In this paper, we investigate the use of probabilistic graphical models, specifically stochastic blockmodels, for the purpose of hierarchical entity clustering on knowledge graphs. These models, seldom used in the Semantic Web community, decompose a graph into a set of probability distributions. The parameters of these distributions are then inferred allowing for their subsequent sampling to generate a random graph. In a non-parametric setting, this allows for the induction of hierarchical clusterings without prior constraints on the hierarchy's structure. Specifically, this is achieved by the integration of the Nested Chinese Restaurant Process and the Stick Breaking Process into the generative model. In this regard, we propose a model leveraging such integration and derive a collapsed Gibbs sampling scheme for its inference. To aid in understanding, we describe the steps in this derivation and provide an implementation for the sampler. We evaluate our model on synthetic and real-world datasets and quantitatively compare against benchmark models. We further evaluate our results qualitatively and find that our model is capable of inducing coherent cluster hierarchies in small scale settings. The work presented in this paper provides the first step for the further application of stochastic blockmodels for knowledge graphs on a larger scale. We conclude the paper with potential avenues for future work on more scalable inference schemes.

This thesis investigates three areas targeted at improving the reliability of machine learning; fairness in machine learning, strategic classification, and algorithmic robustness. Each of these domains has special properties or structure that can complicate learning. A theme throughout this thesis is thinking about ways in which a'plain' empirical risk minimization algorithm will be misleading or ineffective because of a mis-match between classical learning theory assumptions and specific properties of some data distribution in the wild. The overarching research goal for these related topics is to provide a crisp mathematical model for each learning scenario that exposes different failure modes and makes trade-offs between important metrics explicit in order to provide algorithmic advice or recommendations to practitioners and expose gaps for future research. By tuning our learning algorithms to be more distribution specific in these scenarios, the resulting learned system will exhibit higher utility and avoid catastrophic failure modes. This research is grounded in the theory of machine learning and is fundamentally mathematical in nature, with empirical support when appropriate. Theory is particularly important in these sensitive domains as it is unclear which poor behavior in deployed systems is a natural or benign consequence of a learning system with the underlying distribution,contrasting with problematic but correctable behavior caused by an error in algorithm design or implementation, how to mitigate these issues, or what a successful outcome even looks like in each problem. Theoretical understanding in each domain can help guide best practices and allow for the design of effective, reliable, and robust systems.

Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient machine learning applications. Recent research has focused on proposing efficient methods with provable convergence guarantees. However, while many prior works have established convergence to stationary points or local minima, obtaining the global optimum of bilevel optimization remains an important yet open problem. The difficulty lies in the fact that unlike many prior non-convex single-level problems, this bilevel problem does not admit a ``benign" landscape, and may indeed have multiple spurious local solutions. Nevertheless, attaining the global optimality is indispensable for ensuring reliability, safety, and cost-effectiveness, particularly in high-stakes engineering applications that rely on bilevel optimization. In this paper, we first explore the challenges of establishing a global convergence theory for bilevel optimization, and present two sufficient conditions for global convergence. We provide algorithm-specific proofs to rigorously substantiate these sufficient conditions along the optimization trajectory, focusing on two specific bilevel learning scenarios: representation learning and data hypercleaning (a.k.a. reweighting). Experiments corroborate the theoretical findings, demonstrating convergence to global minimum in both cases.

Time series forecasting requires balancing short-term and long-term dependencies for accurate predictions. Existing methods mainly focus on long-term dependency modeling, neglecting the complexities of short-term dynamics, which may hinder performance. Transformers are superior in modeling long-term dependencies but are criticized for their quadratic computational cost. Mamba provides a near-linear alternative but is reported less effective in time series longterm forecasting due to potential information loss. Current architectures fall short in offering both high efficiency and strong performance for long-term dependency modeling. To address these challenges, we introduce Mixture of Universals (MoU), a versatile model to capture both short-term and long-term dependencies for enhancing performance in time series forecasting. MoU is composed of two novel designs: Mixture of Feature Extractors (MoF), an adaptive method designed to improve time series patch representations for short-term dependency, and Mixture of Architectures (MoA), which hierarchically integrates Mamba, FeedForward, Convolution, and Self-Attention architectures in a specialized order to model long-term dependency from a hybrid perspective. The proposed approach achieves state-of-the-art performance while maintaining relatively low computational costs. Extensive experiments on seven real-world datasets demonstrate the superiority of MoU. Code is available at https://github.com/lunaaa95/mou/.

The proliferation of interconnected devices in the Internet of Things (IoT) has led to an exponential increase in data, commonly known as Big IoT Data. Efficient retrieval of this heterogeneous data demands a robust indexing mechanism for effective organization. However, a significant challenge remains: the overlap in data space partitions during index construction. This overlap increases node access during search and retrieval, resulting in higher resource consumption, performance bottlenecks, and impedes system scalability. To address this issue, we propose three innovative heuristics designed to quantify and strategically reduce data space partition overlap. The volume-based method (VBM) offers a detailed assessment by calculating the intersection volume between partitions, providing deeper insights into spatial relationships. The distance-based method (DBM) enhances efficiency by using the distance between partition centers and radii to evaluate overlap, offering a streamlined yet accurate approach. Finally, the object-based method (OBM) provides a practical solution by counting objects across multiple partitions, delivering an intuitive understanding of data space dynamics. Experimental results demonstrate the effectiveness of these methods in reducing search time, underscoring their potential to improve data space partitioning and enhance overall system performance.

Stochastic gradient descent (SGD) has proven effective in solving many inventory control problems with demand learning. However, it often faces the pitfall of an infeasible target inventory level that is lower than the current inventory level. Several recent works (e.g., Huh and Rusmevichientong (2009), Shi et al.(2016)) are successful to resolve this issue in various inventory systems. However, their techniques are rather sophisticated and difficult to be applied to more complicated scenarios such as multi-product and multi-constraint inventory systems. In this paper, we address the infeasible-target-inventory-level issue from a new technical perspective -- we propose a novel minibatch-SGD-based meta-policy. Our meta-policy is flexible enough to be applied to a general inventory systems framework covering a wide range of inventory management problems with myopic clairvoyant optimal policy. By devising the optimal minibatch scheme, our meta-policy achieves a regret bound of $\mathcal{O}(\sqrt{T})$ for the general convex case and $\mathcal{O}(\log T)$ for the strongly convex case. To demonstrate the power and flexibility of our meta-policy, we apply it to three important inventory control problems: multi-product and multi-constraint systems, multi-echelon serial systems, and one-warehouse and multi-store systems by carefully designing application-specific subroutines.We also conduct extensive numerical experiments to demonstrate that our meta-policy enjoys competitive regret performance, high computational efficiency, and low variances among a wide range of applications.

The detection of cyber-attacks in computer networks is a crucial and ongoing research challenge. Machine learning-based attack classification offers a promising solution, as these models can be continuously updated with new data, enhancing the effectiveness of network intrusion detection systems (NIDS). Unlike binary classification models that simply indicate the presence of an attack, multi-class models can identify specific types of attacks, allowing for more targeted and effective incident responses. However, a significant drawback of these classification models is their sensitivity to imbalanced training data. Recent advances suggest that generative models can assist in data augmentation, claiming to offer superior solutions for imbalanced datasets. Classical balancing methods, although less novel, also provide potential remedies for this issue. Despite these claims, a comprehensive comparison of these methods within the NIDS domain is lacking. Most existing studies focus narrowly on individual methods, making it difficult to compare results due to varying experimental setups. To close this gap, we designed a systematic framework to compare classical and generative resampling methods for class balancing across multiple popular classification models in the NIDS domain, evaluated on several NIDS benchmark datasets. Our experiments indicate that resampling methods for balancing training data do not reliably improve classification performance. Although some instances show performance improvements, the majority of results indicate decreased performance, with no consistent trend in favor of a specific resampling technique enhancing a particular classifier.

Detecting and attributing temperature increases due to climate change is crucial for understanding global warming and guiding adaptation strategies. The complexity of distinguishing human-induced climate signals from natural variability has challenged traditional detection and attribution (D&A) approaches, which seek to identify specific "fingerprints" in climate response variables. Deep learning offers potential for discerning these complex patterns in expansive spatial datasets. However, lack of standard protocols has hindered consistent comparisons across studies. We introduce ClimDetect, a standardized dataset of over 816k daily climate snapshots, designed to enhance model accuracy in identifying climate change signals. ClimDetect integrates various input and target variables used in past research, ensuring comparability and consistency. We also explore the application of vision transformers (ViT) to climate data, a novel and modernizing approach in this context. Our open-access data and code serve as a benchmark for advancing climate science through improved model evaluations.

This paper introduces a group of novel datasets representing real-time time-series and streaming data of energy prices in New Zealand, sourced from the Electricity Market Information (EMI) website maintained by the New Zealand government. The datasets are intended to address the scarcity of proper datasets for streaming regression learning tasks. We conduct extensive analyses and experiments on these datasets, covering preprocessing techniques, regression tasks, prediction intervals, concept drift detection, and anomaly detection. Our experiments demonstrate the datasets' utility and highlight the challenges and opportunities for future research in energy price forecasting.

Domain Adaptation or Transfer Learning refer generally to the problem of harnessing data from a source distribution P to improve prediction performance w.r.t. to a target distribution Q for which some or no data is available. This problem has been researched over the last few decades with a recent resurgence in interest driven by modern applications that are often characterized by a scarcity of perfect target data. A fundamental question in the theory of domain adaptation (and variant problems on distribution shifts) is how to measure the relatedness between source P and target Q distributions. Importantly, desired measures of relatedness should not only tightly capture the predictive informationP has onQ, but have to be practically useful: that is, either the measure can be estimated from data to facilitate algorithmic design, or more generally, it should somehow admit adaptive procedures, i.e., procedures whose performance is adaptive to the a priori unknown level of relatedness between P and Q. Many notions have been proposed over the last few decades, starting with the seminal works of Mansour et al. [2009], Ben-David et al. [2010] on refinements of total-variation for domain adaptation in classification, to more recent proposals for domain adaptation in regression, e.g., Wasserstein distances Redko et al. [2017], Shen et al. [2018], or measures relating covariance structures across P and Q as in Mousavi Kalan et al. [2020], Zhang et al. [2022b], Ge et al. [2023]. These various notions of relatedness appear hard to compare at first glance, leading to a disparate theory of domain adaptation at present with no unified set of principles. Interestingly as we show, upon closer look at the existing literature--whether in classification or regression--it turns out that in fact, many seemingly distinct measures of relatedness proposed in domain adaptation actually implicitly bound the same fundamental quantities: we refer to these quantities as weak and strong moduli of transfer, and they roughly measure how fast the Q-risk of predictors decrease as their P -risk decreases. These moduli always yield as tight or tighter rates of transfer than many existing notions, while also admitting adaptive procedures in general settings, as shown via a reduction to the existence of certain confidence sets for the prediction problem at hand. These reductions, while of a theoretical nature, yield insights on general adaptive transfer approaches that are less tied to specific measures of relatedness between source P and target Q.