We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. Leveraging variational inference (VI) and unitary approximate message passing (UAMP), we develop a Bayesian approach to MF with an efficient message passing implementation, called UAMPMF. With proper priors imposed on the factor matrices, UAMPMF can be used to solve many problems that can be formulated as MF, such as non negative matrix factorization, dictionary learning, compressive sensing with matrix uncertainty, robust principal component analysis, and sparse matrix factorization. Extensive numerical examples are provided to show that UAMPMF significantly outperforms state-of-the-art algorithms in terms of recovery accuracy, robustness and computational complexity.

Deep Gaussian Process (DGP) as a model prior in Bayesian learning intuitively exploits the expressive power in function composition. DGPs also offer diverse modeling capabilities, but inference is challenging because marginalization in latent function space is not tractable. With Bochner's theorem, DGP with squared exponential kernel can be viewed as a deep trigonometric network consisting of the random feature layers, sine and cosine activation units, and random weight layers. In the wide limit with a bottleneck, we show that the weight space view yields the same effective covariance functions which were obtained previously in function space. Also, varying the prior distributions over network parameters is equivalent to employing different kernels. As such, DGPs can be translated into the deep bottlenecked trig networks, with which the exact maximum a posteriori estimation can be obtained. Interestingly, the network representation enables the study of DGP's neural tangent kernel, which may also reveal the mean of the intractable predictive distribution. Statistically, unlike the shallow networks, deep networks of finite width have covariance deviating from the limiting kernel, and the inner and outer widths may play different roles in feature learning. Numerical simulations are present to support our findings.

This is evident from popular phenomena such as effects of fake news and online social movements. However the the data obtained from social media presents itself with large volume and velocity, accompanied by significant amount of irrelevant data pertaining to general discussions, personal messages and spam. Social media has been shown to be effective for detecting, forecasting and tracking real world events. The ability to detect real world events is crucial and has applications in disease surveillance, commerce, governance and other areas. Thus extraction of useful information and modelling the characteristics of social media to detect real world events is an important problem. 2 RESEARCH PROBLEM To outline the research problem we need to define events, which has multiple interpretations.

Studies show that Studies that cardiovascular diseases (CVDs) are malignant for human health. Thus, it is important to have an efficient way of CVD prognosis. In response to this, the healthcare industry has adopted machine learning-based smart solutions to alleviate the manual process of CVD prognosis. Thus, this work proposes an information fusion technique that combines key attributes of a person through analysis of variance (ANOVA) and domain experts' knowledge. It also introduces a new collection of CVD data samples for emerging research. There are thirty-eight experiments conducted exhaustively to verify the performance of the proposed framework on four publicly available benchmark datasets and the newly created dataset in this work. The ablation study shows that the proposed approach can achieve a competitive mean average accuracy (mAA) of 99.2% and a mean average AUC of 97.9%.

In the reinforcement learning literature, there are many algorithms developed for either Contextual Bandit (CB) or Markov Decision Processes (MDP) environments. However, when deploying reinforcement learning algorithms in the real world, even with domain expertise, it is often difficult to know whether it is appropriate to treat a sequential decision making problem as a CB or an MDP. In other words, do actions affect future states, or only the immediate rewards? Making the wrong assumption regarding the nature of the environment can lead to inefficient learning, or even prevent the algorithm from ever learning an optimal policy, even with infinite data. In this work we develop an online algorithm that uses a Bayesian hypothesis testing approach to learn the nature of the environment. Our algorithm allows practitioners to incorporate prior knowledge about whether the environment is that of a CB or an MDP, and effectively interpolate between classical CB and MDP-based algorithms to mitigate against the effects of misspecifying the environment. We perform simulations and demonstrate that in CB settings our algorithm achieves lower regret than MDP-based algorithms, while in non-bandit MDP settings our algorithm is able to learn the optimal policy, often achieving comparable regret to MDP-based algorithms.

The recent introduction of gradient-based MCMC for discrete spaces holds great promise, and comes with the tantalising possibility of new discrete counterparts to celebrated continuous methods such as MALA and HMC. Towards this goal, we introduce several discrete Metropolis-Hastings samplers that are conceptually-inspired by MALA, and demonstrate their strong empirical performance across a range of challenging sampling problems in Bayesian inference and energy-based modelling. Methodologically, we identify why discrete analogues to preconditioned MALA are generally intractable, motivating us to introduce a new kind of preconditioning based on auxiliary variables and the `Gaussian integral trick'.

We consider the Bayesian mixture of finite mixtures (MFMs) and Dirichlet process mixture (DPM) models for clustering. Recent asymptotic theory has established that DPMs overestimate the number of clusters for large samples and that estimators from both classes of models are inconsistent for the number of clusters under misspecification, but the implications for finite sample analyses are unclear. The final reported estimate after fitting these models is often a single representative clustering obtained using an MCMC summarisation technique, but it is unknown how well such a summary estimates the number of clusters. Here we investigate these practical considerations through simulations and an application to gene expression data, and find that (i) DPMs overestimate the number of clusters even in finite samples, but only to a limited degree that may be correctable using appropriate summaries, and (ii) misspecification can lead to considerable overestimation of the number of clusters in both DPMs and MFMs, but results are nevertheless often still interpretable. We provide recommendations on MCMC summarisation and suggest that although the more appealing asymptotic properties of MFMs provide strong motivation to prefer them, results obtained using MFMs and DPMs are often very similar in practice.

The presence of outliers (anomalous values) in synthetic aperture radar (SAR) data and the misspecification in statistical image models may result in inaccurate inferences. To avoid such issues, the Rayleigh regression model based on a robust estimation process is proposed as a more realistic approach to model this type of data. This paper aims at obtaining Rayleigh regression model parameter estimators robust to the presence of outliers. The proposed approach considered the weighted maximum likelihood method and was submitted to numerical experiments using simulated and measured SAR images. Monte Carlo simulations were employed for the numerical assessment of the proposed robust estimator performance in finite signal lengths, their sensitivity to outliers, and the breakdown point. For instance, the non-robust estimators show a relative bias value $65$-fold larger than the results provided by the robust approach in corrupted signals. In terms of sensitivity analysis and break down point, the robust scheme resulted in a reduction of about $96\%$ and $10\%$, respectively, in the mean absolute value of both measures, in compassion to the non-robust estimators. Moreover, two SAR data sets were used to compare the ground type and anomaly detection results of the proposed robust scheme with competing methods in the literature.

In view of its power in extracting feature representation, contrastive self-supervised learning has been successfully integrated into the practice of (deep) reinforcement learning (RL), leading to efficient policy learning in various applications. Despite its tremendous empirical successes, the understanding of contrastive learning for RL remains elusive. To narrow such a gap, we study how RL can be empowered by contrastive learning in a class of Markov decision processes (MDPs) and Markov games (MGs) with low-rank transitions. For both models, we propose to extract the correct feature representations of the low-rank model by minimizing a contrastive loss. Moreover, under the online setting, we propose novel upper confidence bound (UCB)-type algorithms that incorporate such a contrastive loss with online RL algorithms for MDPs or MGs. We further theoretically prove that our algorithm recovers the true representations and simultaneously achieves sample efficiency in learning the optimal policy and Nash equilibrium in MDPs and MGs. We also provide empirical studies to demonstrate the efficacy of the UCB-based contrastive learning method for RL. To the best of our knowledge, we provide the first provably efficient online RL algorithm that incorporates contrastive learning for representation learning. Our codes are available at https://github.com/Baichenjia/Contrastive-UCB.

Managing a project properly is one of the factors behind its completion and subsequent success. The same can be said for any artificial intelligence (AI)/machine learning (ML)/deep learning (DL) project. Moreover, efficient management in this segment holds even more prominence as it requires continuous testing before delivering the final product. An efficient project manager will ensure that there is ample time from the concept to the final product so that a client's requirements are met without any delays and issues. As already established, efficient project management is of great importance in AI/ML/DL projects.