We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum likelihood estimator oracle. Our approach establishes a general-purpose reduction from minimax rates for sequential probability assignment for smoothed adversaries to minimax rates for transductive learning. This leads to optimal (logarithmic) fast rates for parametric classes and classes with finite VC dimension. On the algorithmic front, we develop an algorithm that efficiently taps into the MLE oracle, for general classes of functions. We show that under general conditions this algorithmic approach yields sublinear regret.

The Bayesian Learning Rule provides a framework for generic algorithm design but can be difficult to use for three reasons. First, it requires a specific parameterization of exponential family. Second, it uses gradients which can be difficult to compute. Third, its update may not always stay on the manifold. We address these difficulties by proposing an extension based on Lie-groups where posteriors are parametrized through transformations of an arbitrary base distribution and updated via the group's exponential map. This simplifies all three difficulties for many cases, providing flexible parametrizations through group's action, simple gradient computation through reparameterization, and updates that always stay on the manifold. We use the new learning rule to derive a new algorithm for deep learning with desirable biologically-plausible attributes to learn sparse features. Our work opens a new frontier for the design of new algorithms by exploiting Lie-group structures.

Gaining the trust and confidence of customers is the essence of the growth and success of financial institutions and organizations. Of late, the financial industry is significantly impacted by numerous instances of fraudulent activities. Further, owing to the generation of large voluminous datasets, it is highly essential that underlying framework is scalable and meet real time needs. To address this issue, in the study, we proposed ATM fraud detection in static and streaming contexts respectively. In the static context, we investigated a parallel and scalable machine learning algorithms for ATM fraud detection that is built on Spark and trained with a variety of machine learning (ML) models including Naive Bayes (NB), Logistic Regression (LR), Support Vector Machine (SVM), Decision Tree (DT), Random Forest (RF), Gradient Boosting Tree (GBT), and Multi-layer perceptron (MLP). We also employed several balancing techniques like Synthetic Minority Oversampling Technique (SMOTE) and its variants, Generative Adversarial Networks (GAN), to address the rarity in the dataset. In addition, we proposed a streaming based ATM fraud detection in the streaming context. Our sliding window based method collects ATM transactions that are performed within a specified time interval and then utilizes to train several ML models, including NB, RF, DT, and K-Nearest Neighbour (KNN). We selected these models based on their less model complexity and quicker response time. In both contexts, RF turned out to be the best model. RF obtained the best mean AUC of 0.975 in the static context and mean AUC of 0.910 in the streaming context. RF is also empirically proven to be statistically significant than the next-best performing models.

Predictive coding (PC) accounts of perception now form one of the dominant computational theories of the brain, where they prescribe a general algorithm for inference and learning over hierarchical latent probabilistic models. Despite this, they have enjoyed little export to the broader field of machine learning, where comparative generative modelling techniques have flourished. In part, this has been due to the poor performance of models trained with PC when evaluated by both sample quality and marginal likelihood. By adopting the perspective of PC as a variational Bayes algorithm under the Laplace approximation, we identify the source of these deficits to lie in the exclusion of an associated Hessian term in the PC objective function, which would otherwise regularise the sharpness of the probability landscape and prevent over-certainty in the approximate posterior. To remedy this, we make three primary contributions: we begin by suggesting a simple Monte Carlo estimated evidence lower bound which relies on sampling from the Hessian-parameterised variational posterior. We then derive a novel block diagonal approximation to the full Hessian matrix that has lower memory requirements and favourable mathematical properties. Lastly, we present an algorithm that combines our method with standard PC to reduce memory complexity further. We evaluate models trained with our approach against the standard PC framework on image benchmark datasets. Our approach produces higher log-likelihoods and qualitatively better samples that more closely capture the diversity of the data-generating distribution.

Cryptocurrencies, such as Bitcoin, are one of the most controversial and complex technological innovations in today's financial system. This study aims to forecast the movements of Bitcoin prices at a high degree of accuracy. To this aim, four different Machine Learning (ML) algorithms are applied, namely, the Support Vector Machines (SVM), the Artificial Neural Network (ANN), the Naive Bayes (NB) and the Random Forest (RF) besides the logistic regression (LR) as a benchmark model. In order to test these algorithms, besides existing continuous dataset, discrete dataset was also created and used. For the evaluations of algorithm performances, the F statistic, accuracy statistic, the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE) and the Root Absolute Error (RAE) metrics were used. The t test was used to compare the performances of the SVM, ANN, NB and RF with the performance of the LR. Empirical findings reveal that, while the RF has the highest forecasting performance in the continuous dataset, the NB has the lowest. On the other hand, while the ANN has the highest and the NB the lowest performance in the discrete dataset. Furthermore, the discrete dataset improves the overall forecasting performance in all algorithms (models) estimated.

Bayesian Causal Forests (BCF) is a causal inference machine learning model based on a highly flexible non-parametric regression and classification tool called Bayesian Additive Regression Trees (BART). Motivated by data from the Trends in International Mathematics and Science Study (TIMSS), which includes data on student achievement in both mathematics and science, we present a multivariate extension of the BCF algorithm. With the help of simulation studies we show that our approach can accurately estimate causal effects for multiple outcomes subject to the same treatment. We also apply our model to Irish data from TIMSS 2019. Our findings reveal the positive effects of having access to a study desk at home (Mathematics ATE 95% CI: [0.20, 11.67]) while also highlighting the negative consequences of students often feeling hungry at school (Mathematics ATE 95% CI: [-11.15, -2.78] , Science ATE 95% CI: [-10.82,-1.72]) or often being absent (Mathematics ATE 95% CI: [-12.47, -1.55]).

Monitoring the Covid19 pandemic constitutes a critical societal stake that received considerable research efforts. The intensity of the pandemic on a given territory is efficiently measured by the reproduction number, quantifying the rate of growth of daily new infections. Recently, estimates for the time evolution of the reproduction number were produced using an inverse problem formulation with a nonsmooth functional minimization. While it was designed to be robust to the limited quality of the Covid19 data (outliers, missing counts), the procedure lacks the ability to output credibility interval based estimates. This remains a severe limitation for practical use in actual pandemic monitoring by epidemiologists that the present work aims to overcome by use of Monte Carlo sampling. After interpretation of the nonsmooth functional into a Bayesian framework, several sampling schemes are tailored to adjust the nonsmooth nature of the resulting posterior distribution. The originality of the devised algorithms stems from combining a Langevin Monte Carlo sampling scheme with Proximal operators. Performance of the new algorithms in producing relevant credibility intervals for the reproduction number estimates and denoised counts are compared. Assessment is conducted on real daily new infection counts made available by the Johns Hopkins University. The interest of the devised monitoring tools are illustrated on Covid19 data from several different countries.

While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a Bayesian algorithm for constructing quantum kernels for support vector machines that adapts quantum gate sequences to data. The algorithm increases the complexity of quantum circuits incrementally by appending quantum gates selected with Bayesian information criterion as circuit selection metric and Bayesian optimization of the parameters of the locally optimal quantum circuits identified. The goal is to build quantum kernels for SVM that can solve classification problems with as little training data as possible. The performance of the resulting quantum models for the classification problems considered here significantly exceeds that of optimized classical models with conventional kernels.

Normalizing flows are tractable density models that can approximate complicated target distributions, e.g. Boltzmann distributions of physical systems. However, current methods for training flows either suffer from mode-seeking behavior, use samples from the target generated beforehand by expensive MCMC methods, or use stochastic losses that have high variance. To avoid these problems, we augment flows with annealed importance sampling (AIS) and minimize the mass-covering $\alpha$-divergence with $\alpha=2$, which minimizes importance weight variance. Our method, Flow AIS Bootstrap (FAB), uses AIS to generate samples in regions where the flow is a poor approximation of the target, facilitating the discovery of new modes. We apply FAB to multimodal targets and show that we can approximate them very accurately where previous methods fail. To the best of our knowledge, we are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the unnormalized target density, without access to samples generated via Molecular Dynamics (MD) simulations: FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations. After reweighting the samples, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth.

We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation, but the over-approximation may result in inefficient exploration. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values and explicitly characterizes the gap in previous work. Moreover, our uncertainty quantification technique is easily integrated into common exploration strategies and scales naturally beyond the tabular setting by using standard deep reinforcement learning architectures. Experiments in difficult exploration tasks, both in tabular and continuous control settings, show that our sharper uncertainty estimates improve sample-efficiency.