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Register a new userVerifying Probabilistic Specifications with Functional Lagrangians
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Krishnamurthy Dvijotham
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We propose a general framework for verifying input-output specifications of neural networks using functional Lagrange multipliers that generalizes standard Lagrangian duality. We derive theoretical properties of the framework, which can handle arbitrary probabilistic specifications, showing that it provably leads to tight verification when a sufficiently flexible class of functional multipliers is chosen. With a judicious choice of the class of functional multipliers, the framework can accommodate desired trade-offs between tightness and complexity. We demonstrate empirically that the framework can handle a diverse set of networks, including Bayesian neural networks with Gaussian posterior approximations, MC-dropout networks, and verify specifications on adversarial robustness and out-of-distribution(OOD) detection. Our framework improves upon prior work in some settings and also generalizes to new stochastic networks and probabilistic specifications, like distributionally robust OOD detection.
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We consider the problem of generating randomized control sequences for complex networked systems typically actuated by human agents. Our approach leverages a concept known as control improvisation, which is based on a combination of data-driven learning and controller synthesis from formal specifications. We learn from existing data a generative model (for instance, an explicit-duration hidden Markov model, or EDHMM) and then supervise this model in order to guarantee that the generated sequences satisfy some desirable specifications given in Probabilistic Computation Tree Logic (PCTL). We present an implementation of our approach and apply it to the problem of mimicking the use of lighting appliances in a residential unit, with potential applications to home security and resource management. We present experimental results showing that our approach produces realistic control sequences, similar to recorded data based on human actuation, while satisfying suitable formal requirements.
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Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear dependency. However, it is non-trivial to have an in-principle understanding of these variants due to their inherent restrictive assumption on the data and latent code distributions. Although some works have studied probabilistic interpretation for CCA, these models still require the explicit form of the distributions to achieve a tractable solution for the inference. In this work, we study probabilistic interpretation for CCA based on implicit distributions. We present Conditional Mutual Information (CMI) as a new criterion for CCA to consider both linear and nonlinear dependency for arbitrarily distributed data. To eliminate direct estimation for CMI, in which explicit form of the distributions is still required, we derive an objective which can provide an estimation for CMI with efficient inference methods. To facilitate Bayesian inference of multi-view analysis, we propose Adversarial CCA (ACCA), which achieves consistent encoding for multi-view data with the consistent constraint imposed on the marginalization of the implicit posteriors. Such a model would achieve superiority in the alignment of the multi-view data with implicit distributions. It is interesting to note that most of the existing CCA variants can be connected with our proposed CCA model by assigning specific form for the posterior and likelihood distributions. Extensive experiments on nonlinear correlation analysis and cross-view generation on benchmark and real-world datasets demonstrate the superiority of our model.
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