We consider the structured-output prediction problem through probabilistic approaches and generalize the "perturb-and-MAP" framework to more challenging weighted Hamming losses, which are crucial in applications. While in principle our approach is a straightforward marginalization, it requires solving many related MAP inference problems. We show that for log-supermodular pairwise models these operations can be performed efficiently using the machinery of dynamic graph cuts. We also propose to use double stochastic gradient descent, both on the data and on the perturbations, for efficient learning. Our framework can naturally take weak supervision (e.g., partial labels) into account. We conduct a set of experiments on medium-scale character recognition and image segmentation, showing the benefits of our algorithms.

State-space models (SSMs) provide a flexible framework for modelling time-series data. Consequently, SSMs are ubiquitously applied in areas such as engineering, econometrics and epidemiology. In this paper we provide a fast approach for approximate Bayesian inference in SSMs using the tools of deep learning and variational inference.

Today we are going to implement a Bayesian linear regression in R from scratch and use it to forecast US GDP growth. This post is based on a very informative manual from the Bank of England on Applied Bayesian Econometrics. I have translated the original Matlab code into R since its open source and widely used in data analysis/science. My main goal in this post is to try and give people a better understanding of Bayesian statistics, some of it's advantages and also some scenarios where you might want to use it. Let's take a moment to think about why we would we even want to use Bayesian techniques in the first place.

A GPS-denied UAV (Agent B) is localised through INS alignment with the aid of a nearby GPS-equipped UAV (Agent A), which broadcasts its position at several time instants. Agent B measures the signals' direction of arrival with respect to Agent B's inertial navigation frame. Semidefinite programming and the Orthogonal Procrustes algorithm are employed, and accuracy is improved through maximum likelihood estimation. The method is validated using flight data and simulations. A three-agent extension is explored.

Although Neural Machine Translation (NMT) models have advanced state-of-the-art performance in machine translation, they face problems like the inadequate translation. We attribute this to that the standard Maximum Likelihood Estimation (MLE) cannot judge the real translation quality due to its several limitations. In this work, we propose an adequacy-oriented learning mechanism for NMT by casting translation as a stochastic policy in Reinforcement Learning (RL), where the reward is estimated by explicitly measuring translation adequacy. Benefiting from the sequence-level training of RL strategy and a more accurate reward designed specifically for translation, our model outperforms multiple strong baselines, including (1) standard and coverage-augmented attention models with MLE-based training, and (2) advanced reinforcement and adversarial training strategies with rewards based on both word-level BLEU and character-level chrF3. Quantitative and qualitative analyses on different language pairs and NMT architectures demonstrate the effectiveness and universality of the proposed approach.

In real-world recognition/classification tasks, limited by various objective factors, it is usually difficult to collect training samples to exhaust all classes when training a recognizer or classifier. A more realistic scenario is open set recognition (OSR), where incomplete knowledge of the world exists at training time, and unknown classes can be submitted to an algorithm during testing, requiring the classifiers not only to accurately classify the seen classes, but also to effectively deal with the unseen ones. This paper provides a comprehensive survey of existing open set recognition techniques covering various aspects ranging from related definitions, representations of models, datasets, experiment setup and evaluation metrics. Furthermore, we briefly analyze the relationships between OSR and its related tasks including zero-shot, one-shot (few-shot) recognition/learning techniques, classification with reject option, and so forth. Additionally, we also overview the open world recognition which can be seen as a natural extension of OSR. Importantly, we highlight the limitations of existing approaches and point out some promising subsequent research directions in this field.

Population attributes are essential in health for understanding who the data represents and precision medicine efforts. Even within disease infection labels, patients can exhibit significant variability; "fever" may mean something different when reported in a doctor's office versus from an online app, precluding directly learning across different datasets for the same prediction task. This problem falls into the domain adaptation paradigm. However, research in this area has to-date not considered who generates the data; symptoms reported by a woman versus a man, for example, could also have different implications. We propose a novel population-aware domain adaptation approach by formulating the domain adaptation task as a multi-source hierarchical Bayesian framework. The model improves prediction in the case of largely unlabelled target data by harnessing both domain and population invariant information.

Variational dropout (VD) is a generalization of Gaussian dropout, which aims at inferring the posterior of network weights based on a log-uniform prior on them to learn these weights as well as dropout rate simultaneously. The log-uniform prior not only interprets the regularization capacity of Gaussian dropout in network training, but also underpins the inference of such posterior. However, the log-uniform prior is an improper prior (i.e., its integral is infinite) which causes the inference of posterior to be ill-posed, thus restricting the regularization performance of VD. To address this problem, we present a new generalization of Gaussian dropout, termed variational Bayesian dropout (VBD), which turns to exploit a hierarchical prior on the network weights and infer a new joint posterior. Specifically, we implement the hierarchical prior as a zero-mean Gaussian distribution with variance sampled from a uniform hyper-prior. Then, we incorporate such a prior into inferring the joint posterior over network weights and the variance in the hierarchical prior, with which both the network training and the dropout rate estimation can be cast into a joint optimization problem. More importantly, the hierarchical prior is a proper prior which enables the inference of posterior to be well-posed. In addition, we further show that the proposed VBD can be seamlessly applied to network compression. Experiments on both classification and network compression tasks demonstrate the superior performance of the proposed VBD in terms of regularizing network training.

We propose a directed acyclic hypergraph framework for a probabilistic graphical model that we call Bayesian hypergraphs. The space of directed acyclic hypergraphs is much larger than the space of chain graphs. Hence Bayesian hypergraphs can model much finer factorizations than Bayesian networks or LWF chain graphs and provide simpler and more computationally efficient procedures for factorizations and interventions. Bayesian hypergraphs also allow a modeler to represent causal patterns of interaction such as Noisy-OR graphically (without additional annotations). We introduce global, local and pairwise Markov properties of Bayesian hypergraphs and prove under which conditions they are equivalent. We define a projection operator, called shadow, that maps Bayesian hypergraphs to chain graphs, and show that the Markov properties of a Bayesian hypergraph are equivalent to those of its corresponding chain graph. We extend the causal interpretation of LWF chain graphs to Bayesian hypergraphs and provide corresponding formulas and a graphical criterion for intervention.

Learning classifier systems are adaptive learning systems which have been widely applied in a multitude of application domains. However, there are still some generalization problems unsolved. The hurdle is that fitness and niching pressures are difficult to balance. Here, a new algorithm called Self Organizing Classifiers is proposed which faces this problem from a different perspective. Instead of balancing the pressures, both pressures are separated and no balance is necessary. In fact, the proposed algorithm possesses a dynamical population structure that self-organizes itself to better project the input space into a map. The niched fitness concept is defined along with its dynamical population structure, both are indispensable for the understanding of the proposed method. Promising results are shown on two continuous multi-step problems. One of which is yet more challenging than previous problems of this class in the literature.