Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens of dual-graph regularization, which has significantly improved the performance of multidisciplinary machine learning tasks such as recommendation systems, genotype imputation and image inpainting. While the dual-graph regularization contributes a major part of the success, computational costly hyper-parameter tunning is usually involved. To circumvent such a drawback and improve the completion performance, we propose a novel Bayesian learning algorithm that automatically learns the hyper-parameters associated with dual-graph regularization, and at the same time, guarantees the low-rankness of matrix completion. Notably, a novel prior is devised to promote the low-rankness of the matrix and encode the dual-graph information simultaneously, which is more challenging than the single-graph counterpart. A nontrivial conditional conjugacy between the proposed priors and likelihood function is then explored such that an efficient algorithm is derived under variational inference framework. Extensive experiments using synthetic and real-world datasets demonstrate the state-of-the-art performance of the proposed learning algorithm for various data analysis tasks.

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than Variational Inference, and it does not rely on adversarial training (or density ratio estimation). We adopt the recent approach of constructing two models: (1) a primary model, tasked with performing regression or classification; and (2) a secondary, expressive (e.g. implicit) model that defines an approximate posterior distribution over the parameters of the primary model. However, we optimise the parameters of the posterior model via gradient descent according to a Monte Carlo estimate of the posterior predictive distribution -- which is our only approximation (other than the posterior model). Only a likelihood needs to be specified, which can take various forms such as loss functions and synthetic likelihoods, thus providing a form of a likelihood-free approach. Furthermore, we formulate the approach such that the posterior samples can either be independent of, or conditionally dependent upon the inputs to the primary model. The latter approach is shown to be capable of increasing the apparent complexity of the primary model. We see this being useful in applications such as surrogate and physics-based models. To promote how the Bayesian paradigm offers more than just uncertainty quantification, we demonstrate: uncertainty quantification, multi-modality, as well as an application with a recent deep forecasting neural network architecture.

ProBoost, a new boosting algorithm for probabilistic classifiers, is proposed in this work. This algorithm uses the epistemic uncertainty of each training sample to determine the most challenging/uncertain ones; the relevance of these samples is then increased for the next weak learner, producing a sequence that progressively focuses on the samples found to have the highest uncertainty. In the end, the weak learners' outputs are combined into a weighted ensemble of classifiers. Three methods are proposed to manipulate the training set: undersampling, oversampling, and weighting the training samples according to the uncertainty estimated by the weak learners. Furthermore, two approaches are studied regarding the ensemble combination. The weak learner herein considered is a standard convolutional neural network, and the probabilistic models underlying the uncertainty estimation use either variational inference or Monte Carlo dropout. The experimental evaluation carried out on MNIST benchmark datasets shows that ProBoost yields a significant performance improvement. The results are further highlighted by assessing the relative achievable improvement, a metric proposed in this work, which shows that a model with only four weak learners leads to an improvement exceeding 12% in this metric (for either accuracy, sensitivity, or specificity), in comparison to the model learned without ProBoost.

Deception is prevalent in human social settings. However, studies into the effect of deception on reinforcement learning algorithms have been limited to simplistic settings, restricting their applicability to complex real-world problems. This paper addresses this by introducing a new mixed competitive-cooperative multi-agent reinforcement learning (MARL) environment inspired by popular role-based deception games such as Werewolf, Avalon, and Among Us. The environment's unique challenge lies in the necessity to cooperate with other agents despite not knowing if they are friend or foe. Furthermore, we introduce a model of deception, which we call Bayesian belief manipulation (BBM) and demonstrate its effectiveness at deceiving other agents in this environment while also increasing the deceiving agent's performance.

Top-k error has become a popular metric for large-scale classification benchmarks due to the inevitable semantic ambiguity among classes. Existing literature on top-k optimization generally focuses on the optimization method of the top-k objective, while ignoring the limitations of the metric itself. In this paper, we point out that the top-k objective lacks enough discrimination such that the induced predictions may give a totally irrelevant label a top rank. To fix this issue, we develop a novel metric named partial Area Under the top-k Curve (AUTKC). Theoretical analysis shows that AUTKC has a better discrimination ability, and its Bayes optimal score function could give a correct top-K ranking with respect to the conditional probability. This shows that AUTKC does not allow irrelevant labels to appear in the top list. Furthermore, we present an empirical surrogate risk minimization framework to optimize the proposed metric. Theoretically, we present (1) a sufficient condition for Fisher consistency of the Bayes optimal score function; (2) a generalization upper bound which is insensitive to the number of classes under a simple hyperparameter setting. Finally, the experimental results on four benchmark datasets validate the effectiveness of our proposed framework.

While digging in the details of classical classification methods, I found sparse information about the similarities and differences of Gaussian Naive Bayes (GNB), Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA). This post centralises the information I found for the next learner. Summary: All three methods are a specific instance of The Bayes Classifier, they all deal with continuous Gaussian predictors, they differ in the assumptions they makes about the relationships amongst predictors, and across classes (i.e. the way they specify the covariance matrices). We have a set X of p predictors, and a discrete response variable Y (the class) taking values k {1, …, K}, for a sample of n observations. We encounter a new observation for which we know the values of the predictors X, but not the class Y, so we would like to make a guess about Y based on the information we have (our sample).

In the context of modern environmental and societal concerns, there is an increasing demand for methods able to identify management strategies for civil engineering systems, minimizing structural failure risks while optimally planning inspection and maintenance (I&M) processes. Most available methods simplify the I&M decision problem to the component level due to the computational complexity associated with global optimization methodologies under joint system-level state descriptions. In this paper, we propose an efficient algorithmic framework for inference and decision-making under uncertainty for engineering systems exposed to deteriorating environments, providing optimal management strategies directly at the system level. In our approach, the decision problem is formulated as a factored partially observable Markov decision process, whose dynamics are encoded in Bayesian network conditional structures. The methodology can handle environments under equal or general, unequal deterioration correlations among components, through Gaussian hierarchical structures and dynamic Bayesian networks. In terms of policy optimization, we adopt a deep decentralized multi-agent actor-critic (DDMAC) reinforcement learning approach, in which the policies are approximated by actor neural networks guided by a critic network. By including deterioration dependence in the simulated environment, and by formulating the cost model at the system level, DDMAC policies intrinsically consider the underlying system-effects. This is demonstrated through numerical experiments conducted for both a 9-out-of-10 system and a steel frame under fatigue deterioration. Results demonstrate that DDMAC policies offer substantial benefits when compared to state-of-the-art heuristic approaches. The inherent consideration of system-effects by DDMAC strategies is also interpreted based on the learned policies.

Surprising events trigger measurable brain activity and influence human behavior by affecting learning, memory, and decision-making. Currently there is, however, no consensus on the definition of surprise. Here we identify 18 mathematical definitions of surprise in a unifying framework. We first propose a technical classification of these definitions into three groups based on their dependence on an agent's belief, show how they relate to each other, and prove under what conditions they are indistinguishable. Going beyond this technical analysis, we propose a taxonomy of surprise definitions and classify them into four conceptual categories based on the quantity they measure: (i) 'prediction surprise' measures a mismatch between a prediction and an observation; (ii) 'change-point detection surprise' measures the probability of a change in the environment; (iii) 'confidence-corrected surprise' explicitly accounts for the effect of confidence; and (iv) 'information gain surprise' measures the belief-update upon a new observation. The taxonomy poses the foundation for principled studies of the functional roles and physiological signatures of surprise in the brain.

In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems of interest in recent times. This semiparametric procedure can easily combine the flexibility of a non-parametric distribution estimator together with the interpretability of a parametric model. The model is specified by estimating equations-based constraints. Drawing an inference from a Bayesian empirical likelihood (BayesEL) posterior is challenging. The likelihood is computed numerically, so no closed expression of the posterior exists. Moreover, for any sample of finite size, the support of the likelihood is non-convex, which hinders the fast mixing of many Markov Chain Monte Carlo (MCMC) procedures. It has been recently shown that using the properties of the gradient of log empirical likelihood, one can devise an efficient Hamiltonian Monte Carlo (HMC) algorithm to sample from a BayesEL posterior. The package requires the user to specify only the estimating equations, the prior, and their respective gradients. An MCMC sample drawn from the BayesEL posterior of the parameters, with various details required by the user is obtained.

We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising when modeling complex physical systems given by the interconnection of many sub-units where feedback and algebraic loops can be encountered. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. The stable spline covariance is used to include information on smooth exponential decay of the impulse responses. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses. It is based on a variation of Gibbs sampling which updates possibly overlapping blocks of the parameter space on the basis of the level of collinearity affecting the different inputs. Numerical experiments are included to test the goodness of the approach where hundreds of impulse responses form the system and inputs correlation may be very high.