Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling techniques are used to implement Bayesian inference. In the past three decades, MCMC methods have faced a number of challenges in being adapted to larger models (such as in deep learning) and big data problems. Advanced proposals that incorporate gradients, such as a Langevin proposal distribution, provide a means to address some of the limitations of MCMC sampling for Bayesian neural networks. Furthermore, MCMC methods have typically been constrained to use by statisticians and are still not prominent among deep learning researchers. We present a tutorial for MCMC methods that covers simple Bayesian linear and logistic models, and Bayesian neural networks. The aim of this tutorial is to bridge the gap between theory and implementation via coding, given a general sparsity of libraries and tutorials to this end. This tutorial provides code in Python with data and instructions that enable their use and extension. We provide results for some benchmark problems showing the strengths and weaknesses of implementing the respective Bayesian models via MCMC. We highlight the challenges in sampling multi-modal posterior distributions in particular for the case of Bayesian neural networks, and the need for further improvement of convergence diagnosis.

Topic modelling with innovative deep learning methods has gained interest for a wide range of applications that includes COVID-19. Topic modelling can provide, psychological, social and cultural insights for understanding human behaviour in extreme events such as the COVID-19 pandemic. In this paper, we use prominent deep learning-based language models for COVID-19 topic modelling taking into account data from emergence (Alpha) to the Omicron variant. We apply topic modeling to review the public behaviour across the first, second and third waves based on Twitter dataset from India. Our results show that the topics extracted for the subsequent waves had certain overlapping themes such as covers governance, vaccination, and pandemic management while novel issues aroused in political, social and economic situation during COVID-19 pandemic. We also found a strong correlation of the major topics qualitatively to news media prevalent at the respective time period. Hence, our framework has the potential to capture major issues arising during different phases of the COVID-19 pandemic which can be extended to other countries and regions.

Google Translate has been prominent for language translation; however, limited work has been done in evaluating the quality of translation when compared to human experts. Sanskrit one of the oldest written languages in the world. In 2022, the Sanskrit language was added to the Google Translate engine. Sanskrit is known as the mother of languages such as Hindi and an ancient source of the Indo-European group of languages. Sanskrit is the original language for sacred Hindu texts such as the Bhagavad Gita. In this study, we present a framework that evaluates the Google Translate for Sanskrit using the Bhagavad Gita. We first publish a translation of the Bhagavad Gita in Sanskrit using Google Translate. Our framework then compares Google Translate version of Bhagavad Gita with expert translations using sentiment and semantic analysis via BERT-based language models. Our results indicate that in terms of sentiment and semantic analysis, there is low level of similarity in selected verses of Google Translate when compared to expert translations. In the qualitative evaluation, we find that Google translate is unsuitable for translation of certain Sanskrit words and phrases due to its poetic nature, contextual significance, metaphor and imagery. The mistranslations are not surprising since the Bhagavad Gita is known as a difficult text not only to translate, but also to interpret since it relies on contextual, philosophical and historical information. Our framework lays the foundation for automatic evaluation of other languages by Google Translate

Gross domestic product (GDP) is the most widely used indicator in macroeconomics and the main tool for measuring a country's economic ouput. Due to the diversity and complexity of the world economy, a wide range of models have been used, but there are challenges in making decadal GDP forecasts given unexpected changes such as pandemics and wars. Deep learning models are well suited for modeling temporal sequences have been applied for time series forecasting. In this paper, we develop a deep learning framework to forecast the GDP growth rate of the world economy over a decade. We use Penn World Table as the source of our data, taking data from 1980 to 2019, across 13 countries, such as Australia, China, India, the United States and so on. We test multiple deep learning models, LSTM, BD-LSTM, ED-LSTM and CNN, and compared their results with the traditional time series model (ARIMA,VAR). Our results indicate that ED-LSTM is the best performing model. We present a recursive deep learning framework to predict the GDP growth rate in the next ten years. We predict that most countries will experience economic growth slowdown, stagnation or even recession within five years; only China, France and India are predicted to experience stable, or increasing, GDP growth.

Advances in parallel and distributed computing have enabled efficient implementation of the distributed swarm and evolutionary algorithms for complex and computationally expensive models. Evolutionary algorithms provide gradient-free optimisation which is beneficial for models that do not have such information available, for instance, geoscientific landscape evolution models. However, such models are so computationally expensive that even distributed swarm and evolutionary algorithms with the power of parallel computing struggle. We need to incorporate efficient strategies such as surrogate assisted optimisation that further improves their performance; however, this becomes a challenge given parallel processing and inter-process communication for implementing surrogate training and prediction. In this paper, we implement surrogate-based estimation of fitness evaluation in distributed swarm optimisation over a parallel computing architecture. Our results demonstrate very promising results for benchmark functions and geoscientific landscape evolution models. We obtain a reduction in computationally time while retaining optimisation solution accuracy through the use of surrogates in a parallel computing environment.

Class imbalance in a dataset is a major problem for classifiers that results in poor prediction with a high true positive rate (TPR) but a low true negative rate (TNR) for a majority positive training dataset. Generally, the pre-processing technique of oversampling of minority class(es) are used to overcome this deficiency. Our focus is on using the hybridization of Generative Adversarial Network (GAN) and Synthetic Minority Over-Sampling Technique (SMOTE) to address class imbalanced problems. We propose a novel two-phase oversampling approach that has the synergy of SMOTE and GAN. The initial data of minority class(es) generated by SMOTE is further enhanced by GAN that produces better quality samples. We named it SMOTified-GAN as GAN works on pre-sampled minority data produced by SMOTE rather than randomly generating the samples itself. The experimental results prove the sample quality of minority class(es) has been improved in a variety of tested benchmark datasets. Its performance is improved by up to 9\% from the next best algorithm tested on F1-score measurements. Its time complexity is also reasonable which is around $O(N^2d^2T)$ for a sequential algorithm.

Bayes' theorem is used as foundation Autoencoders are a family of unsupervised learning methods for inference in Bayesian neural networks, and Markov that use neural network architectures and learning algorithms chain Monte Carlo (MCMC) sampling methods [25] are used to learn a lower-dimensional representation (encoding) for constructing the posterior distribution. Variational inference of the data, which can then be used to reconstruct a representation [26] is another way to approximate the posterior distribution, close to the original input. They thus facilitate dimensionality which approximates an intractable posterior distribution by a reduction for prediction and classification [1, 2], and have tractable one. This makes it particularly suited to large data been successfully applied to image classification [3, 4], face sets and models, and so it has been popular for autoencoders recognition [5, 6], geoscience and remote sensing [7], speechbased and neural networks [13, 27].

It is well known that recurrent neural networks (RNNs) faced limitations in learning long-term dependencies that have been addressed by memory structures in long short-term memory (LSTM) networks. Matrix neural networks feature matrix representation which inherently preserves the spatial structure of data and has the potential to provide better memory structures when compared to canonical neural networks that use vector representation. Neural Turing machines (NTMs) are novel RNNs that implement notion of programmable computers with neural network controllers to feature algorithms that have copying, sorting, and associative recall tasks. In this paper, we study the augmentation of memory capacity with a matrix representation of RNNs and NTMs (MatNTMs). We investigate if matrix representation has a better memory capacity than the vector representations in conventional neural networks. We use a probabilistic model of the memory capacity using Fisher information and investigate how the memory capacity for matrix representation networks are limited under various constraints, and in general, without any constraints. In the case of memory capacity without any constraints, we found that the upper bound on memory capacity to be $N^2$ for an $N\times N$ state matrix. The results from our experiments using synthetic algorithmic tasks show that MatNTMs have a better learning capacity when compared to its counterparts.

Time series prediction with neural networks have been focus of much research in the past few decades. Given the recent deep learning revolution, there has been much attention in using deep learning models for time series prediction, and hence it is important to evaluate their strengths and weaknesses. In this paper, we present an evaluation study that compares the performance of deep learning models for multi-step ahead time series prediction. Our deep learning methods compromise of simple recurrent neural networks, long short term memory (LSTM) networks, bidirectional LSTM, encoder-decoder LSTM networks, and convolutional neural networks. We also provide comparison with simple neural networks use stochastic gradient descent and adaptive gradient method (Adam) for training. We focus on univariate and multi-step-ahead prediction from benchmark time series datasets and compare with results from from the literature. The results show that bidirectional and encoder-decoder LSTM provide the best performance in accuracy for the given time series problems with different properties.

We have entered an era of a pandemic that has shaken the world with major impact to medical systems, economics and agriculture. Prominent computational and mathematical models have been unreliable due to the complexity of the spread of infections. Moreover, lack of data collection and reporting makes any such modelling attempts unreliable. Hence we need to re-look at the situation with the latest data sources and most comprehensive forecasting models. Deep learning models such as recurrent neural networks are well suited for modelling temporal sequences. In this paper, prominent recurrent neural networks, in particular \textit{long short term memory} (LSTMs) networks, bidirectional LSTM, and encoder-decoder LSTM models for multi-step (short-term) forecasting the spread of COVID-infections among selected states in India. We select states with COVID-19 hotpots in terms of the rate of infections and compare with states where infections have been contained or reached their peak and provide two months ahead forecast that shows that cases will slowly decline. Our results show that long-term forecasts are promising which motivates the application of the method in other countries or areas. We note that although we made some progress in forecasting, the challenges in modelling remain due to data and difficulty in capturing factors such as population density, travel logistics, and social aspects such culture and lifestyle.