Maximum Probability Framework, powered by Maximum Probability Theorem, is a recent theoretical development in artificial intelligence, aiming to formally define probabilistic models, guiding development of objective functions, and regularization of probabilistic models. MPT uses the probability distribution that the models assume on random variables to provide an upper bound on the probability of the model. We apply MPT to challenging out-of-distribution (OOD) detection problems in computer vision by incorporating MPT as a regularization scheme in the training of CNNs and their energy-based variants. We demonstrate the effectiveness of the proposed method on 1080 trained models, with varying hyperparameters, and conclude that the MPT-based regularization strategy stabilizes and improves the generalization and robustness of base models in addition to enhanced OOD performance on CIFAR10, CIFAR100, and MNIST datasets.

Semantic mapping complements geometric modelling of a Mapping, localization and navigation are among the key robot's surroundings with semantic concepts, i.e., an understanding capabilities of autonomous systems. For robots to navigate of what the environment means to the robot. With safely in complex and evolving environments, mapping semantic mapping, these semantic concepts manifest as a can act as a unified framework that addresses multiple representation of the environment, thus lending robots more perception sub-tasks required for a higher-level scene understanding, resources for task planning and execution. The emergence of such as occupancy/traversability estimation, object semantic mapping can be attributed to (i) the limitations of detection and tracking. While some research streams employ purely geometric maps, and (ii) the advancements in deep end-to-end deep neural networks for mapless navigation via neural networks that allow semantic interpretation of raw imitation [1], [2], reinforcement [3], [4] or self-supervised sensory data [6].

In this paper, we present a Bayesian method for statistical model checking (SMC) of probabilistic hyperproperties specified in the logic HyperPCTL* on discrete-time Markov chains (DTMCs). While SMC of HyperPCTL* using sequential probability ratio test (SPRT) has been explored before, we develop an alternative SMC algorithm based on Bayesian hypothesis testing. In comparison to PCTL*, verifying HyperPCTL* formulae is complex owing to their simultaneous interpretation on multiple paths of the DTMC. In addition, extending the bottom-up model-checking algorithm of the non-probabilistic setting is not straight forward due to the fact that SMC does not return exact answers to the satisfiability problems of subformulae, instead, it only returns correct answers with high-confidence. We propose a recursive algorithm for SMC of HyperPCTL* based on a modified Bayes' test that factors in the uncertainty in the recursive satisfiability results. We have implemented our algorithm in a Python toolbox, HyProVer, and compared our approach with the SPRT based SMC. Our experimental evaluation demonstrates that our Bayesian SMC algorithm performs better both in terms of the verification time and the number of samples required to deduce satisfiability of a given HyperPCTL* formula.

Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference; because of the high-dimensional nature, however, one must often use approximate methods for this purpose. Belief propagation performs approximate inference, is efficient, and looks back on a long success-story. Yet, in most cases, belief propagation lacks any performance and convergence guarantees. Many realistic problems are presented by graphical models with loops, however, in which case belief propagation is neither guaranteed to provide accurate estimates nor that it converges at all. This thesis investigates how the model parameters influence the performance of belief propagation. We are particularly interested in their influence on (i) the number of fixed points, (ii) the convergence properties, and (iii) the approximation quality.

The estimation of coverage probabilities, and in particular of the missing mass, is a classical statistical problem with applications in numerous scientific fields. In this paper, we study this problem in relation to randomized data compression, or sketching. This is a novel but practically relevant perspective, and it refers to situations in which coverage probabilities must be estimated based on a compressed and imperfect summary, or sketch, of the true data, because neither the full data nor the empirical frequencies of distinct symbols can be observed directly. Our contribution is a Bayesian nonparametric methodology to estimate coverage probabilities from data sketched through random hashing, which also solves the challenging problems of recovering the numbers of distinct counts in the true data and of distinct counts with a specified empirical frequency of interest. The proposed Bayesian estimators are shown to be easily applicable to large-scale analyses in combination with a Dirichlet process prior, although they involve some open computational challenges under the more general Pitman-Yor process prior. The empirical effectiveness of our methodology is demonstrated through numerical experiments and applications to real data sets of Covid DNA sequences, classic English literature, and IP addresses.

Aided by advances in neural density estimation, considerable progress has been made in recent years towards a suite of simulation-based inference (SBI) methods capable of performing flexible, black-box, approximate Bayesian inference for stochastic simulation models. While it has been demonstrated that neural SBI methods can provide accurate posterior approximations, the simulation studies establishing these results have considered only well-specified problems -- that is, where the model and the data generating process coincide exactly. However, the behaviour of such algorithms in the case of model misspecification has received little attention. In this work, we provide the first comprehensive study of the behaviour of neural SBI algorithms in the presence of various forms of model misspecification. We find that misspecification can have a profoundly deleterious effect on performance. Some mitigation strategies are explored, but no approach tested prevents failure in all cases. We conclude that new approaches are required to address model misspecification if neural SBI algorithms are to be relied upon to derive accurate scientific conclusions.

Automated analysis of electron microscopy datasets poses multiple challenges, such as limitation in the size of the training dataset, variation in data distribution induced by variation in sample quality and experiment conditions, etc. It is crucial for the trained model to continue to provide acceptable segmentation/classification performance on new data, and quantify the uncertainty associated with its predictions. Among the broad applications of machine learning, various approaches have been adopted to quantify uncertainty, such as Bayesian modeling, Monte Carlo dropout, ensembles, etc. With the aim of addressing the challenges specific to the data domain of electron microscopy, two different types of ensembles of pre-trained neural networks were implemented in this work. The ensembles performed semantic segmentation of ice crystal within a two-phase mixture, thereby tracking its phase transformation to water. The first ensemble (EA) is composed of U-net style networks having different underlying architectures, whereas the second series of ensembles (ER-i) are composed of randomly initialized U-net style networks, wherein each base learner has the same underlying architecture 'i'. The encoders of the base learners were pre-trained on the Imagenet dataset. The performance of EA and ER were evaluated on three different metrics: accuracy, calibration, and uncertainty. It is seen that EA exhibits a greater classification accuracy and is better calibrated, as compared to ER. While the uncertainty quantification of these two types of ensembles are comparable, the uncertainty scores exhibited by ER were found to be dependent on the specific architecture of its base member ('i') and not consistently better than EA. Thus, the challenges posed for the analysis of electron microscopy datasets appear to be better addressed by an ensemble design like EA, as compared to an ensemble design like ER.

In a federated learning scenario where multiple parties jointly learn a model from their respective data, there exist two conflicting goals for the choice of appropriate algorithms. On one hand, private and sensitive training data must be kept secure as much as possible in the presence of \textit{semi-honest} partners, while on the other hand, a certain amount of information has to be exchanged among different parties for the sake of learning utility. Such a challenge calls for the privacy-preserving federated learning solution, which maximizes the utility of the learned model and maintains a provable privacy guarantee of participating parties' private data. This article illustrates a general framework that a) formulates the trade-off between privacy loss and utility loss from a unified information-theoretic point of view, and b) delineates quantitative bounds of privacy-utility trade-off when different protection mechanisms including Randomization, Sparsity, and Homomorphic Encryption are used. It was shown that in general \textit{there is no free lunch for the privacy-utility trade-off} and one has to trade the preserving of privacy with a certain degree of degraded utility. The quantitative analysis illustrated in this article may serve as the guidance for the design of practical federated learning algorithms.

Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens of dual-graph regularization, which has significantly improved the performance of multidisciplinary machine learning tasks such as recommendation systems, genotype imputation and image inpainting. While the dual-graph regularization contributes a major part of the success, computational costly hyper-parameter tunning is usually involved. To circumvent such a drawback and improve the completion performance, we propose a novel Bayesian learning algorithm that automatically learns the hyper-parameters associated with dual-graph regularization, and at the same time, guarantees the low-rankness of matrix completion. Notably, a novel prior is devised to promote the low-rankness of the matrix and encode the dual-graph information simultaneously, which is more challenging than the single-graph counterpart. A nontrivial conditional conjugacy between the proposed priors and likelihood function is then explored such that an efficient algorithm is derived under variational inference framework. Extensive experiments using synthetic and real-world datasets demonstrate the state-of-the-art performance of the proposed learning algorithm for various data analysis tasks.

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than Variational Inference, and it does not rely on adversarial training (or density ratio estimation). We adopt the recent approach of constructing two models: (1) a primary model, tasked with performing regression or classification; and (2) a secondary, expressive (e.g. implicit) model that defines an approximate posterior distribution over the parameters of the primary model. However, we optimise the parameters of the posterior model via gradient descent according to a Monte Carlo estimate of the posterior predictive distribution -- which is our only approximation (other than the posterior model). Only a likelihood needs to be specified, which can take various forms such as loss functions and synthetic likelihoods, thus providing a form of a likelihood-free approach. Furthermore, we formulate the approach such that the posterior samples can either be independent of, or conditionally dependent upon the inputs to the primary model. The latter approach is shown to be capable of increasing the apparent complexity of the primary model. We see this being useful in applications such as surrogate and physics-based models. To promote how the Bayesian paradigm offers more than just uncertainty quantification, we demonstrate: uncertainty quantification, multi-modality, as well as an application with a recent deep forecasting neural network architecture.