Approximate Markov Chain Monte Carlo Algorithms for Large Scale Bayesian Inference

Traditional algorithms for Bayesian posterior inference require processing the entire dataset in each iteration and are quickly getting obsoleted by the proliferation of massive datasets in various application domains. Most successful applications of learning with big data have been with simple minibatch-based algorithms such as Stochastic Gradient Descent, because they are the only ones that can computationally handle today's large datasets. However, by restricting ourselves to these algorithms, we miss out on all the advantages of Bayesian modeling, such as controlling over-fitting, estimating uncertainty and the ability to incorporate prior knowledge. In this thesis, we attempt to scale up Bayesian posterior inference to large datasets by developing a new generation of approximate Markov Chain Monte Carlo algorithms that process only a mini-batch of data to generate each posterior sample. The approximation introduces a bias in the stationary distribution of the Markov chain, but we show that this bias is more than compensated by accelerated burn-in and lower variance due to the ability to generate a larger number of samples per unit of computational time.Our main contributions are the following. First, we develop a fast Metropolis-Hastings (MH) algorithm by approximating each accept/reject decision using a sequential hypothesis test that processes only an adaptive mini-batch of data instead of the complete dataset. Then, we show that the same idea can be used to speed up the slice sampling algorithm. Next, we present a theoretical analysis of Stochastic Gradient Langevin Dynamics (SGLD), a posterior sampling algorithm derived by adding Gaussian noise to Stochastic Gradient Ascent updates. We also show that the bias in SGLD can be reduced by combining it with our approximate MH test. We then propose a new algorithm called Stochastic Gradient Fisher Scoring (SGFS) which improves the mixing rate of SGLD using a preconditioning matrix that captures the curvature of the posterior distribution. Finally, we develop an efficient algorithm for Bayesian Probabilistic Matrix Factorization using a combination of SGLD and approximate Metropolis-Hastings updates

Approximate Markov Chain Monte Carlo Algorithms for Large Scale Bayesian Inference

Traditional algorithms for Bayesian posterior inference require processing the entire dataset in each iteration and are quickly getting obsoleted by the proliferation of massive datasets in various application domains. Most successful applications of learning with big data have been with simple minibatch-based algorithms such as Stochastic Gradient Descent, because they are the only ones that can computationally handle today's large datasets. However, by restricting ourselves to these algorithms, we miss out on all the advantages of Bayesian modeling, such as controlling over-fitting, estimating uncertainty and the ability to incorporate prior knowledge. In this thesis, we attempt to scale up Bayesian posterior inference to large datasets by developing a new generation of approximate Markov Chain Monte Carlo algorithms that process only a mini-batch of data to generate each posterior sample. The approximation introduces a bias in the stationary distribution of the Markov chain, but we show that this bias is more than compensated by accelerated burn-in and lower variance due to the ability to generate a larger number of samples per unit of computational time.Our main contributions are the following. First, we develop a fast Metropolis-Hastings (MH) algorithm by approximating each accept/reject decision using a sequential hypothesis test that processes only an adaptive mini-batch of data instead of the complete dataset. Then, we show that the same idea can be used to speed up the slice sampling algorithm. Next, we present a theoretical analysis of Stochastic Gradient Langevin Dynamics (SGLD), a posterior sampling algorithm derived by adding Gaussian noise to Stochastic Gradient Ascent updates. We also show that the bias in SGLD can be reduced by combining it with our approximate MH test. We then propose a new algorithm called Stochastic Gradient Fisher Scoring (SGFS) which improves the mixing rate of SGLD using a preconditioning matrix that captures the curvature of the posterior distribution. Finally, we develop an efficient algorithm for Bayesian Probabilistic Matrix Factorization using a combination of SGLD and approximate Metropolis-Hastings updates

Orchestrating the Development Lifecycle of Machine Learning-based IoT Applications: A Taxonomy and Survey

Machine Learning (ML) and Internet of Things (IoT) are complementary advances: ML techniques unlock the potential of IoT with intelligence, and IoT applications increasingly feed data collected by sensors into ML models, thereby employing results to improve their business processes and services. Hence, orchestrating ML pipelines that encompass model training and implication involved in the holistic development lifecycle of an IoT application often leads to complex system integration. This article provides a comprehensive and systematic survey of the development lifecycle of ML-based IoT applications. We outline the core roadmap and taxonomy and subsequently assess and compare existing standard techniques used at individual stages