We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences between neighbouring data points. Subsequently, such differences are integrated, weighted by their associated uncertainties, using a maximum-likelihood formulation. This procedure can be seen as an extension to a multidimensional setting of the thermodynamic integration, a technique developed in statistical physics. The method leverages the manifold hypothesis, estimating quantities within the intrinsic data manifold without defining an explicit coordinate map. It does not rely on any binning or space partitioning, but rather on the construction of a neighbourhood graph based on an adaptive bandwidth selection procedure. BMTI mitigates the limitations commonly associated with traditional nonparametric density estimators, effectively reconstructing smooth profiles even in high-dimensional embedding spaces. The method is tested on a variety of complex synthetic high-dimensional datasets, where it is shown to outperform traditional estimators, and is benchmarked on realistic datasets from the chemical physics literature.

Kernel ridge regression (KRR) is a fundamental computational tool, appearing in problems that range from computational chemistry to health analytics, with a particular interest due to its starring role in Gaussian process regression. However, it is challenging to scale KRR solvers to large datasets: with $n$ training points, a direct solver (i.e., Cholesky decomposition) uses $O(n^2)$ storage and $O(n^3)$ flops. Iterative methods for KRR, such as preconditioned conjugate gradient (PCG), avoid the cubic scaling of direct solvers and often use low-rank preconditioners; a rank $r$ preconditioner uses $O(rn)$ storage and each iteration requires $O(n^2)$ flops. To reduce the storage and iteration complexity of iterative solvers for KRR, we propose ASkotch ($\textbf{A}$ccelerated $\textbf{s}$calable $\textbf{k}$ernel $\textbf{o}$p$\textbf{t}$imization using block $\textbf{c}$oordinate descent with $\textbf{H}$essian preconditioning). For a given block size $|b| << n$, each iteration of ASkotch uses $O(r|b| + n)$ storage and $O(n|b|)$ flops, so ASkotch scales better than Cholesky decomposition and PCG. We prove that ASkotch obtains linear convergence to the optimum, with the convergence rate depending on the square roots of the $\textit{preconditioned}$ block condition numbers. Furthermore, we solve KRR problems that were considered to be impossibly large while using limited computational resources: we show that ASkotch outperforms PCG methods with respect to generalization error on large-scale KRR (up to $n = 10^8$) and KRR classification tasks (up to $n = 10^7$) while running each of our experiments on $\textit{a single 12 GB Titan V GPU}$. Our work opens up the possibility of as-yet-unimagined applications of KRR across a wide range of disciplines.

Drug-target relationships may now be predicted computationally using bioinformatics data, which is a valuable tool for understanding pharmacological effects, enhancing drug development efficiency, and advancing related research. A number of structure-based, ligand-based and network-based approaches have now emerged. Furthermore, the integration of graph attention networks with intricate drug target studies is an application area of growing interest. In our work, we formulate a model called MKDTI by extracting kernel information from various layer embeddings of a graph attention network. This combination improves the prediction ability with respect to novel drug-target relationships. We first build a drug-target heterogeneous network using heterogeneous data of drugs and targets, and then use a self-enhanced multi-head graph attention network to extract potential features in each layer. Next, we utilize embeddings of each layer to computationally extract kernel matrices and fuse multiple kernel matrices. Finally, we use a Dual Laplacian Regularized Least Squares framework to forecast novel drug-target entity connections. This prediction can be facilitated by integrating the kernel matrix associated with the drug-target. We measured our model's efficacy using AUPR and AUC. Compared to the benchmark algorithms, our model outperforms them in the prediction outcomes. In addition, we conducted an experiment on kernel selection. The results show that the multi-kernel fusion approach combined with the kernel matrix generated by the graph attention network provides complementary insights into the model. The fusion of this information helps to enhance the accuracy of the predictions.

Tabular datasets play a crucial role in various applications. Thus, developing efficient, effective, and widely compatible prediction algorithms for tabular data is important. Currently, two prominent model types, Gradient Boosted Decision Trees (GBDTs) and Deep Neural Networks (DNNs), have demonstrated performance advantages on distinct tabular prediction tasks. However, selecting an effective model for a specific tabular dataset is challenging, often demanding time-consuming hyperparameter tuning. To address this model selection dilemma, this paper proposes a new framework that amalgamates the advantages of both GBDTs and DNNs, resulting in a DNN algorithm that is as efficient as GBDTs and is competitively effective regardless of dataset preferences for GBDTs or DNNs. Our idea is rooted in an observation that deep learning (DL) offers a larger parameter space that can represent a well-performing GBDT model, yet the current back-propagation optimizer struggles to efficiently discover such optimal functionality. On the other hand, during GBDT development, hard tree pruning, entropy-driven feature gate, and model ensemble have proved to be more adaptable to tabular data. By combining these key components, we present a Tree-hybrid simple MLP (T-MLP). In our framework, a tensorized, rapidly trained GBDT feature gate, a DNN architecture pruning approach, as well as a vanilla back-propagation optimizer collaboratively train a randomly initialized MLP model. Comprehensive experiments show that T-MLP is competitive with extensively tuned DNNs and GBDTs in their dominating tabular benchmarks (88 datasets) respectively, all achieved with compact model storage and significantly reduced training duration.

Emotion recognition is the technology-driven process of identifying and categorizing human emotions from various data sources, such as facial expressions, voice patterns, body motion, and physiological signals, such as EEG. These physiological indicators, though rich in data, present challenges due to their complexity and variability, necessitating sophisticated feature selection and extraction methods. NGN, an unsupervised learning algorithm, effectively adapts to input spaces without predefined grid structures, improving feature extraction from physiological data. Furthermore, the incorporation of fuzzy logic enables the handling of fuzzy data by introducing reasoning that mimics human decision-making. The combination of PSO with XGBoost aids in optimizing model performance through efficient hyperparameter tuning and decision process optimization. This study explores the integration of Neural-Gas Network (NGN), XGBoost, Particle Swarm Optimization (PSO), and fuzzy logic to enhance emotion recognition using physiological signals. Our research addresses three critical questions concerning the improvement of XGBoost with PSO and fuzzy logic, NGN's effectiveness in feature selection, and the performance comparison of the PSO-fuzzy XGBoost classifier with standard benchmarks. Acquired results indicate that our methodologies enhance the accuracy of emotion recognition systems and outperform other feature selection techniques using the majority of classifiers, offering significant implications for both theoretical advancement and practical application in emotion recognition technology.

Through this comprehensive survey of Kolmogorov-Arnold Networks(KAN), we have gained a thorough understanding of its theoretical foundation, architectural design, application scenarios, and current research progress. KAN, with its unique architecture and flexible activation functions, excels in handling complex data patterns and nonlinear relationships, demonstrating wide-ranging application potential. While challenges remain, KAN is poised to pave the way for innovative solutions in various fields, potentially revolutionizing how we approach complex computational problems.

The support vector machine algorithm with a quantum kernel estimator (QSVM-Kernel), as a leading example of a quantum machine learning technique, has undergone significant advancements. Nevertheless, its integration with classical data presents unique challenges. While quantum computers primarily interact with data in quantum states, embedding classical data into quantum states using feature mapping techniques is essential for leveraging quantum algorithms Despite the recognized importance of feature mapping, its specific impact on data classification outcomes remains largely unexplored. This study addresses this gap by comprehensively assessing the effects of various feature mapping methods on classification results, taking medical data analysis as a case study. In this study, the QSVM-Kernel method was applied to classification problems in two different and publicly available medical datasets, namely, the Wisconsin Breast Cancer (original) and The Cancer Genome Atlas (TCGA) Glioma datasets. In the QSVM-Kernel algorithm, quantum kernel matrices obtained from 9 different quantum feature maps were used. Thus, the effects of these quantum feature maps on the classification results of the QSVM-Kernel algorithm were examined in terms of both classifier performance and total execution time. As a result, in the Wisconsin Breast Cancer (original) and TCGA Glioma datasets, when Rx and Ry rotational gates were used, respectively, as feature maps in the QSVM-Kernel algorithm, the best classification performances were achieved both in terms of classification performance and total execution time. The contributions of this study are that (1) it highlights the significant impact of feature mapping techniques on medical data classification outcomes using the QSVM-Kernel algorithm, and (2) it also guides undertaking research for improved QSVM classification performance.

Recently, there has been a surge of interest in developing graph neural networks that utilize the invariance principle on graphs to generalize the out-of-distribution (OOD) data. Due to the limited knowledge about OOD data, existing approaches often pose assumptions about the correlation strengths of the underlying spurious features and the target labels. However, this prior is often unavailable and will change arbitrarily in the real-world scenarios, which may lead to severe failures of the existing graph invariance learning methods. To bridge this gap, we introduce a novel graph invariance learning paradigm, which induces a robust and general inductive bias. The paradigm is built upon the observation that the infomax principle encourages learning spurious features regardless of spurious correlation strengths. We further propose the EQuAD framework that realizes this learning paradigm and employs tailored learning objectives that provably elicit invariant features by disentangling them from the spurious features learned through infomax. Notably, EQuAD shows stable and enhanced performance across different degrees of bias in synthetic datasets and challenging real-world datasets up to $31.76\%$. Our code is available at \url{https://github.com/tianyao-aka/EQuAD}.

Recent research has shown that Transformers with linear attention are capable of in-context learning (ICL) by implementing a linear estimator through gradient descent steps. However, the existing results on the optimization landscape apply under stylized settings where task and feature vectors are assumed to be IID and the attention weights are fully parameterized. In this work, we develop a stronger characterization of the optimization and generalization landscape of ICL through contributions on architectures, low-rank parameterization, and correlated designs: (1) We study the landscape of 1-layer linear attention and 1-layer H3, a state-space model. Under a suitable correlated design assumption, we prove that both implement 1-step preconditioned gradient descent. We show that thanks to its native convolution filters, H3 also has the advantage of implementing sample weighting and outperforming linear attention in suitable settings. (2) By studying correlated designs, we provide new risk bounds for retrieval augmented generation (RAG) and task-feature alignment which reveal how ICL sample complexity benefits from distributional alignment. (3) We derive the optimal risk for low-rank parameterized attention weights in terms of covariance spectrum. Through this, we also shed light on how LoRA can adapt to a new distribution by capturing the shift between task covariances. Experimental results corroborate our theoretical findings. Overall, this work explores the optimization and risk landscape of ICL in practically meaningful settings and contributes to a more thorough understanding of its mechanics.

Combining machine clustering with deep models has shown remarkable superiority in deep clustering. It modifies the data processing pipeline into two alternating phases: feature clustering and model training. However, such alternating schedule may lead to instability and computational burden issues. We propose a centerless clustering algorithm called Probability Aggregation Clustering (PAC) to proactively adapt deep learning technologies, enabling easy deployment in online deep clustering. PAC circumvents the cluster center and aligns the probability space and distribution space by formulating clustering as an optimization problem with a novel objective function. Based on the computation mechanism of the PAC, we propose a general online probability aggregation module to perform stable and flexible feature clustering over mini-batch data and further construct a deep visual clustering framework deep PAC (DPAC). Extensive experiments demonstrate that PAC has superior clustering robustness and performance and DPAC remarkably outperforms the state-of-the-art deep clustering methods.