Marginal-based methods achieve promising performance in the synthetic data competition hosted by the National Institute of Standards and Technology (NIST). To deal with high-dimensional data, the distribution of synthetic data is represented by a probabilistic graphical model (e.g., a Bayesian network), while the raw data distribution is approximated by a collection of low-dimensional marginals. Differential privacy (DP) is guaranteed by introducing random noise to each lowdimensional marginal distribution. Despite its promising performance in practice, the statistical properties of marginal-based methods are rarely studied in the literature. In this paper, we study DP data synthesis algorithms based on Bayesian networks (BN) from a statistical perspective. Related to downstream machine learning tasks, an upper bound for the utility error of the DP synthetic data is also derived. To complete the picture, we establish a lower bound for TV accuracy that holds for everyǫ-DP synthetic data generator. In recent years, the problem of privacy-preserving data analysis has become increasingly important and differential privacy (Dwork et al., 2006) appears as the foundation of data privacy. Differential privacy (DP) techniques are widely adopted by industrial companies and the U.S. Census Bureau (Johnson et al., 2017; Erlingsson et al., 2014; Nguyên et al., 2016; The U.S. Census Bureau, 2020; Abowd, 2018).

Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network architectures. We present a simple approach to incorporate prior knowledge in BNNs based on external summary information about the predicted classification probabilities for a given dataset. The available summary information is incorporated as augmented data and modeled with a Dirichlet process, and we derive the corresponding \emph{Summary Evidence Lower BOund}. The approach is founded on Bayesian principles, and all hyperparameters have a proper probabilistic interpretation. We show how the method can inform the model about task difficulty and class imbalance. Extensive experiments show that, with negligible computational overhead, our method parallels and in many cases outperforms popular alternatives in accuracy, uncertainty calibration, and robustness against corruptions with both balanced and imbalanced data.

Several years ago, before learning much about methods for reasoning with uncertainty, I and my colleagues began work on a large expert system, called Pathfinder, that assists community pathologists with the diagnosis of lymph node pathology. Because the Dempster-Shafer theory of belief was quite popular in our research group at the time, we developed a inference method for our expert system inspired by this theory. The program performed fairly well in the opinion of the expert pathologist who provided the knowledge for the system. In the months following the initial development of Pathfinder, several of us in the research group began exploring other methods for reasoning under uncertainty. We identified the Bayesian approach as a candidate for a new inference procedure. We realized that the measures of uncertainty we assessed from the expert could be interpreted as probabilities and we implemented a new inference method-- a special case of Bayes' theorem. During this time, the expert was running cases through the program to test the system's diagnostic performance. One day, without telling him, we changed the inference procedure to the Bayesian approach. After running several cases with the new approach, the expert exclaimed, "What did you do to the program?

A lot of news sources picked up on Typhoon Rai (also known locally as Typhoon Odette), along with fake news outlets. The study honed in on the issue, to create a model that can identify between legitimate and illegitimate news articles. With this in mind, we chose the following machine learning algorithms in our development: Logistic Regression, Random Forest and Multinomial Naive Bayes. Bag of Words, TF-IDF and Lemmatization were implemented in the Model. Gathering 160 datasets from legitimate and illegitimate sources, the machine learning was trained and tested. By combining all the machine learning techniques, the Combined BOW model was able to reach an accuracy of 91.07%, precision of 88.33%, recall of 94.64%, and F1 score of 91.38% and Combined TF-IDF model was able to reach an accuracy of 91.18%, precision of 86.89%, recall of 94.64%, and F1 score of 90.60%.

This is a master's thesis concerning the theoretical ideas of geometric deep learning. Geometric deep learning aims to provide a structured characterization of neural network architectures, specifically focused on the ideas of invariance and equivariance of data with respect to given transformations. This thesis aims to provide a theoretical evaluation of geometric deep learning, compiling theoretical results that characterize the properties of invariant neural networks with respect to learning performance.

We study a normalizing flow in the latent space of a top-down generator model, in which the normalizing flow model plays the role of the informative prior model of the generator. We propose to jointly learn the latent space normalizing flow prior model and the top-down generator model by a Markov chain Monte Carlo (MCMC)-based maximum likelihood algorithm, where a short-run Langevin sampling from the intractable posterior distribution is performed to infer the latent variables for each observed example, so that the parameters of the normalizing flow prior and the generator can be updated with the inferred latent variables. We show that, under the scenario of non-convergent short-run MCMC, the finite step Langevin dynamics is a flow-like approximate inference model and the learning objective actually follows the perturbation of the maximum likelihood estimation (MLE). We further point out that the learning framework seeks to (i) match the latent space normalizing flow and the aggregated posterior produced by the short-run Langevin flow, and (ii) bias the model from MLE such that the short-run Langevin flow inference is close to the true posterior. Empirical results of extensive experiments validate the effectiveness of the proposed latent space normalizing flow model in the tasks of image generation, image reconstruction, anomaly detection, supervised image inpainting and unsupervised image recovery.

In this paper, the novel Distributed Bayesian (D-Bay) algorithm is presented for solving multi-agent problems within the Continuous Distributed Constraint Optimization Problem (C-DCOP) framework. This framework extends the classical DCOP framework towards utility functions with continuous domains. D-Bay solves a C-DCOP by utilizing Bayesian optimization for the adaptive sampling of variables. We theoretically show that D-Bay converges to the global optimum of the C-DCOP for Lipschitz continuous utility functions. The performance of the algorithm is evaluated empirically based on the sample efficiency. The proposed algorithm is compared to state-of-the-art DCOP and C-DCOP solvers. The algorithm generates better solutions while requiring fewer samples.

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC. Unforunately, this can be slow, especially when considering large volumes of data. It is hard to parallelise the accept-reject component of the MCMC. None-the-less, we propose two methods for exploiting parallelism in the MCMC: in the first, we replace the MCMC with another numerical Bayesian approach, the Sequential Monte Carlo (SMC) sampler, which has the appealing property that it is an inherently parallel algorithm; in the second, we consider data partitioning. Both methods use multi-core processing with a High-Performance Computing (HPC) resource. We test the two methods in various study settings to determine which method is the most beneficial for each test case. Experiments show that data partitioning has limited utility in the settings we consider and that the use of the SMC sampler can improve run-time (compared to the sequential implementation) by up to a factor of 343.

Quality education, one of the seventeen sustainable development goals (SDGs) identified by the United Nations General Assembly, stands to benefit enormously from the adoption of artificial intelligence (AI) driven tools and technologies. The concurrent boom of necessary infrastructure, digitized data and general social awareness has propelled massive research and development efforts in the artificial intelligence for education (AIEd) sector. In this review article, we investigate how artificial intelligence, machine learning and deep learning methods are being utilized to support students, educators and administrative staff. We do this through the lens of a novel categorization approach. We consider the involvement of AI-driven methods in the education process in its entirety - from students admissions, course scheduling etc. in the proactive planning phase to knowledge delivery, performance assessment etc. in the reactive execution phase. We outline and analyze the major research directions under proactive and reactive engagement of AI in education using a representative group of 194 original research articles published in the past two decades i.e., 2003 - 2022. We discuss the paradigm shifts in the solution approaches proposed, i.e., in the choice of data and algorithms used over this time. We further dive into how the COVID-19 pandemic challenged and reshaped the education landscape at the fag end of this time period. Finally, we pinpoint existing limitations in adopting artificial intelligence for education and reflect on the path forward.

In district-based elections, electors cast votes in their respective districts. In each district, the party with maximum votes wins the corresponding seat in the governing body. The election result is based on the number of seats won by different parties. In this system, locations of electors across the districts may severely affect the election result even if the total number of votes obtained by different parties remains unchanged. A less popular party may end up winning more seats if their supporters are suitably distributed spatially. This happens due to various regional and social influences on individual voters which modulate their voting choice. In this paper, we explore agent-based models for district-based elections, where we consider each elector as an agent, and try to represent their social and geographical attributes and political inclinations using probability distributions. This model can be used to simulate election results by Monte Carlo sampling. The models allow us to explore the full space of possible outcomes of an electoral setting, though they can also be calibrated to actual election results for suitable values of parameters. We use Approximate Bayesian Computation (ABC) framework to estimate model parameters. We show that our model can reproduce the results of elections held in India and USA, and can also produce counterfactual scenarios.