Stochastic approximation (SA) is a key method used in statistical learning. Recently, its nonasymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased gradient estimates and convex objective function, which significantly limit their applications to sophisticated tasks such as online and reinforcement learning. These restrictions are all essentially relaxed in this work. In particular, we analyze a general SA scheme to minimize a non-convex, smooth objective function. We consider update procedure whose drift term depends on a state-dependent Markov chain and the mean field is not necessarily of gradient type, covering approximate second-order method and allowing asymptotic bias for the one-step updates. We illustrate these settings with the online EM algorithm and the policy-gradient method for average reward maximization in reinforcement learning.

Modeling visual question answering (VQA) through scene graphs can significantly improve the reasoning accuracy and interpretability. However, existing models answer poorly for complex reasoning questions with attributes or relations, which causes false attribute selection or missing relation in Figure 1(a). It is because these models cannot balance all kinds of information in scene graphs, neglecting relation and attribute information. In this paper, we introduce a novel Dual Message-passing enhanced Graph Neural Network (DM-GNN), which can obtain a balanced representation by properly encoding multi-scale scene graph information. Specifically, we (i) transform the scene graph into two graphs with diversified focuses on objects and relations; Then we design a dual structure to encode them, which increases the weights from relations (ii) fuse the encoder output with attribute features, which increases the weights from attributes; (iii) propose a message-passing mechanism to enhance the information transfer between objects, relations and attributes. We conduct extensive experiments on datasets including GQA, VG, motif-VG and achieve new state of the art.

No abstract

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge slowly for medium dimension problems, or when the joint structure of the distributions to sample is complex. We propose a Metropolis-Hastings (MH) algorithm based on a multidimensional Gaussian proposal that takes into account the joint conditional distribution of the random effects and does not require any tuning, in contrast with more sophisticated samplers such as the Metropolis Adjusted Langevin Algorithm or the No-U-Turn Sampler that involve costly tuning runs or intensive computation. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the original model. We show that such approximation is equivalent to linearizing the model in the case of continuous data. Numerical experiments based on real data highlight the very good performances of the proposed method for continuous data model.

Variational inference and MCMC methods have been two popular methods in order to sample from a posterior distribution. Whereas the former extends the computation feasibility to higher dimension, the latter takes advantage of nice convergence properties to the exact posterior distribution. In this work we'll draw the parallel between a famous MCMC scheme called the Independent Metropolis Hastings and Variational inference. We'll explain our work on both Linear and Non-linear Gaussian cases. In the non linear case, a new proposal will be introduced motivated by a faster convergence of the Markov chain.