Due to privacy or commercial constraints, large pre-trained language models (PLMs) are often offered as black-box APIs. Fine-tuning such models to downstream tasks is challenging because one can neither access the model's internal representations nor propagate gradients through it. This paper addresses these challenges by developing techniques for adapting PLMs with only API access. Building on recent work on soft prompt tuning, we develop methods to tune the soft prompts without requiring gradient computation. Further, we develop extensions that in addition to not requiring gradients also do not need to access any internal representation of the PLM beyond the input embeddings. Moreover, instead of learning a single prompt, our methods learn a distribution over prompts allowing us to quantify predictive uncertainty. Ours is the first work to consider uncertainty in prompts when only having API access to the PLM. Finally, through extensive experiments, we carefully vet the proposed methods and find them competitive with (and sometimes even improving on) gradient-based approaches with full access to the PLM.

The problem of testing the equality of the generating processes of two categorical time series is addressed in this work. To this aim, we propose three tests relying on a dissimilarity measure between categorical processes. Particular versions of these tests are constructed by considering three specific distances evaluating discrepancy between the marginal distributions and the serial dependence patterns of both processes. Proper estimates of these dissimilarities are an essential element of the constructed tests, which are based on the bootstrap. Specifically, a parametric bootstrap method assuming the true generating models and extensions of the moving blocks bootstrap and the stationary bootstrap are considered. The approaches are assessed in a broad simulation study including several types of categorical models with different degrees of complexity. Advantages and disadvantages of each one of the methods are properly discussed according to their behavior under the null and the alternative hypothesis. The impact that some important input parameters have on the results of the tests is also analyzed. An application involving biological sequences highlights the usefulness of the proposed techniques.

Among generalized additive models, additive Mat\'ern Gaussian Processes (GPs) are one of the most popular for scalable high-dimensional problems. Thanks to their additive structure and stochastic differential equation representation, back-fitting-based algorithms can reduce the time complexity of computing the posterior mean from $O(n^3)$ to $O(n\log n)$ time where $n$ is the data size. However, generalizing these algorithms to efficiently compute the posterior variance and maximum log-likelihood remains an open problem. In this study, we demonstrate that for Additive Mat\'ern GPs, not only the posterior mean, but also the posterior variance, log-likelihood, and gradient of these three functions can be represented by formulas involving only sparse matrices and sparse vectors. We show how to use these sparse formulas to generalize back-fitting-based algorithms to efficiently compute the posterior mean, posterior variance, log-likelihood, and gradient of these three functions for additive GPs, all in $O(n \log n)$ time. We apply our algorithms to Bayesian optimization and propose efficient algorithms for posterior updates, hyperparameters learning, and computations of the acquisition function and its gradient in Bayesian optimization. Given the posterior, our algorithms significantly reduce the time complexity of computing the acquisition function and its gradient from $O(n^2)$ to $O(\log n)$ for general learning rate, and even to $O(1)$ for small learning rate.

Bayesian inference is a ubiquitous and flexible tool for updating a belief (i.e., learning) about a quantity of interest when data are observed, which ultimately can be used to inform downstream decision-making. In particular, Bayesian inverse problems allow one to derive knowledge from data through the lens of physicsbased models. These problems can be formulated as follows: given observational data, a physics-based model, and prior information about the model inputs, find a posterior probability distribution for the inputs that reflects the knowledge about the inputs in terms of the observed data and prior. Typically, the physicsbased models are given in the form of an input-to-observation map that is based on a system of partial differential equations (PDEs). The computational task underlying Bayesian inference is approximating posterior probability distributions to compute expectations and to quantify uncertainties. There are multiple ways of computationally exploring posterior distributions to gain insights, reaching from Markov chain Monte Carlo to variational methods [24, 42, 28]. In this work, we make use of Stein variational gradient descent (SVGD) [32], which is a method for particle-based variational inference, to approximate posterior distributions. It builds on Stein's identity to formulate an update step for the particles that can be realized numerically in an efficient manner via

Providing guarantees on the safe operation of robots against edge cases is challenging as testing methods such as traditional Monte-Carlo require too many samples to provide reasonable statistics. Built upon recent advancements in rare-event sampling, we present a model-based method to verify if a robotic system satisfies a Signal Temporal Logic (STL) specification in the face of environment variations and sensor/actuator noises. Our method is efficient and applicable to both linear and nonlinear and even black-box systems with arbitrary, but known, uncertainty distributions. For linear systems with Gaussian uncertainties, we exploit a feature to find optimal parameters that minimize the probability of failure. We demonstrate illustrative examples on applying our approach to real-world autonomous robotic systems.

Simulation-based falsification is a practical testing method to increase confidence that the system will meet safety requirements. Because full-fidelity simulations can be computationally demanding, we investigate the use of simulators with different levels of fidelity. As a first step, we express the overall safety specification in terms of environmental parameters and structure this safety specification as an optimization problem. We propose a multi-fidelity falsification framework using Bayesian optimization, which is able to determine at which level of fidelity we should conduct a safety evaluation in addition to finding possible instances from the environment that cause the system to fail. This method allows us to automatically switch between inexpensive, inaccurate information from a low-fidelity simulator and expensive, accurate information from a high-fidelity simulator in a cost-effective way. Our experiments on various environments in simulation demonstrate that multi-fidelity Bayesian optimization has falsification performance comparable to single-fidelity Bayesian optimization but with much lower cost.

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of conditional reasoning: (i) a logic C of inference from certain premises; and (ii) a logic U of inference from uncertain premises. But whereas C is monotonic for the conditional, U is not, and whereas C obeys Modus Ponens, U does not without restrictions. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and we use the distinction between the two systems to cast light, in particular, on McGee's puzzle about Modus Ponens. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences.

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. This tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

This work studies the problem of ad hoc teamwork in teams composed of agents with differing computational capabilities. We consider cooperative multi-player games in which each agent's policy is constrained by a private capability parameter, and agents with higher capabilities are able to simulate the behavior of agents with lower capabilities (but not vice-versa). To address this challenge, we propose an algorithm that maintains a belief over the other agents' capabilities and incorporates this belief into the planning process. Our primary innovation is a novel framework based on capability type structures, which ensures that the belief updates remain consistent and informative without constructing the infinite hierarchy of beliefs. We also extend our techniques to settings where the agents' observations are subject to noise. We provide examples of games in which deviations in capability between oblivious agents can lead to arbitrarily poor outcomes, and experimentally validate that our capability-aware algorithm avoids the anti-cooperative behavior of the naive approach in these toy settings as well as a more complex cooperative checkers environment.

Vehicle detection in real-time scenarios is challenging because of the time constraints and the presence of multiple types of vehicles with different speeds, shapes, structures, etc. This paper presents a new method relied on generating a confidence map-for robust and faster vehicle detection. To reduce the adverse effect of different speeds, shapes, structures, and the presence of several vehicles in a single image, we introduce the concept of augmentation which highlights the region of interest containing the vehicles. The augmented map is generated by exploring the combination of multiresolution analysis and maximally stable extremal regions (MR-MSER). The output of MR-MSER is supplied to fast CNN to generate a confidence map, which results in candidate regions. Furthermore, unlike existing models that implement complicated models for vehicle detection, we explore the combination of a rough set and fuzzy-based models for robust vehicle detection. To show the effectiveness of the proposed method, we conduct experiments on our dataset captured by drones and on several vehicle detection benchmark datasets, namely, KITTI and UA-DETRAC. The results on our dataset and the benchmark datasets show that the proposed method outperforms the existing methods in terms of time efficiency and achieves a good detection rate.