Multi-label classification is the task of assigning a subset of labels to a given query instance. For evaluating such predictions, the set of predicted labels needs to be compared to the ground-truth label set associated with that instance, and various loss functions have been proposed for this purpose. In addition to assessing predictive accuracy, a key concern in this regard is to foster and to analyze a learner's ability to capture label dependencies. In this paper, we introduce a new class of loss functions for multi-label classification, which overcome disadvantages of commonly used losses such as Hamming and subset 0/1. To this end, we leverage the mathematical framework of non-additive measures and integrals. Roughly speaking, a non-additive measure allows for modeling the importance of correct predictions of label subsets (instead of single labels), and thereby their impact on the overall evaluation, in a flexible way - by giving full importance to single labels and the entire label set, respectively, Hamming and subset 0/1 are rather extreme in this regard. We present concrete instantiations of this class, which comprise Hamming and subset 0/1 as special cases, and which appear to be especially appealing from a modeling perspective. The assessment of multi-label classifiers in terms of these losses is illustrated in an empirical study.

The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the possible times. As a result, maximum likelihood estimation is expensive. We show how to instead apply a version of noise-contrastive estimation---a general parameter estimation method with a less expensive stochastic objective. Our specific instantiation of this general idea works out in an interestingly non-trivial way and has provable guarantees for its optimality, consistency and efficiency. On several synthetic and real-world datasets, our method shows benefits: for the model to achieve the same level of log-likelihood on held-out data, our method needs considerably fewer function evaluations and less wall-clock time.

The neural attention mechanism plays an important role in many natural language processing applications. In particular, the use of multi-head attention extends single-head attention by allowing a model to jointly attend information from different perspectives. Without explicit constraining, however, multi-head attention may suffer from attention collapse, an issue that makes different heads extract similar attentive features, thus limiting the model's representation power. In this paper, for the first time, we provide a novel understanding of multi-head attention from a Bayesian perspective. Based on the recently developed particle-optimization sampling techniques, we propose a non-parametric approach that explicitly improves the repulsiveness in multi-head attention and consequently strengthens model's expressiveness. Remarkably, our Bayesian interpretation provides theoretical inspirations on the not-well-understood questions: why and how one uses multi-head attention. Extensive experiments on various attention models and applications demonstrate that the proposed repulsive attention can improve the learned feature diversity, leading to more informative representations with consistent performance improvement on various tasks.

Block modeling is widely used in studies on complex networks. The cornerstone model is the stochastic block model (SBM), widely used over the past decades. However, the SBM is limited in analyzing complex networks as the model is, in essence, a random graph model that cannot reproduce the basic properties of many complex networks, such as sparsity and heavy-tailed degree distribution. In this paper, we provide an edge exchangeable block model that incorporates such basic features and simultaneously infers the latent block structure of a given complex network. Our model is a Bayesian nonparametric model that flexibly estimates the number of blocks and takes into account the possibility of unseen nodes. Using one synthetic dataset and one real-world stock ownership dataset, we show that our model outperforms state-of-the-art SBMs for held-out link prediction tasks.

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space.

Inter-domain Gaussian processes (GPs) allow for high flexibility and low computational cost when performing approximate inference in GP models. They are particularly suitable for modeling data exhibiting global structure but are limited to stationary covariance functions and thus fail to model non-stationary data effectively. We propose Inter-domain Deep Gaussian Processes, an extension of inter-domain shallow GPs that combines the advantages of inter-domain and deep Gaussian processes (DGPs), and demonstrate how to leverage existing approximate inference methods to perform simple and scalable approximate inference using inter-domain features in DGPs. We assess the performance of our method on a range of regression tasks and demonstrate that it outperforms inter-domain shallow GPs and conventional DGPs on challenging large-scale real-world datasets exhibiting both global structure as well as a high-degree of non-stationarity.

Savage (1972) lays down the foundation of Bayesian decision theory, but asserts that it is not applicable in big worlds where the environment is complex. Using the theory of finite automaton to model belief formation, this paper studies the characteristics of optimal learning behavior in small and big worlds, where the complexity of the environment is low and high, respectively, relative to the cognitive ability of the decision maker. Confirming Savage's claim, optimal learning behavior is closed to Bayesian in small worlds but significantly different in big worlds. In addition, I show that in big worlds, the optimal learning behavior could exhibit a wide range of well-documented non-Bayesian learning behavior, including the use of heuristic, correlation neglect, persistent over-confidence, inattentive learning, and other behaviors of model simplification or misspecification. These results establish a clear and testable relationship between the prominence of non-Bayesian learning behavior, complexity and cognitive ability.

This paper studies the source (event) localization problem in decentralized wireless sensor networks (WSNs) under the fault model without knowing the sensor parameters. Event localizations have many applications such as localizing intruders, Wifi hotspots and users, and faults in power systems. Previous studies assume the true knowledge (or good estimates) of sensor parameters (e.g., fault model probability or Region of Influence (ROI) of the source) for source localization. However, we propose two methods to estimate the source location in this paper under the fault model: hitting set approach and feature selection method, which only utilize the noisy data set at the fusion center for estimation of the source location without knowing the sensor parameters. The proposed methods have been shown to localize the source effectively. We also study the lower bound on the sample complexity requirement for hitting set method. These methods have also been extended for multiple sources localizations. In addition, we modify the proposed feature selection approach to use maximum likelihood. Finally, extensive simulations are carried out for different settings (i.e., the number of sensor nodes and sample complexity) to validate our proposed methods in comparison to centroid, maximum likelihood, FTML, SNAP estimators.

In this paper, we propose and prove the theorem regarding the stability of attributes in a decision system. Based on the theorem, we propose the LRA framework for accelerating rough set algorithms. It is a general-purpose framework which can be applied to almost all rough set methods significantly . Theoretical analysis guarantees high efficiency. Note that the enhancement of efficiency will not lead to any decrease of the classification accuracy. Besides, we provide a simpler prove for the positive approximation acceleration framework.

In recent years, bankruptcy forecasting has gained lot of attention from researchers as well as practitioners in the field of financial risk management. For bankruptcy prediction, various approaches proposed in the past and currently in practice relies on accounting ratios and using statistical modeling or machine learning methods. These models have had varying degrees of successes. Models such as Linear Discriminant Analysis or Artificial Neural Network employ discriminative classification techniques. They lack explicit provision to include prior expert knowledge. In this paper, we propose another route of generative modeling using Expert Bayesian framework. The biggest advantage of the proposed framework is an explicit inclusion of expert judgment in the modeling process. Also the proposed methodology provides a way to quantify uncertainty in prediction. As a result the model built using Bayesian framework is highly flexible, interpretable and intuitive in nature. The proposed approach is well suited for highly regulated or safety critical applications such as in finance or in medical diagnosis. In such cases accuracy in the prediction is not the only concern for decision makers. Decision makers and other stakeholders are also interested in uncertainty in the prediction as well as interpretability of the model. We empirically demonstrate these benefits of proposed framework on real world dataset using Stan, a probabilistic programming language. We found that the proposed model is either comparable or superior to the other existing methods. Also resulting model has much less False Positive Rate compared to many existing state of the art methods. The corresponding R code for the experiments is available at Github repository.