"AI systems–like people–must often act despite partial and uncertain information. First, the information received may be unreliable (e.g., a patient may mis-remember when a disease started, or may not have noticed a symptom that is important to a diagnosis). In addition, rules connecting real-world events can never include all the factors that might determine whether their conclusions really apply (e.g., the correctness of basing a diagnosis on a lab test depends whether there were conditions that might have caused a false positive, on the test being done correctly, on the results being associated with the right patient, etc.) Thus in order to draw useful conclusions, AI systems must be able to reason about the probability of events, given their current knowledge." – from David Leake, Reasoning Under Uncertainty
In this work, we treat variational flows as dynamical systems, and leverage shadowing theory to elucidate this behavior via theoretical guarantees on the error of sampling, density evaluation, and ELBO estimation.
Machine learning tools often rely on embedding text as vectors of real numbers. In this paper, we study how the semantic structure of language is encoded in the algebraic structure of such embeddings.
In addition to being a challenging problem due to the super-exponentially large search space, learning a single DAG structure from data may also lead to confident but incorrect predictions (Madigan et al.,