The sample complexity of learning fixed-structure bayesian networks

Abstract. We consider the problem of PAC learning probabilistic networks in the case where the structure of the net is specified beforehand. We allow the conditional probabilities to be represented in any manner (as tables or specialized functions) and obtain sample complexity bounds for learning nets with and without hidden nodes

Empirical Risk Minimization with Approximations of Probabilistic Grammars

Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of the parameters of a fixed probabilistic grammar using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting.

Robust Learning of Fixed-Structure Bayesian Networks

We investigate the problem of learning Bayesian networks in a robust model where an $\epsilon$-fraction of the samples are adversarially corrupted. In this work, we study the fully observable discrete case where the structure of the network is given. Even in this basic setting, previous learning algorithms either run in exponential time or lose dimension-dependent factors in their error guarantees. We provide the first computationally efficient robust learning algorithm for this problem with dimension-independent error guarantees. Our algorithm has near-optimal sample complexity, runs in polynomial time, and achieves error that scales nearly-linearly with the fraction of adversarially corrupted samples. Finally, we show on both synthetic and semi-synthetic data that our algorithm performs well in practice

Towards Probabilistic Estimation of Quality of Online Services

Accurate estimation of quality of online services is both an important and difficult problem, since a service has many interdependent quality attributes influenced by several contextual factors. It is even more challenging as quality ratings come from sources with unknown reliability, each source may rate a service on different quality aspects. Although several solutions have been proposed, there is little work addressing all these issues thoroughly. In this paper, we show that domain knowledge on service structure and related constraints, such as causal dependencies among quality attributes and contextual factors, while widely available, can be exploited to effectively address the above issues in a theoretically-sound framework. Theoretical analysis shows that computational cost of the approach is acceptable, and accurate evaluation of service quality requires a reasonable number of user feedback, provided services have a small number of quality attributes and contextual factors

Probabilistic Estimation Quality Ratings of Online Services

Accurate estimation of quality of online services is both an important and difficult problem, since a service has many interdependent quality attributes influenced by several contextual factors. It is even more challenging as quality ratings come from sources with unknown reliability, each source may rate a service on different quality aspects. Although several solutions have been proposed, there is little work addressing all these issues thoroughly. In this paper, we show that domain knowledge on service structure and related constraints, such as causal dependencies among quality attributes and contextual factors, while widely available, can be exploited to effectively address the above issues in a theoretically-sound framework. Theoretical analysis shows that computational cost of the approach is acceptable, and accurate evaluation of service quality requires a reasonable number of user feedback, provided services have a small number of quality attributes and contextual factors