Dual Coordinate Descent (DCD) and Block Dual Coordinate Descent (BDCD) are important iterative methods for solving convex optimization problems. In this work, we develop scalable DCD and BDCD methods for the kernel support vector machines (K-SVM) and kernel ridge regression (K-RR) problems. On distributed-memory parallel machines the scalability of these methods is limited by the need to communicate every iteration. On modern hardware where communication is orders of magnitude more expensive, the running time of the DCD and BDCD methods is dominated by communication cost. We address this communication bottleneck by deriving $s$-step variants of DCD and BDCD for solving the K-SVM and K-RR problems, respectively. The $s$-step variants reduce the frequency of communication by a tunable factor of $s$ at the expense of additional bandwidth and computation. The $s$-step variants compute the same solution as the existing methods in exact arithmetic. We perform numerical experiments to illustrate that the $s$-step variants are also numerically stable in finite-arithmetic, even for large values of $s$. We perform theoretical analysis to bound the computation and communication costs of the newly designed variants, up to leading order. Finally, we develop high performance implementations written in C and MPI and present scaling experiments performed on a Cray EX cluster. The new $s$-step variants achieved strong scaling speedups of up to $9.8\times$ over existing methods using up to $512$ cores.

When studying ecosystems, hierarchical trees are often used to organize entities based on proximity criteria, such as the taxonomy in microbiology, social classes in geography, or product types in retail businesses, offering valuable insights into entity relationships. Despite their significance, current count-data models do not leverage this structured information. In particular, the widely used Poisson log-normal (PLN) model, known for its ability to model interactions between entities from count data, lacks the possibility to incorporate such hierarchical tree structures, limiting its applicability in domains characterized by such complexities. To address this matter, we introduce the PLN-Tree model as an extension of the PLN model, specifically designed for modeling hierarchical count data. By integrating structured variational inference techniques, we propose an adapted training procedure and establish identifiability results, enhancisng both theoretical foundations and practical interpretability. Additionally, we extend our framework to classification tasks as a preprocessing pipeline, showcasing its versatility. Experimental evaluations on synthetic datasets as well as real-world microbiome data demonstrate the superior performance of the PLN-Tree model in capturing hierarchical dependencies and providing valuable insights into complex data structures, showing the practical interest of knowledge graphs like the taxonomy in ecosystems modeling.

Personalized medicine is expected to advance healthcare in the near future [Vicente et al., 2020]. In contrast to a one-size-fits-all approach, personalized medicine advocates for treatments tailored to individual patients based on their clinical characteristics. Responder analysis in clinical trials is a method used to evaluate the effectiveness of a treatment by identifying and analyzing the subset of participants who respond significantly to the treatment [Henschke et al., 2014]. This approach contrasts with the traditional method of evaluating average effects across all participants, which can sometimes obscure the benefits seen in a particular group of responders [Guyatt et al., 1998]. This approach is particularly important in trials with heterogeneous treatment effects, where understanding individual responses can lead to more effective therapies. Responder analysis is a common practice in clinical trials [Moore et al., 2010, Straube et al., 2010, Chuang et al., 2022].

The scope for the accurate calculation of the Loss Given Default (LGD) parameter is comprehensive in terms of financial data. In this research, we aim to explore methods for improving the approximation of realized LGD in conditions of limited access to the cash-flow data. We enhance the performance of the method which relies on the differences between exposure values (delta outstanding approach) by employing machine learning (ML) techniques. The research utilizes the data from the mortgage portfolio of one of the European countries and assumes a close resemblance to similar economic contexts. It incorporates non-financial variables and macroeconomic data related to the housing market, improving the accuracy of loss severity approximation. The proposed methodology attempts to mitigate the country-specific (related to the local legal) or portfolio-specific factors in aim to show the general advantage of applying ML techniques, rather than case-specific relation. We developed an XGBoost model that does not rely on cash-flow data yet enhances the accuracy of realized LGD estimation compared to results obtained with the delta outstanding approach. A novel aspect of our work is the detailed exploration of the delta outstanding approach and the methodology for addressing conditions of limited access to cash-flow data through machine learning models.

This paper investigates the problem of regression model generation. A model is a superposition of primitive functions. The model structure is described by a weighted colored graph. Each graph vertex corresponds to some primitive function. An edge assigns a superposition of two functions. The weight of an edge equals the probability of superposition. To generate an optimal model one has to reconstruct its structure from its graph adjacency matrix. The proposed algorithm reconstructs the~minimum spanning tree from the~weighted colored graph. This paper presents a novel solution based on the prize-collecting Steiner tree algorithm. This algorithm is compared with its alternatives.

Bandits with preference feedback present a powerful tool for optimizing unknown target functions when only pairwise comparisons are allowed instead of direct value queries. This model allows for incorporating human feedback into online inference and optimization and has been employed in systems for fine-tuning large language models. The problem is well understood in simplified settings with linear target functions or over finite small domains that limit practical interest. Taking the next step, we consider infinite domains and nonlinear (kernelized) rewards. In this setting, selecting a pair of actions is quite challenging and requires balancing exploration and exploitation at two levels: within the pair, and along the iterations of the algorithm. We propose MAXMINLCB, which emulates this trade-off as a zero-sum Stackelberg game, and chooses action pairs that are informative and yield favorable rewards. MAXMINLCB consistently outperforms existing algorithms and satisfies an anytime-valid rate-optimal regret guarantee. This is due to our novel preference-based confidence sequences for kernelized logistic estimators.

Local intrinsic dimension (LID) estimation methods have received a lot of attention in recent years thanks to the progress in deep neural networks and generative modeling. In opposition to old non-parametric methods, new methods use generative models to approximate diffused dataset density and scale the methods to high-dimensional datasets like images. In this paper, we investigate the recent state-of-the-art parametric LID estimation methods from the perspective of the Wiener process. We explore how these methods behave when their assumptions are not met. We give an extended mathematical description of those methods and their error as a function of the probability density of the data.

Continual learning (CL) has garnered significant attention because of its ability to adapt to new tasks that arrive over time. Catastrophic forgetting (of old tasks) has been identified as a major issue in CL, as the model adapts to new tasks. The Mixture-of-Experts (MoE) model has recently been shown to effectively mitigate catastrophic forgetting in CL, by employing a gating network to sparsify and distribute diverse tasks among multiple experts. However, there is a lack of theoretical analysis of MoE and its impact on the learning performance in CL. This paper provides the first theoretical results to characterize the impact of MoE in CL via the lens of overparameterized linear regression tasks. We establish the benefit of MoE over a single expert by proving that the MoE model can diversify its experts to specialize in different tasks, while its router learns to select the right expert for each task and balance the loads across all experts. Our study further suggests an intriguing fact that the MoE in CL needs to terminate the update of the gating network after sufficient training rounds to attain system convergence, which is not needed in the existing MoE studies that do not consider the continual task arrival. Furthermore, we provide explicit expressions for the expected forgetting and overall generalization error to characterize the benefit of MoE in the learning performance in CL. Interestingly, adding more experts requires additional rounds before convergence, which may not enhance the learning performance. Finally, we conduct experiments on both synthetic and real datasets to extend these insights from linear models to deep neural networks (DNNs), which also shed light on the practical algorithm design for MoE in CL.

Data clones are defined as multiple copies of the same data among datasets. Presence of data clones between datasets can cause issues such as difficulties in managing data assets and data license violations when using datasets with clones to build AI software. However, detecting data clones is not trivial. Majority of the prior studies in this area rely on structural information to detect data clones (e.g., font size, column header). However, tabular datasets used to build AI software are typically stored without any structural information. In this paper, we propose a novel method called SimClone for data clone detection in tabular datasets without relying on structural information. SimClone method utilizes value similarities for data clone detection. We also propose a visualization approach as a part of our SimClone method to help locate the exact position of the cloned data between a dataset pair. Our results show that our SimClone outperforms the current state-of-the-art method by at least 20\% in terms of both F1-score and AUC. In addition, SimClone's visualization component helps identify the exact location of the data clone in a dataset with a Precision@10 value of 0.80 in the top 20 true positive predictions.

To overcome the restriction of identical distribution assumption, invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities. In UDA scenario, the training and test data belong to different domains while the task model is learned to be invariant. Recently, empirical connections between transferability and discriminability have received increasing attention, which is the key to understanding the invariant representations. However, theoretical study of these abilities and in-depth analysis of the learned feature structures are unexplored yet. In this work, we systematically analyze the essentials of transferability and discriminability from the geometric perspective. Our theoretical results provide insights into understanding the co-regularization relation and prove the possibility of learning these abilities. From methodology aspect, the abilities are formulated as geometric properties between domain/cluster subspaces (i.e., orthogonality and equivalence) and characterized as the relation between the norms/ranks of multiple matrices. Two optimization-friendly learning principles are derived, which also ensure some intuitive explanations. Moreover, a feasible range for the co-regularization parameters is deduced to balance the learning of geometric structures. Based on the theoretical results, a geometry-oriented model is proposed for enhancing the transferability and discriminability via nuclear norm optimization. Extensive experiment results validate the effectiveness of the proposed model in empirical applications, and verify that the geometric abilities can be sufficiently learned in the derived feasible range.