RKHS
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Related Articles from SNS
Superdirectivity as a Spectral-Collision RKHS Limit
arXiv:2606.08174v1 Announce Type: new Abstract: We develop a reproducing-kernel Hilbert space interpretation of array superdirectivity based on spectral-collision limits and polynomial jet geometry. As the spacing of an $M$-element linear array tends to zero, the exponential family generated by a linear array undergoes a spectral collision, and the associated finite-dimensional subspaces converge in reproducing kernel to a polynomial jet space. Array gain equals the diagonal evaluation of...
SHAP-Guided Kernel Actor-Critic for Explainable Reinforcement Learning
arXiv:2512.05291v3 Announce Type: replace Abstract: Actor-critic (AC) methods are a cornerstone of reinforcement learning (RL) but offer limited interpretability. Current explainable RL methods seldom use state attributions to assist training. Rather, they treat all state features equally, thereby neglecting the heterogeneous impacts of individual state dimensions on the reward.
Are Two Datasets Close Enough With Statistical Significance? A Kernel Distributional Closeness Testing Approach
arXiv:2507.12843v3 Announce Type: replace Abstract: Are two distributions close to each other with statistical significance? Distribution closeness testing (DCT) formalizes this question by testing whether the distance between a distribution pair is at least epsilon-far. Existing DCT methods mainly measure discrepancies between distribution pairs defined on discrete spaces, for example using total variation, which limits their application to complex data such as images.
Interventional Processes for Causal Uncertainty Quantification
arXiv:2410.14483v3 Announce Type: replace-cross Abstract: Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a...
Spectral Truncation Kernels: Noncommutativity in $C^*$-algebraic Kernel Machines
arXiv:2405.17823v5 Announce Type: replace-cross Abstract: A central question in vector- and function-valued learning is how to design kernels that capture both local and non-local interactions while remaining computationally tractable. Existing operator-valued kernels offer only partial answers: separable kernels are efficient but fail to model interactions across the function domain, while commutative kernels capture only pointwise structure. To address this, we propose spectral truncation...
AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression
Announce Type: new Abstract: Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency. However, nonlinear dynamics are so complex that capturing dynamically changing nonlinear patterns and utilizing them for downstream tasks under strict time constraints is nontrivial. To bridge the gap between nonlinear complexity and computational tractability, this study applies Koopman...
Kernel Affine Hull Machines as Compute-Efficient Encoders for Frozen Semantic Spaces
Announce Type: replace Abstract: Transformer-based semantic encoders are effective for retrieval, but in many deployments the recurring bottleneck is online query encoding rather than offline corpus indexing. This paper studies whether, once a strong teacher representation space and corpus index are fixed, repeated neural query encoding can be replaced by a substantially lighter and analytically explicit estimator. We formulate fixed-teacher lexical-to-semantic encoding as a conditional-mean...
Koopman Subspace Pruning in Reproducing Kernel Hilbert Spaces via Principal Vectors
arXiv:2604.01459v2 Announce Type: replace Abstract: Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, which formally corresponds to the largest principal angle between the subspace and its image under the...