If there was something that always frustrated me was not fully understanding Bayesian inference. Sometime last year, I came across an article about a TensorFlow-supported R package for Bayesian analysis, called greta. Back then, I searched for greta tutorials and stumbled on this blog post that praised a textbook called Statistical Rethinking: A Bayesian Course with Examples in R and Stan by Richard McElreath. I had found a solution to my lingering frustration so I bought a copy straight away. I spent the last few months reading it cover to cover and solving the proposed exercises, which are heavily based on the rethinking package. I cannot recommend it highly enough to whoever seeks a solid grip on Bayesian statistics, both in theory and application. This post ought to be my most gratifying blogging experience so far, in that I am essentially reporting my own recent learning. I am convinced this will make the storytelling all the more effective. As a demonstration, the female cuckoo reproductive output data recently analysed by Riehl et al., 2019 [1] will be modelled using In the process, we will conduct the MCMC sampling, visualise posterior distributions, generate predictions and ultimately assess the influence of social parasitism in female reproductive output. You should have some familiarity with standard statistical models. If you need to refresh some basics of probabilities using R have a look into my first post. I hope you enjoy as much as I did!

This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a general picture of the architectures developed by researchers over the past 30 years. The learning dynamics of these ART models are briefly described, and their distinctive characteristics such as code representation, long-term memory and corresponding geometric interpretation are discussed. Useful engineering properties of ART (speed, configurability, explainability, parallelization and hardware implementation) are examined along with current challenges. Finally, a compilation of online software libraries is provided. It is expected that this overview will be helpful to new and seasoned ART researchers.

We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) is used to form the noisy log-likelihood estimates using computationally costly forward simulations. We frame the inference task as a Bayesian sequential design problem, where the log-likelihood function is modelled with a hierarchical Gaussian process (GP) surrogate model, which is used to efficiently select additional log-likelihood evaluation locations. Motivated by recent progress in batch Bayesian optimisation, we develop various batch-sequential strategies where multiple simulations are adaptively selected to minimise either the expected or median loss function measuring the uncertainty in the resulting posterior. We analyse the properties of the resulting method theoretically and empirically. Experiments with toy problems and three simulation models suggest that our method is robust, highly parallelisable, and sample-efficient.

In machine learning, classification models need to be trained in order to predict class labels. When the training data contains personal information about individuals, collecting training data becomes difficult due to privacy concerns. Local differential privacy is a definition to measure the individual privacy when there is no trusted data curator. Individuals interact with an untrusted data aggregator who obtains statistical information about the population without learning personal data. In order to train a Naive Bayes classifier in an untrusted setting, we propose to use methods satisfying local differential privacy. Individuals send their perturbed inputs that keep the relationship between the feature values and class labels. The data aggregator estimates all probabilities needed by the Naive Bayes classifier. Then, new instances can be classified based on the estimated probabilities. We propose solutions for both discrete and continuous data. In order to eliminate high amount of noise and decrease communication cost in multi-dimensional data, we propose utilizing dimensionality reduction techniques which can be applied by individuals before perturbing their inputs. Our experimental results show that the accuracy of the Naive Bayes classifier is maintained even when the individual privacy is guaranteed under local differential privacy, and that using dimensionality reduction enhances the accuracy.

Coordination recognition and subtle pattern prediction of future trajectories play a significant role when modeling interactive behaviors of multiple agents. Due to the essential property of uncertainty in the future evolution, deterministic predictors are not sufficiently safe and robust. In order to tackle the task of probabilistic prediction for multiple, interactive entities, we propose a coordination and trajectory prediction system (CTPS), which has a hierarchical structure including a macro-level coordination recognition module and a micro-level subtle pattern prediction module which solves a probabilistic generation task. We illustrate two types of representation of the coordination variable: categorized and real-valued, and compare their effects and advantages based on empirical studies. We also bring the ideas of Bayesian deep learning into deep generative models to generate diversified prediction hypotheses. The proposed system is tested on multiple driving datasets in various traffic scenarios, which achieves better performance than baseline approaches in terms of a set of evaluation metrics. The results also show that using categorized coordination can better capture multi-modality and generate more diversified samples than the real-valued coordination, while the latter can generate prediction hypotheses with smaller errors with a sacrifice of sample diversity. Moreover, employing neural networks with weight uncertainty is able to generate samples with larger variance and diversity.

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. The Bayesian optimization routine involves learning a response surface and maximizing a score to select the most valuable inputs to be queried at the next iteration. These key steps are subject to the curse of dimensionality so that Bayesian optimization does not scale beyond 10--20 parameters. In this work, we address this issue and propose a high-dimensional BO method that learns a nonlinear low-dimensional manifold of the input space. We achieve this with a multi-layer neural network embedded in the covariance function of a Gaussian process. This approach applies unsupervised dimensionality reduction as a byproduct of a supervised regression solution. This also allows exploiting data efficiency of Gaussian process models in a Bayesian framework. We also introduce a nonlinear mapping from the manifold to the high-dimensional space based on multi-output Gaussian processes and jointly train it end-to-end via marginal likelihood maximization. We show this intrinsically low-dimensional optimization outperforms recent baselines in high-dimensional BO literature on a set of benchmark functions in 60 dimensions.

Modern intelligent transportation systems provide data that allow real-time demand prediction, which is essential for planning and operations. The main challenge of prediction of Origin-Destination (O-D) flow matrices is that demands cannot be directly measured by traffic sensors; instead, they have to be inferred from aggregate traffic flow data on traffic links. Specifically, spatial correlation, congestion and time dependent factors need to be considered in general transportation networks. In this paper we propose a novel O-D prediction framework based on Fusion Line Graph Convolutional Networks (FL-GCNs). We use FL-GCN to recognize spatial and temporal patterns simultaneously. The underlying road network topology is transformed into a corresponding line graph. This structure provides a general framework for predicting spatial-temporal O-D information from link traffic flows. Data from a New Jersey Turnpike network is used to evaluate the proposed model. The results show that FL-GCN can recognize spatial and temporal patterns. We also compare FL-GCN with Kalman filter; the results show that our model can outperform Kalman filter by 17.87% in predicting the whole O-D pairs.

Brain tumor segmentation from Magnetic Resonance Images (MRIs) is an important task to measure tumor responses to treatments. However, automatic segmentation is very challenging. This paper presents an automatic brain tumor segmentation method based on a Normalized Gaussian Bayesian classification and a new 3D Fluid Vector Flow (FVF) algorithm. In our method, a Normalized Gaussian Mixture Model (NGMM) is proposed and used to model the healthy brain tissues. Gaussian Bayesian Classifier is exploited to acquire a Gaussian Bayesian Brain Map (GBBM) from the test brain MR images. GBBM is further processed to initialize the 3D FVF algorithm, which segments the brain tumor. This algorithm has two major contributions. First, we present a NGMM to model healthy brains. Second, we extend our 2D FVF algorithm to 3D space and use it for brain tumor segmentation. The proposed method is validated on a publicly available dataset.

Statistical learning theory has been studied for general function estimation from data since the late 1960's [22]. However, it was only widely adopted in practice after the introduction of the learning algorithms known as Support Vector Machines (SVMs) [23]. Using the so-called kernel trick, which replaces dot products between features and model parameters by evaluations of a kernel function, SVMs can learn nonlinear relations from training patterns by solving a convex optimization problem [16]. An important variant of the SVM is the Least Squares Support Vector Machine (LS-SVM) [20], which is obtained by making all data points supportvectors. LS-SVM avoids the constrained quadratic optimization step of standard SVMs by replacing the training procedure with one that reduces to solving a system of linear equations, which can be performed via ordinary least squares. The first SVM formulation was derived for classification tasks, but it has been readily adapted to tackle regression problems, being usually named Support Vector Regression (SVR) [6]. Similarly, the regression counterpart of LS-SVM is the LS-SVR [20]. 1

We introduce a probabilistic framework for quantifying the semantic similarity between two groups of embeddings. We formulate the task of semantic similarity as a model comparison task in which we contrast a generative model which jointly models two sentences versus one that does not. We illustrate how this framework can be used for the Semantic Textual Similarity tasks using clear assumptions about how the embeddings of words are generated. We apply model comparison that utilises information criteria to address some of the shortcomings of Bayesian model comparison, whilst still penalising model complexity. We achieve competitive results by applying the proposed framework with an appropriate choice of likelihood on the STS datasets.