The application of kernel-based Machine Learning (ML) techniques to discrete choice modelling using large datasets often faces challenges due to memory requirements and the considerable number of parameters involved in these models. This complexity hampers the efficient training of large-scale models. This paper addresses these problems of scalability by introducing the Nystr\"om approximation for Kernel Logistic Regression (KLR) on large datasets. The study begins by presenting a theoretical analysis in which: i) the set of KLR solutions is characterised, ii) an upper bound to the solution of KLR with Nystr\"om approximation is provided, and finally iii) a specialisation of the optimisation algorithms to Nystr\"om KLR is described. After this, the Nystr\"om KLR is computationally validated. Four landmark selection methods are tested, including basic uniform sampling, a k-means sampling strategy, and two non-uniform methods grounded in leverage scores. The performance of these strategies is evaluated using large-scale transport mode choice datasets and is compared with traditional methods such as Multinomial Logit (MNL) and contemporary ML techniques. The study also assesses the efficiency of various optimisation techniques for the proposed Nystr\"om KLR model. The performance of gradient descent, Momentum, Adam, and L-BFGS-B optimisation methods is examined on these datasets. Among these strategies, the k-means Nystr\"om KLR approach emerges as a successful solution for applying KLR to large datasets, particularly when combined with the L-BFGS-B and Adam optimisation methods. The results highlight the ability of this strategy to handle datasets exceeding 200,000 observations while maintaining robust performance.

We study the problem of symmetric matrix completion, where the goal is to reconstruct a positive semidefinite matrix $\rm{X}^\star \in \mathbb{R}^{d\times d}$ of rank-$r$, parameterized by $\rm{U}\rm{U}^{\top}$, from only a subset of its observed entries. We show that the vanilla gradient descent (GD) with small initialization provably converges to the ground truth $\rm{X}^\star$ without requiring any explicit regularization. This convergence result holds true even in the over-parameterized scenario, where the true rank $r$ is unknown and conservatively over-estimated by a search rank $r'\gg r$. The existing results for this problem either require explicit regularization, a sufficiently accurate initial point, or exact knowledge of the true rank $r$. In the over-parameterized regime where $r'\geq r$, we show that, with $\widetilde\Omega(dr^9)$ observations, GD with an initial point $\|\rm{U}_0\| \leq \epsilon$ converges near-linearly to an $\epsilon$-neighborhood of $\rm{X}^\star$. Consequently, smaller initial points result in increasingly accurate solutions. Surprisingly, neither the convergence rate nor the final accuracy depends on the over-parameterized search rank $r'$, and they are only governed by the true rank $r$. In the exactly-parameterized regime where $r'=r$, we further enhance this result by proving that GD converges at a faster rate to achieve an arbitrarily small accuracy $\epsilon>0$, provided the initial point satisfies $\|\rm{U}_0\| = O(1/d)$. At the crux of our method lies a novel weakly-coupled leave-one-out analysis, which allows us to establish the global convergence of GD, extending beyond what was previously possible using the classical leave-one-out analysis.

Self-supervised Learning (SSL) has emerged as a powerful technique in pre-training deep learning models without relying on expensive annotated labels, instead leveraging embedded signals in unlabeled data. While SSL has shown remarkable success in computer vision tasks through intuitive data augmentation, its application to graph-structured data poses challenges due to the semantic-altering and counter-intuitive nature of graph augmentations. Addressing this limitation, this paper introduces a novel non-contrastive SSL approach to Explicitly Generate a compositional Relation Graph (ExGRG) instead of relying solely on the conventional augmentation-based implicit relation graph. ExGRG offers a framework for incorporating prior domain knowledge and online extracted information into the SSL invariance objective, drawing inspiration from the Laplacian Eigenmap and Expectation-Maximization (EM). Employing an EM perspective on SSL, our E-step involves relation graph generation to identify candidates to guide the SSL invariance objective, and M-step updates the model parameters by integrating the derived relational information. Extensive experimentation on diverse node classification datasets demonstrates the superiority of our method over state-of-the-art techniques, affirming ExGRG as an effective adoption of SSL for graph representation learning.

We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$ points $P$ in a metric space, let $\delta(x)$ for $x\in P$ be the radius of the smallest ball around $x$ containing at least $n / k$ points. A clustering is then called individually fair if it has centers within distance $\delta(x)$ of $x$ for each $x\in P$. While good approximation algorithms are known for this problem no efficient practical algorithms with good theoretical guarantees have been presented. We design the first fast local-search algorithm that runs in ~$O(nk^2)$ time and obtains a bicriteria $(O(1), 6)$ approximation. Then we show empirically that not only is our algorithm much faster than prior work, but it also produces lower-cost solutions.

The continuing deployment of renewables and battery energy storage systems is likely to lead to increased price volatility Martinez-Anido et al. (2016); Eurostat (2022). The Balancing Market (BM) is the last stage for trading electric energy, exhibiting far higher volatility compared to both the Day-Ahead Market (DAM) and Intra Day Market (IDM). It plays an essential role (in particular in regions where storage of large quantities of electric energy is not economically convenient Mazzi & Pinson (2017)) as production and consumption levels must match during the operation of electric power systems. The growing importance of accurate forecasts of BM prices to participants is outlined in Ortner & Totschnig (2019), where forecast errors of variable renewable electricity will drive demand for BM participation. Historically, the focus on the DAM is intuitive, given that it is a cornerstone of the European electricity market. In addition, the datasets required for forecasting the DAM are widely available. The lack of analysis of the BM is likely the result of a combination of factors including not all jurisdictions having a BM, the rules governing it can differ from region to region and the identification and acquisition of the relevant datasets can be complicated and expensive (with no open access dataset). In recent years, given access to additional datasets and increasing GPU speeds, the application of Deep Learning (DL) models has become an attractive option.

Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path distance. However, stress optimization presents computational challenges due to its inherent complexity and is usually solved using heuristics in practice. We introduce a scalable Graph Neural Network (GNN) based Graph Drawing framework with sub-quadratic runtime that can learn to optimize stress. Inspired by classical stress optimization techniques and force-directed layout algorithms, we create a coarsening hierarchy for the input graph. Beginning at the coarsest level, we iteratively refine and un-coarsen the layout, until we generate an embedding for the original graph. To enhance information propagation within the network, we propose a novel positional rewiring technique based on intermediate node positions. Our empirical evaluation demonstrates that the framework achieves state-of-the-art performance while remaining scalable.

Private selection mechanisms (e.g., Report Noisy Max, Sparse Vector) are fundamental primitives of differentially private (DP) data analysis with wide applications to private query release, voting, and hyperparameter tuning. Recent work (Liu and Talwar, 2019; Papernot and Steinke, 2022) has made significant progress in both generalizing private selection mechanisms and tightening their privacy analysis using modern numerical privacy accounting tools, e.g., R\'enyi DP. But R\'enyi DP is known to be lossy when $(\epsilon,\delta)$-DP is ultimately needed, and there is a trend to close the gap by directly handling privacy profiles, i.e., $\delta$ as a function of $\epsilon$ or its equivalent dual form known as $f$-DPs. In this paper, we work out an easy-to-use recipe that bounds the privacy profiles of ReportNoisyMax and PrivateTuning using the privacy profiles of the base algorithms they corral. Numerically, our approach improves over the RDP-based accounting in all regimes of interest and leads to substantial benefits in end-to-end private learning experiments. Our analysis also suggests new distributions, e.g., binomial distribution for randomizing the number of rounds that leads to more substantial improvements in certain regimes.

The rise of IoT devices has prompted the demand for deploying machine learning at-the-edge with real-time, efficient, and secure data processing. In this context, implementing machine learning (ML) models with real-valued weight parameters can prove to be impractical particularly for large models, and there is a need to train models with quantized discrete weights. At the same time, these low-dimensional models also need to preserve privacy of the underlying dataset. In this work, we present RQP-SGD, a new approach for privacy-preserving quantization to train machine learning models for low-memory ML-at-the-edge. This approach combines differentially private stochastic gradient descent (DP-SGD) with randomized quantization, providing a measurable privacy guarantee in machine learning. In particular, we study the utility convergence of implementing RQP-SGD on ML tasks with convex objectives and quantization constraints and demonstrate its efficacy over deterministic quantization. Through experiments conducted on two datasets, we show the practical effectiveness of RQP-SGD.

Semantic segmentation is a key prerequisite to robust image understanding for applications in \acrlong{ai} and Robotics. \acrlong{fss}, in particular, concerns the extension and optimization of traditional segmentation methods in challenging conditions where limited training examples are available. A predominant approach in \acrlong{fss} is to rely on a single backbone for visual feature extraction. Choosing which backbone to leverage is a deciding factor contributing to the overall performance. In this work, we interrogate on whether fusing features from different backbones can improve the ability of \acrlong{fss} models to capture richer visual features. To tackle this question, we propose and compare two ensembling techniques-Independent Voting and Feature Fusion. Among the available \acrlong{fss} methods, we implement the proposed ensembling techniques on PANet. The module dedicated to predicting segmentation masks from the backbone embeddings in PANet avoids trainable parameters, creating a controlled `in vitro' setting for isolating the impact of different ensembling strategies. Leveraging the complementary strengths of different backbones, our approach outperforms the original single-backbone PANet across standard benchmarks even in challenging one-shot learning scenarios. Specifically, it achieved a performance improvement of +7.37\% on PASCAL-5\textsuperscript{i} and of +10.68\% on COCO-20\textsuperscript{i} in the top-performing scenario where three backbones are combined. These results, together with the qualitative inspection of the predicted subject masks, suggest that relying on multiple backbones in PANet leads to a more comprehensive feature representation, thus expediting the successful application of \acrlong{fss} methods in challenging, data-scarce environments.

Electronic patient records (EPRs) produce a wealth of data but contain significant missing information. Understanding and handling this missing data is an important part of clinical data analysis and if left unaddressed could result in bias in analysis and distortion in critical conclusions. Missing data may be linked to health care professional practice patterns and imputation of missing data can increase the validity of clinical decisions. This study focuses on statistical approaches for understanding and interpreting the missing data and machine learning based clinical data imputation using a single centre's paediatric emergency data and the data from UK's largest clinical audit for traumatic injury database (TARN). In the study of 56,961 data points related to initial vital signs and observations taken on children presenting to an Emergency Department, we have shown that missing data are likely to be non-random and how these are linked to health care professional practice patterns. We have then examined 79 TARN fields with missing values for 5,791 trauma cases. Singular Value Decomposition (SVD) and k-Nearest Neighbour (kNN) based missing data imputation methods are used and imputation results against the original dataset are compared and statistically tested. We have concluded that the 1NN imputer is the best imputation which indicates a usual pattern of clinical decision making: find the most similar patients and take their attributes as imputation.