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Adaptive multi-fidelity optimization with fast learning rates Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction Sample Complexity Bounds for Stochastic Shortest Path with a Generative Model The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback Stylistic-STORM (ST-STORM) : Perceiving the Semantic Nature of Appearance Collective Kernel EFT for Pre-activation ResNets PRIM-cipal components analysis One-Shot Generative Flows: Existence and Obstructions Structural interpretability in SVMs with truncated orthogonal polynomial kernels Amortized Optimal Transport from Sliced Potentials MinShap: A Modified Shapley Value Approach for Feature Selection Unsupervised feature selection using Bayesian Tucker decomposition Multi-User mmWave Beam and Rate Adaptation via Combinatorial Satisficing Bandits Best of both worlds: Stochastic & adversarial best-arm identification Scalable Model-Based Clustering with Sequential Monte Carlo Expert-Guided Class-Conditional Goodness-of-Fit Scores for Interpretable Classification with Informative Missingness: An Application to Seismic Monitoring Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks Gating Enables Curvature: A Geometric Expressivity Gap in Attention Zeroth-Order Optimization at the Edge of Stability Differentially Private Conformal Prediction CLion: Efficient Cautious Lion Optimizer with Enhanced Generalization Generative Augmented Inference Improving Machine Learning Performance with Synthetic Augmentation PAC-MCTS: Bias-Aware Pruning for Robust LLM-Guided Search and Planning Path-Sampled Integrated Gradients Heat and Matérn Kernels on Matchings Doubly Outlier-Robust Online Infinite Hidden Markov Model Momentum Further Constrains Sharpness at the Edge of Stochastic Stability Multistage Conditional Compositional Optimization BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization Sandpile Economics: Theory, Identification, and Evidence Online learning with noisy side observations Spectral Thompson sampling Covariance-adapting algorithm for semi-bandits with application to sparse rewards Ordinary Least Squares is a Special Case of Transformer Metric-Aware Principal Component Analysis (MAPCA):A Unified Framework for Scale-Invariant Representation Learning Robust Low-Rank Tensor Completion based on M-product with Weighted Correlated Total Variation and Sparse Regularization Joint Representation Learning and Clustering via Gradient-Based Manifold Optimization Universality of Gaussian-Mixture Reverse Kernels in Conditional Diffusion Interpretable and Explainable Surrogate Modeling for Simulations: A State-of-the-Art Survey and Perspectives on Explainable AI for Decision-Making Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression A short proof of near-linear convergence of adaptive gradient descent under fourth-order growth and convexity Some Theoretical Limitations of t-SNE Bias-Corrected Adaptive Conformal Inference for Multi-Horizon Time Series Forecasting Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing Rare Event Analysis via Stochastic Optimal Control Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. 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Learning in RKHM: a $C^*$-Algebraic Twist for Kernel Machines
Yuka Hashimoto, Masahiro Ikeda, Hachem Kadri · 2022-10-21 · via stat.ML updates on arXiv.org

Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist to this rich literature by generalizing supervised learning in RKHS and vvRKHS to reproducing kernel Hilbert $C^*$-module (RKHM), and show how to construct effective positive-definite kernels by considering the perspective of $C^*$-algebra. Unlike the cases of RKHS and vvRKHS, we can use $C^*$-algebras to enlarge representation spaces. This enables us to construct RKHMs whose representation power goes beyond RKHSs, vvRKHSs, and existing methods such as convolutional neural networks. Our framework is suitable, for example, for effectively analyzing image data by allowing the interaction of Fourier components.

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