Probabilistic Numerics and Uncertainty in Computations

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data has led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimisers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl

Learning and Reasoning for Robot Sequential Decision Making under Uncertainty

Robots frequently face complex tasks that require more than one action, where sequential decision-making (SDM) capabilities become necessary. The key contribution of this work is a robot SDM framework, called LCORPP, that supports the simultaneous capabilities of supervised learning for passive state estimation, automated reasoning with declarative human knowledge, and planning under uncertainty toward achieving long-term goals. In particular, we use a hybrid reasoning paradigm to refine the state estimator, and provide informative priors for the probabilistic planner. In experiments, a mobile robot is tasked with estimating human intentions using their motion trajectories, declarative contextual knowledge, and human-robot interaction (dialog-based and motion-based). Results suggest that, in efficiency and accuracy, our framework performs better than its no-learning and no-reasoning counterparts in office environment.Comment: In proceedings of 34th AAAI conference on Artificial Intelligence, 202

Interpretable Probabilistic Password Strength Meters via Deep Learning

Probabilistic password strength meters have been proved to be the most accurate tools to measure password strength. Unfortunately, by construction, they are limited to solely produce an opaque security estimation that fails to fully support the user during the password composition. In the present work, we move the first steps towards cracking the intelligibility barrier of this compelling class of meters. We show that probabilistic password meters inherently own the capability of describing the latent relation occurring between password strength and password structure. In our approach, the security contribution of each character composing a password is disentangled and used to provide explicit fine-grained feedback for the user. Furthermore, unlike existing heuristic constructions, our method is free from any human bias, and, more importantly, its feedback has a clear probabilistic interpretation. In our contribution: (1) we formulate the theoretical foundations of interpretable probabilistic password strength meters; (2) we describe how they can be implemented via an efficient and lightweight deep learning framework suitable for client-side operability.Comment: An abridged version of this paper appears in the proceedings of the 25th European Symposium on Research in Computer Security (ESORICS) 202

Committee-Based Sample Selection for Probabilistic Classifiers

In many real-world learning tasks, it is expensive to acquire a sufficient number of labeled examples for training. This paper investigates methods for reducing annotation cost by `sample selection'. In this approach, during training the learning program examines many unlabeled examples and selects for labeling only those that are most informative at each stage. This avoids redundantly labeling examples that contribute little new information. Our work follows on previous research on Query By Committee, extending the committee-based paradigm to the context of probabilistic classification. We describe a family of empirical methods for committee-based sample selection in probabilistic classification models, which evaluate the informativeness of an example by measuring the degree of disagreement between several model variants. These variants (the committee) are drawn randomly from a probability distribution conditioned by the training set labeled so far. The method was applied to the real-world natural language processing task of stochastic part-of-speech tagging. We find that all variants of the method achieve a significant reduction in annotation cost, although their computational efficiency differs. In particular, the simplest variant, a two member committee with no parameters to tune, gives excellent results. We also show that sample selection yields a significant reduction in the size of the model used by the tagger