirical CME estimator under the misspecified setting. Our analysis reveals that our rates match the optimal $O(\log n / n)$ rates without assuming $\mathcal{H}_Y$ to be finite dimensional. We further establish a lower bound on the learning rate, which shows that the obtained upper bound is optimal.

Human annotations are vital to supervised learning, yet annotators often disagree on the correct label, especially as annotation tasks increase in complexity. A common strategy to improve label quality is to ask multiple annotators to label the same item and then aggregate their labels. To date, many aggregation models have been proposed for simple categorical or numerical annotation tasks, but far less work has considered more complex annotation tasks, such as those involving open-ended, multivariate, or structured responses. Similarly, while a variety of bespoke models have been proposed for specific tasks, our work is the first we are aware of to introduce aggregation methods that generalize across many, diverse complex tasks, including sequence labeling, translation, syntactic parsing, ranking, bounding boxes, and keypoints. This generality is achieved by applying readily available task-specific distance functions, then devising a task-agnostic method to model these distances between labels, rather than the labels themselves. This article presents a unified treatment of our prior work on complex annotation modeling and extends that work with investigation of three new research questions. First, how do complex annotation task and dataset properties impact aggregation accuracy? Second, how should a task owner navigate the many modeling choices in order to maximize aggregation accuracy? Finally, what tests and diagnoses can verify that aggregation models are specified correctly for the given data? To understand how various factors impact accuracy and to inform model selection, we conduct large-scale simulation studies and broad experiments on real, complex datasets. Regarding testing, we introduce the concept of unit tests for aggregation models and present a suite of such tests to ensure that a given model is not mis-specified and exhibits expected behavior. Beyond investigating these research questions above, we discuss the foundational concept and nature of annotation complexity, present a new aggregation model as a conceptual bridge between traditional models and our own, and contribute a new general semisupervised learning method for complex label aggregation that outperforms prior work.

Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is well measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is however challenging because the computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality together with tools from sequential Monte-Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA) in which each walker acquires a weight that enables the estimation of the gradient of the cross-entropy at any step during GD, thereby bypassing sampling biases induced by slow mixing of ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST and CIFAR-10 datasets. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.

In this work, we consider the problem of regularization in minimum mean-squared error (MMSE) linear filters. Exploiting the relationship with statistical machine learning methods, the regularization parameter is found from the observed signals in a simple and automatic manner. The proposed approach is illustrated through system identification examples, where the automatic regularization yields near-optimal results. Minimum mean-squared error (MMSE) linear filters are ubiquitous in many signal processing applications such as channel equalization [1, Ch. 5.4], system identification [2], antenna beamforming [1, Ch. 6.5], and many others. The core idea is to use a linear transformation of the input signal that approximates the desired signal with the smallest average squared error.

Quantification of the number of variables needed to locally explain complex data is often the first step to better understanding it. Existing techniques from intrinsic dimension estimation leverage statistical models to glean this information from samples within a neighborhood. However, existing methods often rely on well-picked hyperparameters and ample data as manifold dimension and curvature increases. Leveraging insight into the fixed point of the score matching objective as the score map is regularized by its Dirichlet energy, we show that it is possible to retrieve the topological dimension of the manifold learned by the score map. We then introduce a novel method to measure the learned manifold's topological dimension (i.e., local intrinsic dimension) using adversarial attacks, thereby generating useful interpretations of the learned manifold.

Prediction of vehicle lane change maneuvers has gained a lot of momentum in the last few years. Some recent works focus on predicting a vehicle's intention by predicting its trajectory first. This is not enough, as it ignores the context of the scene and the state of the surrounding vehicles (as they might be risky to the target vehicle). Other works assessed the risk made by the surrounding vehicles only by considering their existence around the target vehicle, or by considering the distance and relative velocities between them and the target vehicle as two separate numerical features. In this work, we propose a solution that leverages Knowledge Graphs (KGs) to anticipate lane changes based on linguistic contextual information in a way that goes well beyond the capabilities of current perception systems. Our solution takes the Time To Collision (TTC) with surrounding vehicles as input to assess the risk on the target vehicle. Moreover, our KG is trained on the HighD dataset using the TransE model to obtain the Knowledge Graph Embeddings (KGE). Then, we apply Bayesian inference on top of the KG using the embeddings learned during training. Finally, the model can predict lane changes two seconds ahead with 97.95% f1-score, which surpassed the state of the art, and three seconds before changing lanes with 93.60% f1-score.

There is no denying that the use of Information Technology (IT) is undergoing exponential growth in today's world. This digital transformation has also given rise to a multitude of security challenges, notably in the realm of cybercrime. In response to these growing threats, public and private sectors have prioritized the strengthening of IT security measures. In light of the growing security concern, Artificial Intelligence (AI) has gained prominence within the cybersecurity landscape. This paper presents a comprehensive survey of recent advancements in AI-driven threat response systems. To the best of our knowledge, the most recent survey covering the AI reaction domain was conducted in 2017. Since then, considerable literature has been published and therefore it is worth reviewing it. By means of several shared features, each of the studies is compared on a common ground. Through an analysis of the research papers conducted on a standardized basis, this survey aims to unravel the complexities and opportunities of integrating AI into cyber defense. The conclusions drawn from this collective analysis provide a comprehensive snapshot of the evolving landscape at the intersection of AI and cybersecurity. This landscape underscores the growing significance of not only anticipating and detecting threats but also responding to them effectively. Additionally, from these reviews, various research challenges for the future are presented. These challenges serve as a roadmap for researchers and practitioners in the field of AI-integrated reactive strategies.

This paper introduces a modular framework for Mixed-variable and Combinatorial Bayesian Optimization (MCBO) to address the lack of systematic benchmarking and standardized evaluation in the field. Current MCBO papers often introduce non-diverse or non-standard benchmarks to evaluate their methods, impeding the proper assessment of different MCBO primitives and their combinations. Additionally, papers introducing a solution for a single MCBO primitive often omit benchmarking against baselines that utilize the same methods for the remaining primitives [1-4]. This omission is primarily due to the significant implementation overhead involved, resulting in a lack of controlled assessments and an inability to showcase the merits of a contribution effectively. To overcome these challenges, our proposed framework enables an effortless combination of Bayesian Optimization components, and provides a diverse set of synthetic and real-world benchmarking tasks. Leveraging this flexibility, we implement 47 novel MCBO algorithms and benchmark them against seven existing MCBO solvers and five standard black-box optimization algorithms on ten tasks, conducting over 4000 experiments. Our findings reveal a superior combination of MCBO primitives outperforming existing approaches and illustrate the significance of model fit and the use of a trust region.

Autonomous robots used in infrastructure inspection, space exploration and other critical missions operate in highly dynamic environments. As such, they must continually verify their ability to complete the tasks associated with these missions safely and effectively. Here we present a Bayesian learning framework that enables this runtime verification of autonomous robots. The framework uses prior knowledge and observations of the verified robot to learn expected ranges for the occurrence rates of regular and singular (e.g., catastrophic failure) events. Interval continuous-time Markov models defined using these ranges are then analysed to obtain expected intervals of variation for system properties such as mission duration and success probability. We apply the framework to an autonomous robotic mission for underwater infrastructure inspection and repair. The formal proofs and experiments presented in the paper show that our framework produces results that reflect the uncertainty intrinsic to many real-world systems, enabling the robust verification of their quantitative properties under parametric uncertainty.