Algorithm reduces regret in distributed kernel bandits with shared randomness.
problem Minimizing regret in collaborative function maximization.
method Uniform exploration at local agents and shared randomness with central server.
result Achieves optimal regret order with sublinear communication cost.
Improved supervised EM learning for shared kernel models with feature space partitioning.
problem Lack of rigour in EM derivation and high computational complexity.
method Detailed derivation of EM for Gaussian shared kernel model, feature space partitioning to reduce complexity.
result Improved performance at reduced complexity achieved.
Despite the effectiveness of multitask deep neural network (MTDNN), there is a limited theoretical understanding on how the information is shared across different tasks in MTDNN. In this work, we establish a formal connection between MTDNN with infinitely-wide hidden layers and multitask Gaussian Process (GP). We deriv…
This paper introduces a novel framework for generative models based on Restricted Kernel Machines (RKMs) with joint multi-view generation and uncorrelated feature learning, called Gen-RKM. To enable joint multi-view generation, this mechanism uses a shared representation of data from various views. Furthermore, the mod…
Kernel method embeds noisy datasets, capturing shared structures.
problem Limited power in capturing nonlinear structures, noisiness, high-dimensionality, and interpretability issues.
method Kernel spectral joint embeddings using duo-landmark integral operators.
result Consistent recovery of low-dimensional noiseless signals and convergence to eigenfunctions of integral operators.
Shared Keyboard design improves phase I clinical trials by borrowing information across doses.
problem Interim decisions based on current dose data may overlook signals from neighboring doses.
method Bayesian model-assisted design using Beta kernel process with kernel-weighted pseudo-counts.
result Significant improvements in identifying maximum tolerated dose and safety.
In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and corresponding Gaussian Process kernels are derived. Experimen- tal results demonstrat…
New algorithms optimize multiple tasks with shared similarities, reducing regret.
problem Optimizing multiple objectives with shared similarities in non-parametric Bayesian optimization.
method Developed two novel BO algorithms using multi-task kernels and random scalarizations.
result Derived worst-case regret bounds capturing inter-task similarities.
Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, severa…
There has been great interest recently in applying nonparametric kernel mixtures in a hierarchical manner to model multiple related data samples jointly. In such settings several data features are commonly present: (i) the related samples often share some, if not all, of the mixture components but with differing weight…
We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation pr…
Quantum kernels show no advantage in stock return prediction, but differ in stability metrics.
problem Determining if quantum kernels improve stock return prediction.
method Controlled horse race on Chinese A-share market with identical training subsamples and tuning budgets.
result Quantum kernels do not outperform classical RBF controls in cross-sectional stock return prediction.
The paper explores unique properties of Kähler manifolds without shared CR-submanifolds.
problem Characterizing Kähler manifolds with specific CR-submanifolds.
method Analyzing properties of Kähler and CR-submanifolds in complex manifolds.
result Kähler manifolds without shared CR-submanifolds have distinct properties.
We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes that capture across-task dependencies. We propose two different methods for segmen…
The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent's set of st…
Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GP with …
The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. F…
This study examines the practical equivalence of Laplace and neural tangent kernels.
problem Understanding the practical equivalence of Laplace and neural tangent kernels.
method The study matches the kernels exactly and by matching posteriors of a Gaussian process. It also analyzes the kernels in R^d and experiments with them in regression tasks.
result The Laplace and neural tangent kernels are practically equivalent.
Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind t…
Recurrent convolution (RC) shares the same convolutional kernels and unrolls them multiple steps, which is originally proposed to model time-space signals. We argue that RC can be viewed as a model compression strategy for deep convolutional neural networks. RC reduces the redundancy across layers. However, the perform…
A new kernel method improves Poisson process intensity estimation.
problem Estimating intensity functions of inhomogeneous Poisson processes.
method Kernel method-based intensity estimator using least squares loss.
result K2IE achieves comparable predictive performance with improved efficiency. BENK estimates treatment effects with neural kernels for censored data.
problem Estimating heterogeneous treatment effects with censored time-to-event data.
method Proposes a method using the Beran estimator with neural kernels for survival functions.
result Shows improved accuracy compared to existing methods in various scenarios.
Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.
problem Selecting an appropriate kernel for Kernelized Diffusion Maps.
method Two complementary approaches: variational outer loop and unsupervised cross-validation.
result Both methods improve the quality and stability of the recovered eigenfunctions.
Training-free source selection for LLM families with shared vocabularies
problem Source selection for LLM families with shared vocabularies
method Fisher alignment at vocabulary scale
result Fisher alignment is a cosine between kernel mean embeddings in the joint activation-error space
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …
Paper introduces a new Poisson kernel for strongly pseudoconvex domains.
problem Developing a new mathematical tool for strongly pseudoconvex domains.
method Introducing a maximal plurisubharmonic function called the pluricomplex Poisson kernel.
result The pluricomplex Poisson kernel shares properties with the classical Poisson kernel and reproduces pluriharmonic functions.
Graph-coupled causal Bayesian optimization transfers information across related interventions.
problem Optimizing expensive systems where interventions are costly and causal effects are confounded.
method Ties intervention effects together through shared causal parameters, improving estimation.
result Information-gain and regret bounds show improved performance with shared mechanisms.
DEOT method compares distributions across agents with privacy and efficiency.
problem Comparing distributions across agents in a distributed system.
method Decentralized entropic optimal transport with mini-batch randomized block-coordinate descent and decentralized kernel approximation.
result The method provides a privacy-preserving and communication-efficient solution to distributed distribution comparison.
The paper proposes a novel MKL approach for OCC using ℓp-norm constraints.
problem Addressing the MKL problem for one-class classification.
method A min-max saddle point Lagrangian optimisation problem is formulated and solved efficiently.
result The proposed method outperforms baselines and other algorithms on various data sets.
Entropy analysis via kernel methods for probabilistic inference.
problem Entropy analysis of probability distributions.
method Kernel methods and reproducing kernel Hilbert spaces for entropy estimation.
result New upper-bounds on log partition functions for probabilistic inference.
Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has been significantly improved by compositional covariance structures. In this paper…
Bayesian model connects KMs and ELMs for multitask regression.
problem Multitask regression with shared features and sparsity.
method Bayesian framework using RFFs and RBF kernels.
result Significant performance improvements over state-of-the-art methods.
TopoNTK kernel captures higher-order interactions in simplicial complexes.
problem Graph neural networks miss higher-order interactions in relational systems.
method Introduces TopoNTK, an infinite-width kernel for simplicial message passing.
result TopoNTK captures topology invisible to graph kernels, improving expressivity and interpretability.
MetaVRF learns adaptive kernels for fast few-shot learning.
problem Few-shot learning with limited data.
method MetaVRF with latent variable model and variational inference.
result MetaVRF produces kernels with high representational power and fast adaptation.
Proposes a meta-learning method for Bayesian optimization with neural network kernels.
problem Improving BO performance on high-dimensional data with complex structure.
method Meta-learning approach that trains a neural network policy to select the next data point to evaluate, using a reinforcement learning framework.
result The proposed method achieves better BO performance than existing methods on text document datasets.
A new method TNW-CATE estimates treatment effects using neural networks.
problem Estimating heterogeneous treatment effects with limited controls and many treatments.
method Trainable Nadaraya-Watson regression with shared parameters neural network.
result TNW-CATE outperforms traditional methods in various simulation experiments.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Combines physics-based ML with hierarchical Bayesian techniques for better model performance.
problem Lack of physical knowledge in black-box machine learning models.
method Embeds physics-based models into Gaussian Process mean function and uses kernel machines to characterize discrepancies.
result Improved model performance under blind conditions through integration of physics-based knowledge.
LIBO optimizes repeated bandit tasks without prior knowledge or regret.
problem Optimizing repeated bandit tasks without prior knowledge or regret.
method LIBO sequentially meta-learns a kernel to adapt to the environment and solve tasks with the latest estimate.
result LIBO achieves sublinear lifelong regret, converging to oracle performance as more tasks are solved.
Meta-learning improves Gaussian process uncertainty estimation.
problem Poor uncertainty estimation in Gaussian processes with deep kernels.
method Meta-learning to calibrate deep kernel GPs using task-specific uncalibrated and calibrated distributions.
result Improves uncertainty estimation performance with high regression performance.
The paper proposes a learning-theoretic perspective on representation alignment.
problem Understanding how AI models' representations become aligned as they scale.
method Reviewing and connecting different notions of alignment, focusing on stitching.
result Relating properties of stitching to kernel alignment of representations.
Unsupervised learning on imbalanced data is challenging because, when given imbalanced data, current model is often dominated by the major category and ignores the categories with small amount of data. We develop a latent variable model that can cope with imbalanced data by dividing the latent space into a shared space…
pFedGP uses Gaussian processes for personalized federated learning with improved kernel learning.
problem Learning personalized models across clients with limited data.
method pFedGP uses Gaussian processes with deep kernel learning, including a shared neural network kernel and inducing points.
result pFedGP achieves well-calibrated predictions and significantly outperforms baseline methods.
The one-class kernel spectral regression (OC-KSR), the regression-based formulation of the kernel null-space approach has been found to be an effective Fisher criterion-based methodology for one-class classification (OCC), achieving state-of-the-art performance in one-class classification while providing relatively hig…
SPIRE enables efficient federated learning for diffusion models by separating client-specific embeddings from a shared backbone.
problem Large diffusion models are impractical for federated learning due to their size.
method SPIRE separates the network into a global backbone and client-specific embeddings, enabling efficient finetuning.
result SPIRE achieves parameter-efficient finetuning, updating only a small fraction of weights.
Paper tackles robust decision-making from multiple sites with shared structure.
problem Learning robust sequential decisions from heterogeneous multi-site datasets.
method Group-Robust MDPs with d-rectangular uncertainty sets, feature-wise worst-case aggregation, and cluster-level pooling.
result Proves suboptimality bound for robust planning policy under robust partial coverage assumption.
BKTF uses tensor factorization for Bayesian optimization of complex functions.
problem Complex functions with nonstationary, nonseparable, and multimodal features.
method Bayesian Kernelized Tensor Factorization (BKTF) approximates complex functions using a low-rank tensor CP decomposition with GP priors.
result BKTF provides flexible and effective surrogate modeling with uncertainty quantification.
Enhances random forests by smoothing predictions for better performance.
problem Suboptimal performance due to piecewise constant predictions in random forests.
method Kernel-based smoothing mechanism to introduce local regularity.
result Smoothed random forest model consistently improves predictive performance.