This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model's expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability.

Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of Bayes' theorem. We present a treatment of this Bayesian updating process as a continuous dynamical system. Statistical inference is then governed by a first order differential equation describing a trajectory or flow in the information geometry determined by a parametric family of models. We solve this equation for some simple models and show that when the Cram\'{e}r-Rao bound is saturated the learning rate is governed by a simple $1/T$ power-law, with $T$ a time-like variable denoting the quantity of data. The presence of hidden variables can be incorporated in this setting, leading to an additional driving term in the resulting flow equation. We illustrate this with both analytic and numerical examples based on Gaussians and Gaussian Random Processes and inference of the coupling constant in the 1D Ising model. Finally we compare the qualitative behaviour exhibited by Bayesian flows to the training of various neural networks on benchmarked data sets such as MNIST and CIFAR10 and show how that for networks exhibiting small final losses the simple power-law is also satisfied.

The Bayesian information criterion (BIC), defined as the observed data log likelihood minus a penalty term based on the sample size $N$, is a popular model selection criterion for factor analysis with complete data. This definition has also been suggested for incomplete data. However, the penalty term based on the `complete' sample size $N$ is the same no matter whether in a complete or incomplete data case. For incomplete data, there are often only $N_i

In unsupervised learning, Bayesian Nonparametric (BNP) mixture models, exemplified by the Dirichlet-Process Mixture Model (DPMM), provide a principled approach for Bayesian modeling while adapting the model complexity to the data. This contrasts with finite mixture models whose complexity is determined manually or via model-selection methods. To fix ideas, an important DPMM example is the Dirichlet-Process Gaussian Mixture Model (DPGMM), a Bayesian -dimensional extension of the classical Gaussian Mixture Model (GMM). Despite their potential, however, and although researchers have used them successfully in numerous applications during the last two decades, DPMMs still do not enjoy wide popularity among practitioners, largely due to computational bottlenecks that exist in current algorithms and/or implementations. In particular, one of the missing pieces is the availability of software tools that: 1) can efficiently handle DPMM inference in large datasets; 2) are user-friendly and can also be easily modified. We argue that in order for DPMMs to become a practical choice for large-scale data analysis, implementations of DPMM inference must leverage parallel-and distributed-computing resources (in an analogy, consider how advances in GPU computing and GPU software contributed to the success of deep learning). This is because of not only potential speedups but also memory and storage considerations. For example, this is especially true in distributed mobile robotic sensing applications where multiple autonomous agents working together have limited computational and communication resources. As another motivating example, consider unsupervised dataanalysis tasks in large and high-dimensional computer-vision datasets.

As a powerful statistical tool that has revolutionized modern molecular evolutionary analysis, Bayesian phylogenetic inference has been widely used for tasks ranging from genomic epidemiology [Dudas et al., 2017, du Plessis et al., 2021] to conservation genetics [DeSalle and Amato, 2004]. Given aligned sequence data (e.g., DNA, RNA or protein sequences) and a model of evolution, Bayesian phylogenetics provides principled approaches to quantify the uncertainty of the evolutionary process in terms of the posterior probabilities of phylogenetic trees [Huelsenbeck et al., 2001]. In addition to uncertainty quantification, Bayesian methods enable integrating out tree uncertainty in order to get more confident estimates of parameters of interest, such as factors in the transmission of Ebolavirus [Dudas et al., 2017]. Bayesian methods also allow complex substitution models [Lartillot and Philippe, 2004], which are important in elucidating deep phylogenetic relationships [Feuda et al., 2017]. Ever since its introduction to the phylogenetic community in the 1990s, Bayesian phylogenetic inference has been dominated by random-walk Markov chain Monte Carlo (MCMC) approaches [Yang and Rannala, 1997, Mau et al., 1999, Huelsenbeck and Ronquist, 2001, Drummond et al., 2002, 2005]. However, this approach is fundamentally limited by the complexities of tree space.

Photoacoustic tomography (PAT) is a hybrid biomedical imaging modality based on the photoacoustic effect [6, 44, 32]. In PAT, the imaged target is illuminated with a short pulse of light. Absorption of light creates localized areas of thermal expansion, resulting in localized pressure increases within the imaged target. This pressure distribution, called the initial pressure, relaxes as broadband ultrasound waves that are measured on the boundary of the imaged target. In the inverse problem of PAT, the initial pressure distribution is estimated from a set of measured ultrasound data.

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference algorithm can be used as a probabilistic programming back-end that is simultaneously reliable, efficient, black-box, and general. Probabilistic programming languages often choose a single algorithm to apply to a given problem, thus inheriting its limitations. While substantial work has been done both to formalise probabilistic programming and to improve efficiency of inference, there has been little work that makes use of the available program structure, by formally analysing it, to better utilise the underlying inference algorithm. This dissertation presents three novel techniques (both static and dynamic), which aim to improve probabilistic programming using program analysis. The techniques analyse a probabilistic program and adapt it to make inference more efficient, sometimes in a way that would have been tedious or impossible to do by hand.

Predicting the results of matches in sport is a challenging and interesting task. In this paper, we review a selection of studies from 1996 to 2019 that used machine learning for predicting match results in team sport. Considering both invasion sports and striking/fielding sports, we discuss commonly applied machine learning algorithms, as well as common approaches related to data and evaluation. Our study considers accuracies that have been achieved across different sports, and explores whether evidence exists to support the notion that outcomes of some sports may be inherently more difficult to predict. We also uncover common themes of future research directions and propose recommendations for future researchers. Although there remains a lack of benchmark datasets (apart from in soccer), and the differences between sports, datasets and features makes between-study comparisons difficult, as we discuss, it is possible to evaluate accuracy performance in other ways. Artificial Neural Networks were commonly applied in early studies, however, our findings suggest that a range of models should instead be compared. Selecting and engineering an appropriate feature set appears to be more important than having a large number of instances. For feature selection, we see potential for greater inter-disciplinary collaboration between sport performance analysis, a sub-discipline of sport science, and machine learning.

The course covers Machine Learning in exhaustive way. The presentations and hands-on practical are made such that it's made easy. The knowledge gained through this tutorial series can be applied to various real world scenarios. UnSupervised learning does not require to supervise the model. Instead, it allows the model to work on its own to discover patterns and information that was previously undetected. It mainly deals with the unlabeled data.

COVID-19 is one of the deadliest viruses, which has killed millions of people around the world to this date. The reason for peoples' death is not only linked to its infection but also to peoples' mental states and sentiments triggered by the fear of the virus. People's sentiments, which are predominantly available in the form of posts/tweets on social media, can be interpreted using two kinds of information: syntactical and semantic. Herein, we propose to analyze peoples' sentiment using both kinds of information (syntactical and semantic) on the COVID-19-related twitter dataset available in the Nepali language. For this, we, first, use two widely used text representation methods: TF-IDF and FastText and then combine them to achieve the hybrid features to capture the highly discriminating features. Second, we implement nine widely used machine learning classifiers (Logistic Regression, Support Vector Machine, Naive Bayes, K-Nearest Neighbor, Decision Trees, Random Forest, Extreme Tree classifier, AdaBoost, and Multilayer Perceptron), based on the three feature representation methods: TF-IDF, FastText, and Hybrid. To evaluate our methods, we use a publicly available Nepali-COVID-19 tweets dataset, NepCov19Tweets, which consists of Nepali tweets categorized into three classes (Positive, Negative, and Neutral). The evaluation results on the NepCOV19Tweets show that the hybrid feature extraction method not only outperforms the other two individual feature extraction methods while using nine different machine learning algorithms but also provides excellent performance when compared with the state-of-the-art methods. Natural language processing (NLP) techniques have been developed to assess peoples' sentiments on various topics.