This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates centroids based on the mean of assigned points. This process continues until convergence, forming k clusters where each point belongs to the closest centroid. This research investigates the prediction of the last component of data points obtained from a distribution of clustered data using the online balanced k-means approach. Through extensive experimentation and analysis, key findings have emerged. It is observed that a larger number of clusters or partitions tends to yield lower errors while increasing the number of assigned data points does not significantly improve inference errors. Reducing losses in the learning process does not significantly impact overall inference errors. Indicating that as learning is going on inference errors remain unchanged. Recommendations include the need for specialized inference techniques to estimate better data points derived from multi-clustered data and exploring methods that yield improved results with larger assigned datasets. By addressing these recommendations, this research advances the accuracy and reliability of inferences made with the k-means algorithm, bridging the gap between clustering and non-parametric density estimation and inference.

The last decade in deep learning has brought on increasingly capable systems that are deployed on a wide variety of applications. In natural language processing, the field has been transformed by a number of breakthroughs including large language models, which are used in increasingly many user-facing applications. In order to reap the benefits of this technology and reduce potential harms, it is important to quantify the reliability of model predictions and the uncertainties that shroud their development. This thesis studies how uncertainty in natural language processing can be characterized from a linguistic, statistical and neural perspective, and how it can be reduced and quantified through the design of the experimental pipeline. We further explore uncertainty quantification in modeling by theoretically and empirically investigating the effect of inductive model biases in text classification tasks. The corresponding experiments include data for three different languages (Danish, English and Finnish) and tasks as well as a large set of different uncertainty quantification approaches. Additionally, we propose a method for calibrated sampling in natural language generation based on non-exchangeable conformal prediction, which provides tighter token sets with better coverage of the actual continuation. Lastly, we develop an approach to quantify confidence in large black-box language models using auxiliary predictors, where the confidence is predicted from the input to and generated output text of the target model alone.

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

Although binary classification is a well-studied problem, training reliable classifiers under severe class imbalance remains a challenge. Recent techniques mitigate the ill effects of imbalance on training by modifying the loss functions or optimization methods. We observe that different hyperparameter values on these loss functions perform better at different recall values. We propose to exploit this fact by training one model over a distribution of hyperparameter values-instead of a single value-via Loss Conditional Training (LCT). Experiments show that training over a distribution of hyperparameters not only approximates the performance of several models but actually improves the overall performance of models on both CIFAR and real medical imaging applications, such as melanoma and diabetic retinopathy detection. Furthermore, training models with LCT is more efficient because some hyperparameter tuning can be conducted after training to meet individual needs without needing to retrain from scratch. Consider a classifier that takes images of skin lesions and predicts whether they are melanoma or benign (Rotemberg et al., 2020). Such a system could be especially valuable in underdeveloped countries where expert resources for screening are scarce (Cassidy et al., 2022). The dataset for this problem, along with many other practical problems, is inherently imbalanced (i.e., there are far more benign samples than melanoma samples). Furthermore, there are un-even costs associated with misclassifying the two classes because predicting a benign lesion as melanoma would result in the cost of a biopsy while predicting a melanoma lesion as benign could result in the melanoma spreading before the patient can receive appropriate treatment. Unfortunately, the exact difference in the misclassification costs may not be known a priori and may even change after deployment. For example, the costs may change depending on the amount of biopsy resources available or the prior may change depending on the age and condition of the patient. Thus, a good classifier for this problem should (a) have good performance across a wide range of Precision-Recall tradeoffs and (b) be able to adapt to changes in the prior or misclassification costs.

Human agents routinely reason on instances with incomplete and muddied data (and weigh the cost of obtaining further features). In contrast, much of ML is devoted to the unrealistic, sterile environment where all features are observed and further information on an instance is obviated. Here we extend past static ML and develop an active feature acquisition (AFA) framework that interacts with the environment to obtain new information on-the-fly and can: 1) make inferences on an instance in the face of incomplete features, 2) determine a plan for feature acquisitions to obtain additional information on the instance at hand. We build our AFA framework on a backbone of understanding the information and conditional dependencies that are present in the data. First, we show how to build generative models that can capture dependencies over arbitrary subsets of features and employ these models for acquisitions in a greedy scheme. After, we show that it is possible to guide the training of RL agents for AFA via side-information and auxiliary rewards stemming from our generative models. We also examine two important factors for deploying AFA models in real-world scenarios, namely interpretability and robustness. Extensive experiments demonstrate the state-of-the-art performance of our AFA framework.

Unsupervised Domain Adaptation (UDA) is crucial for reducing the need for extensive manual data annotation when training deep networks on point cloud data. A significant challenge of UDA lies in effectively bridging the domain gap. To tackle this challenge, we propose \textbf{C}urvature \textbf{D}iversity-Driven \textbf{N}uclear-Norm Wasserstein \textbf{D}omain Alignment (CDND). Our approach first introduces a \textit{\textbf{Curv}ature Diversity-driven Deformation \textbf{Rec}onstruction (CurvRec)} task, which effectively mitigates the gap between the source and target domains by enabling the model to extract salient features from semantically rich regions of a given point cloud. We then propose \textit{\textbf{D}eformation-based \textbf{N}uclear-norm \textbf{W}asserstein \textbf{D}iscrepancy (D-NWD)}, which applies the Nuclear-norm Wasserstein Discrepancy to both \textit{deformed and original} data samples to align the source and target domains. Furthermore, we contribute a theoretical justification for the effectiveness of D-NWD in distribution alignment and demonstrate that it is \textit{generic} enough to be applied to \textbf{any} deformations. To validate our method, we conduct extensive experiments on two public domain adaptation datasets for point cloud classification and segmentation tasks. Empirical experiment results show that our CDND achieves state-of-the-art performance by a noticeable margin over existing approaches.

Group fairness in machine learning is a critical area of research focused on achieving equitable outcomes across different groups defined by sensitive attributes such as race or gender. Federated learning, a decentralized approach to training machine learning models across multiple devices or organizations without sharing raw data, amplifies the need for fairness due to the heterogeneous data distributions across clients, which can exacerbate biases. The intersection of federated learning and group fairness has attracted significant interest, with 47 research works specifically dedicated to addressing this issue. However, no dedicated survey has focused comprehensively on group fairness in federated learning. In this work, we present an in-depth survey on this topic, addressing the critical challenges and reviewing related works in the field. We create a novel taxonomy of these approaches based on key criteria such as data partitioning, location, and applied strategies. Additionally, we explore broader concerns related to this problem and investigate how different approaches handle the complexities of various sensitive groups and their intersections. Finally, we review the datasets and applications commonly used in current research. We conclude by highlighting key areas for future research, emphasizing the need for more methods to address the complexities of achieving group fairness in federated systems.

We deal with the task of sampling from an unnormalized Boltzmann density $\rho_D$ by learning a Boltzmann curve given by energies $f_t$ starting in a simple density $\rho_Z$. First, we examine conditions under which Fisher-Rao flows are absolutely continuous in the Wasserstein geometry. Second, we address specific interpolations $f_t$ and the learning of the related density/velocity pairs $(\rho_t,v_t)$. It was numerically observed that the linear interpolation, which requires only a parametrization of the velocity field $v_t$, suffers from a "teleportation-of-mass" issue. Using tools from the Wasserstein geometry, we give an analytical example, where we can precisely measure the explosion of the velocity field. Inspired by M\'at\'e and Fleuret, who parametrize both $f_t$ and $v_t$, we propose an interpolation which parametrizes only $f_t$ and fixes an appropriate $v_t$. This corresponds to the Wasserstein gradient flow of the Kullback-Leibler divergence related to Langevin dynamics. We demonstrate by numerical examples that our model provides a well-behaved flow field which successfully solves the above sampling task.

In various applications, the multivariate time series often suffers from missing data. This issue can significantly disrupt systems that rely on the data. Spatial and temporal dependencies can be leveraged to impute the missing samples. Existing imputation methods often ignore dynamic changes in spatial dependencies. We propose a Spatial Dynamic Aware Graph Recurrent Imputation Network (SDA-GRIN) which is capable of capturing dynamic changes in spatial dependencies.SDA-GRIN leverages a multi-head attention mechanism to adapt graph structures with time. SDA-GRIN models multivariate time series as a sequence of temporal graphs and uses a recurrent message-passing architecture for imputation. We evaluate SDA-GRIN on four real-world datasets: SDA-GRIN improves MSE by 9.51% for the AQI and 9.40% for AQI-36. On the PEMS-BAY dataset, it achieves a 1.94% improvement in MSE. Detailed ablation study demonstrates the effect of window sizes and missing data on the performance of the method. Project page:https://ameskandari.github.io/sda-grin/

The Prototypical Network (ProtoNet) has emerged as a popular choice in Few-shot Learning (FSL) scenarios due to its remarkable performance and straightforward implementation. Building upon such success, we first propose a simple (yet novel) method to fine-tune a ProtoNet on the (labeled) support set of the test episode of a C-way-K-shot test episode (without using the query set which is only used for evaluation). We then propose an algorithmic framework that combines ProtoNet with optimization-based FSL algorithms (MAML and Meta-Curvature) to work with such a fine-tuning method. Since optimization-based algorithms endow the target learner model with the ability to fast adaption to only a few samples, we utilize ProtoNet as the target model to enhance its fine-tuning performance with the help of a specifically designed episodic fine-tuning strategy. The experimental results confirm that our proposed models, MAML-Proto and MC-Proto, combined with our unique fine-tuning method, outperform regular ProtoNet by a large margin in few-shot audio classification tasks on the ESC-50 and Speech Commands v2 datasets. We note that although we have only applied our model to the audio domain, it is a general method and can be easily extended to other domains.