Learning from distributed data without accessing them is undoubtedly a challenging and non-trivial task. Nevertheless, the necessity for distributed training of a statistical model has been increasing, due to the privacy concerns of local data owners and the cost in centralizing the massively distributed data. Federated learning (FL) is currently the de facto standard of training a machine learning model across heterogeneous data owners, without leaving the raw data out of local silos. Nevertheless, several challenges must be addressed in order for FL to be more practical in reality. Among these challenges, the statistical heterogeneity problem is the most significant and requires immediate attention. From the main objective of FL, three major factors can be considered as starting points -- \textit{parameter}, textit{mixing coefficient}, and \textit{local data distributions}. In alignment with the components, this dissertation is organized into three parts. In Chapter II, a novel personalization method, \texttt{SuPerFed}, inspired by the mode-connectivity is introduced. In Chapter III, an adaptive decision-making algorithm, \texttt{AAggFF}, is introduced for inducing uniform performance distributions in participating clients, which is realized by online convex optimization framework. Finally, in Chapter IV, a collaborative synthetic data generation method, \texttt{FedEvg}, is introduced, leveraging the flexibility and compositionality of an energy-based modeling approach. Taken together, all of these approaches provide practical solutions to mitigate the statistical heterogeneity problem in data-decentralized settings, paving the way for distributed systems and applications using collaborative machine learning methods.

Purpose: Artificial intelligence (AI) techniques have been extensively utilized for diagnosing and prognosis of several diseases in recent years. This study identifies, appraises and synthesizes published studies on the use of AI for the prognosis of COVID-19. Method: Electronic search was performed using Medline, Google Scholar, Scopus, Embase, Cochrane and ProQuest. Studies that examined machine learning or deep learning methods to determine the prognosis of COVID-19 using CT or chest X-ray images were included. Polled sensitivity, specificity area under the curve and diagnostic odds ratio were calculated. Result: A total of 36 articles were included; various prognosis-related issues, including disease severity, mechanical ventilation or admission to the intensive care unit and mortality, were investigated. Several AI models and architectures were employed, such as the Siamense model, support vector machine, Random Forest , eXtreme Gradient Boosting, and convolutional neural networks. The models achieved 71%, 88% and 67% sensitivity for mortality, severity assessment and need for ventilation, respectively. The specificity of 69%, 89% and 89% were reported for the aforementioned variables. Conclusion: Based on the included articles, machine learning and deep learning methods used for the prognosis of COVID-19 patients using radiomic features from CT or CXR images can help clinicians manage patients and allocate resources more effectively. These studies also demonstrate that combining patient demographic, clinical data, laboratory tests and radiomic features improves model performances.

This study investigates different approaches to classify human interactions in an artificial intelligence-based environment, specifically for Applus+ IDIADA's intelligent agent AIDA. The main objective is to develop a classifier that accurately identifies the type of interaction received (Conversation, Services, or Document Translation) to direct requests to the appropriate channel and provide a more specialized and efficient service. Various models are compared, including LLM-based classifiers, KNN using Titan and Cohere embeddings, SVM, and artificial neural networks. Results show that SVM and ANN models with Cohere embeddings achieve the best overall performance, with superior F1 scores and faster execution times compared to LLM-based approaches. The study concludes that the SVM model with Cohere embeddings is the most suitable option for classifying human interactions in the AIDA environment, offering an optimal balance between accuracy and computational efficiency.

We introduce MOSCITO (MOlecular Dynamics Subspace Clustering with Temporal Observance), a subspace clustering for molecular dynamics data. MOSCITO groups those timesteps of a molecular dynamics trajectory together into clusters in which the molecule has similar conformations. In contrast to state-of-the-art methods, MOSCITO takes advantage of sequential relationships found in time series data. Unlike existing work, MOSCITO does not need a two-step procedure with tedious post-processing, but directly models essential properties of the data. Interpreting clusters as Markov states allows us to evaluate the clustering performance based on the resulting Markov state models. In experiments on 60 trajectories and 4 different proteins, we show that the performance of MOSCITO achieves state-of-the-art performance in a novel single-step method. Moreover, by modeling temporal aspects, MOSCITO obtains better segmentation of trajectories, especially for small numbers of clusters.

Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample paths of GPs is of interest. As GP sampling requires generating high-dimensional Gaussian random vectors, it is computationally challenging if a direct method, such as the Cholesky decomposition, is used. In this paper, we propose a scalable algorithm for sampling random realizations of the prior and posterior of GP models. The proposed algorithm leverages inducing points approximation with sparse grids, as well as additive Schwarz preconditioners, which reduce computational complexity, and ensure fast convergence. We demonstrate the efficacy and accuracy of the proposed method through a series of experiments and comparisons with other recent works.

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an It\^o equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. EFI involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. EFI also provides an innovative framework for semi-supervised learning.

This paper is about the recent notion of computably probably approximately correct learning, which lies between the statistical learning theory where there is no computational requirement on the learner and efficient PAC where the learner must be polynomially bounded. Examples have recently been given of hypothesis classes which are PAC learnable but not computably PAC learnable, but these hypothesis classes are unnatural or non-canonical in the sense that they depend on a numbering of proofs, formulas, or programs. We use the on-a-cone machinery from computability theory to prove that, under mild assumptions such as that the hypothesis class can be computably listable, any natural hypothesis class which is learnable must be computably learnable. Thus the counterexamples given previously are necessarily unnatural.

In recent studies, line search methods have been demonstrated to significantly enhance the performance of conventional stochastic gradient descent techniques across various datasets and architectures, while making an otherwise critical choice of learning rate schedule superfluous. In this paper, we identify problems of current state-of-the-art of line search methods, propose enhancements, and rigorously assess their effectiveness. Furthermore, we evaluate these methods on orders of magnitude larger datasets and more complex data domains than previously done. More specifically, we enhance the Armijo line search method by speeding up its computation and incorporating a momentum term into the Armijo criterion, making it better suited for stochastic mini-batching. Our optimization approach outperforms both the previous Armijo implementation and a tuned learning rate schedule for the Adam and SGD optimizers. Our evaluation covers a diverse range of architectures, such as Transformers, CNNs, and MLPs, as well as data domains, including NLP and image data. Our work is publicly available as a Python package, which provides a simple Pytorch optimizer.

The rapid evolution of multimedia and computer vision technologies requires adaptive visual model deployment strategies to effectively handle diverse tasks and varying environments. This work introduces AxiomVision, a novel framework that can guarantee accuracy by leveraging edge computing to dynamically select the most efficient visual models for video analytics under diverse scenarios. Utilizing a tiered edge-cloud architecture, AxiomVision enables the deployment of a broad spectrum of visual models, from lightweight to complex DNNs, that can be tailored to specific scenarios while considering camera source impacts. In addition, AxiomVision provides three core innovations: (1) a dynamic visual model selection mechanism utilizing continual online learning, (2) an efficient online method that efficiently takes into account the influence of the camera's perspective, and (3) a topology-driven grouping approach that accelerates the model selection process. With rigorous theoretical guarantees, these advancements provide a scalable and effective solution for visual tasks inherent to multimedia systems, such as object detection, classification, and counting. Empirically, AxiomVision achieves a 25.7\% improvement in accuracy.