Variance Computation for Weighted Model Counting with Knowledge Compilation Approach

One of the most important queries in knowledge compilation is weighted model counting (WMC), which has been applied to probabilistic inference on various models, such as Bayesian networks. In practical situations on inference tasks, the model's parameters have uncertainty because they are often learned from data, and thus we want to compute the degree of uncertainty in the inference outcome. One possible approach is to regard the inference outcome as a random variable by introducing distributions for the parameters and evaluate the variance of the outcome. Unfortunately, the tractability of computing such a variance is hardly known. Motivated by this, we consider the problem of computing the variance of WMC and investigate this problem's tractability. First, we derive a polynomial time algorithm to evaluate the WMC variance when the input is given as a structured d-DNNF. Second, we prove the hardness of this problem for structured DNNFs, d-DNNFs, and FBDDs, which is intriguing because the latter two allow polynomial time WMC algorithms. Finally, we show an application that measures the uncertainty in the inference of Bayesian networks. We empirically show that our algorithm can evaluate the variance of the marginal probability on real-world Bayesian networks and analyze the impact of the variances of parameters on the variance of the marginal.

A Japanese-Chinese Parallel Corpus Using Crowdsourcing for Web Mining

Using crowdsourcing, we collected more than 10,000 URL pairs (parallel top page pairs) of bilingual websites that contain parallel documents and created a Japanese-Chinese parallel corpus of 4.6M sentence pairs from these websites. We used a Japanese-Chinese bilingual dictionary of 160K word pairs for document and sentence alignment. We then used high-quality 1.2M Japanese-Chinese sentence pairs to train a parallel corpus filter based on statistical language models and word translation probabilities. We compared the translation accuracy of the model trained on these 4.6M sentence pairs with that of the model trained on Japanese-Chinese sentence pairs from CCMatrix (12.4M), a parallel corpus from global web mining. Although our corpus is only one-third the size of CCMatrix, we found that the accuracy of the two models was comparable and confirmed that it is feasible to use crowdsourcing for web mining of parallel data.

Generalization Analysis on Learning with a Concurrent Verifier

Machine learning technologies have been used in a wide range of practical systems. In practical situations, it is natural to expect the input-output pairs of a machine learning model to satisfy some requirements. However, it is difficult to obtain a model that satisfies requirements by just learning from examples. A simple solution is to add a module that checks whether the input-output pairs meet the requirements and then modifies the model's outputs. Such a module, which we call a {\em concurrent verifier} (CV), can give a certification, although how the generalizability of the machine learning model changes using a CV is unclear. This paper gives a generalization analysis of learning with a CV. We analyze how the learnability of a machine learning model changes with a CV and show a condition where we can obtain a guaranteed hypothesis using a verifier only in the inference time. We also show that typical error bounds based on Rademacher complexity will be no larger than that of the original model when using a CV in multi-class classification and structured prediction settings.